After the talk I spoke with Jan Verbeek and Gartjan Grijzen of Be Informed and reviewed their software, which is excellent.  They have been quite successful with various government agencies in applying  the event-centric methodology to produce goal-driven processing.  Their approach is elegant and effective.  It clearly demonstrates the merits of an event-centric approach and the power that emerges from understanding event-dependencies.  Also, it is very semantic, ontological, and logic-programming oriented in its approach (e.g., they use OWL and a backward-chaining inference engine).

They do not have the top-down knowledge management approach that I advocate nor do they provide the logical verification of governing policies and compliance (i.e., using theorem provers) that I mention in the talk (see Guido Governatori’s 2010 publications and Travis Breaux’s research at CMU, for example) but theirs is the best commercially deployed work in separating business process description from procedural implementation that comes to mind. (Note that Ed Barkmeyer of NIST reports some use of SBVR descriptions of manufacturing processes with theorem provers.  Some in automotive and aerospace industries have been interested in this approach for quality purposes, too.)

BeInformed is now expanding into the United States with the assistance of Mills Davis and others.  Their software is definitely worth consideration and, in my opinion, is more elegant and effective than the generic BPMN approach.

So, although you may want to say that birds fly, you’re ontology will be broken (or become much more complicated) when you realize there are birds that can’t fly, such as penguins or ostriches, or even sick or injured birds.

Practically speaking, you need something like courteous logic or the defeasibility in SILK to handle this (or any 1980s expert system shell or even earlier frame system).  OWL is very hard on mortal man (e.g., mainstream IT) in this regard.

How can I tell OWL that a pronoun is a noun but that pronouns are a closed class of words, unlike nouns, verbs, adjectives, and adverbs (in general).  Well, I’ll have to tell it about open-class nouns versus closed class nouns.  What a pain!

This is why we use Protege primarily as a drafting tool and, for example, SILK, to do reasoning.   Non-defeasible description logic and first-order reasoners are difficult to get along with, in practice (and make sustainable knowledge repositories too difficult – which inhibits adoption, obviously).

Although alethic typically refers to necessary vs. possible, it clearly subsumes the probable or expected (albeit excluding deontics⁰).  For example, consider the notion of ‘disposition’ (shown below as rendered in Protege):

For example, cells might be disposed to undergo the cell cycle, which consists of interphase, mitosis, and cytokinesis.  Iron is disposed to rust.  Certain customers might be disposed to comment, complain, or inquire.

Disposition is nice because it reflects things that have an unexpected high probability of occurring¹ but that may not be a necessary part of a process.   It seems, however, that disposition is lacking from most business process models.  It is prevalent in the soft and hard sciences, though.  And it is important in medicine.

Disposition is distinct from what should occur or be attempted next in a process.  Just because something is disposed to happen does not mean that it should or will.  Although disposition is clearly related to business events and processes, it seems surprisingly lacking from business models (and CEP/BPM tooling).²

A teleological aspect of BFO is the notion of purpose or intended ‘function’, as shown below:

Function is about what something is expected to do or what it is for.  For example, what is the function of an actuary?  Representing such functionality of individuals or departments within enterprises may be atypical today, but is clearly relevant to skills-based routing, human resource optimization and business modeling in general.

Understanding disposition and function is clearly relevant to business modeling (including organizational structure), planning and performance optimization.    Without an understanding of disposition, anticipation and foresight will be lacking.  Without an understanding of function, measurement, reporting, and performance improvement will be lacking.

¹ Thanks to BG for “politicians are disposed to corruption” which indicates a population that is more likely than a larger population to be involved in certain situations.

² Cyc’s notion of ‘disposition’ or ‘tendency’ is focused on properties rather than probabilities, as in the following citation from OpenCyc.  Such a notion is similarly lacking from most business models, probably because its utility requires more significant reasoning and business intelligence than is common within enterprises. 

The collection of all the different quantities of dispositional properties; e.g. a particular degree of thermal conductivity. The various specializations of this collection are the collections of all the degrees of a particular dispositional property. For example, ThermalConductivity is a specialization of this collection and its instances are usually denoted with the generic value functions as in (HighAmountFn ThermalConductivity).

Some of the bubble in raising those funds has burst.  The economy would crimp the valuation and investment if made today.  And the semantic web has yet to produce a winner, so with less enthusiasm, the investment would again be less favorable today.  All this is modulo the business plan.  If the business plan withstands scrutiny and the rate of return from credibly achievable projections justifies investment, they could get the money again, even now.  But no one that I have heard or read over the past few years can explain the business plan adequately – that is, concretely.  I would appreciate any insights or opinions on the topic.  I believe these are smart people, in the company and among its investors, so I am sure it is there.  I just don’t believe in the “we’ll figure out how to make money eventually” business plan in this case. 

Some Freebase terms that are worth knowing but are commercially reasonable for any site that provides a free service include:

1. The terms of service are subject to change (upon posting).
2. The service may be changed or discontinued at any time and without notice.
3. Limits concerning access to or use of the services may be established.
4. Any disputes shall be heard in San Francisco and governed by California law.

Such terms would stop me from basing a business on Freebase without a written agreement with Metaweb.  Other Freebase terms are interesting, and potentially controversial:

1. Advertising is explicitly permitted.
2. Content contributed may not be stored or displayed and may be deleted.
3. Users and content providers indemnify Metaweb against any claims arising out of use.

I have not noticed any advertising on Freebase, but it is permitted.  I really don’t care if there is advertising.  My concern would be more with the utility of the site and service, especially the API.  Others certainly feel otherwise, however.  Of course, advertising interacts with privacy, which concerns me, but perhaps not enough to preclude my doing business with Metaweb.

Indemnifying Metaweb rather than simply holding them harmless is a over the top.  Indemnification might make more sense for content contributors, but this policy applies even to users who do not contribute content.

Failing to store content that is in conformance with all terms of the agreements is not a necessary component of a free service.  This effectively precludes Freebase from providing a free RDF store, as Google and so many others do for limited amounts of data, whether files or email, for example.  I don’t fault this policy but it seems somewhat arbitrary and perhaps misguided (versus limitations on the volume of conforming content that is not displayed that will be stored).  Such a limitation probably interferes with some applications that would otherwise be developed using Freebase.

The following terms, aside from the possibility of advertising, may give some visibility to monetization:

1. Registration, including an email address and “limited information about yourself” may be required.
2. Volume is currently limited to 100,000 API calls per day.
   1. Is the API the primary monetization vehicle?
   2. The API may be used only “as outlined in the documentation… on the site”.

As I read the privacy policy, Metaweb claims that IP addresses are “recorded for security and monitoring purposes” but does not preclude the sharing of personally identifiable information with third parties.  In addition, Metaweb uses cookies and links to third party web sites which may also introduce cookies, as in the Google/DoubleClick advertising network, which uses the DART cookie, for example.  Generally, I am uncomfortable with the Metaweb privacy policy in that it does not say what they will not do to my satisfaction.

Starting from the data, and with its social aspects, Freebase is headed for the intersection of Facebook and Wikipedia.  Commercial incentive and social gravity will propel Freebase content far beyond its foundation in Wikipedia attribution.  And the attraction of social content and data will concretely and economically motivate the Freebase community to grow beyond “meaningless” Facebook.  Will every student need a Freebase account?

I believe Freebase can get there and that the advertising network revenues and downstream user access channels will be phenomenal.  Imagine the questions that will be answer-able using Freebase data.  Metaweb is probably rubbing hands together as Wolfram, IBM, Vulcan and others work on question answering.  Or maybe they are working on it, too, with some of that $42.5 million….

If Freebase introduces a True Knowledge or a better Bing/Powerset, Google will not want to link to Freebase unless (for example) Freebase uses Google’s DoubleClick advertising network.  There is either an acquisition, deep collaboration, or a war looming as Freebase builds momentum and moves into search and question answering, if not simply query (once the user authored content is several times Wikipedia).

Google could be in trouble… It’s probably too late (or too embarrassing?) to follow Metaweb’s lead.  And if so, Freebase is worth a great deal.

If this was indeed the business plan, I am tremendously impressed.  Having the insight to set out on such a path – realizing that answers lie more explicitly within data than text and that social networking and attribution with commercial resources would overtake Wikipedia and build an extremely large community rooted deeply in data, discussion, interests, research, query, and more – with such long term vision and communicating it clearly and compelling enough to attract long term investors who grasped the then abstract but executable plan would be a tremendous achievement of capitalism.

This post was motivated by work on a retail e-commerce opportunity that may commoditize product information across search and comparison shopping engines, for example.  The challenge I am considering is how to realize value from semantic web content that needs to be licensed for broad use but the investment in which needs to be protected both in terms of integrity (i.e., as a standard) and from commoditization by competitors or lack of copyright enforcability.  Freebase licensing of content and APIs are of particular interest but not worth pursuing further here given the title of the article. 

• However, if you have thoughts on Freebase’s business model or on how to provide value to the semantic web without losing the invested capital, please share by email (mailto:paul@haleyai.com) or comment here. 
• For those interested, Scott Brinker’s blog has interesting discussion but lacks examples or specifity with regard to commercial business models.

Google now shows the following “The Empire State Building rises to 1250 ft (381 m) at the 102nd floor” in response to the classic semantic web test question.

Also, Google leverages more of the content of text or structure of linked data in its Rich Snippet answers:

As search engines increase their understanding of concepts and how to extract them from content or linked data and present them as Google does here or above in a sentence, the web will begin to feel a lot smarter. 

As these simple enhancements indicate, the intelligent web is taking off and that feeling of intelligence will come sooner than expected.  Of course, there is a long way to go.   For more on that, I here there is an upcoming issue of AI Magazine that will survey the state of the art in question answering, including coverage of Vulcan’s Project Halo and IBM’s Jeopardy effort, among others.  Also, if you are interested in what bright minds are looking forward to in this regard, see Nova Spivak’s recent blogging and his post on “will the web become conscious?”

First, let’s establish that there is plenty of semantics available for reuse now.  There are existing models, some of which are well-designed, mature, and widely used.  Unfortunately, most of what exists has little apparent relevance to enterprises.  There is little on this diagram that would draw the attention of an enterprise architect, for example.

Now, if there was an ontology for customer relationship management (CRM) or eXtensible Business Reporting Language (XBRL) in this diagram, it would get more attention.  I suggest that semantic web technology will be approaching the enterprise when one of these shows up.

Still, some mature and widely-used ontologies may offer enterprise benefits.  For example, the “friend-of-a-friend” ontology provides the following concepts:

Every enterprise has some of FOAF’s basic elements, like surnames, organizations, and projects.  By linking their enterprise models to FOAF ontology, directly or indirectly, people across the enterprise and its value chain gain visibility to and flexibility in using information that would otherwise be expensive to provide and use.  There is a lot to this that I will not go into here, including its relationship to business intelligence and enterprise performance management (but see entity analytics at IBM, for example).  Suffice it to say that there is meat on this bone.

As ontologies go, FOAF is small, at least in terms of its model, which consists of classes and properties.  Generally speaking, the more mature and widely-used ontologies today are small models.  Unfortunately, they are also isolated from one another.  They have been developed by small communities that are substantially independent of one another.  This reality is a symptom of a hurdle that needs to be crossed before semantics will cross the chasm to the mainstream.

Without collaboration, ontologies will remain small and independent.  There will be isolated examples of large ontologies, such as OpenCyc and interesting combinations of multiple ontologies, such as UMBEL, but they will have no uptake until they are managed by a large community that includes enterprise members.

Let’s look at the problem of enterprise modeling head on.  Consider, for example, defining the model underlying Oracle CRM and Salesforce.COM.  Or consider defining an application that produces the XML format now required of public companies by the Securities and Exchange Commission: XBRL.  These ontologies would be huge compared to any that has been widely adopted on the semantic web.  And yet, if such an ontology existed for SEC filings, it would have tremendous corporate relevance, especially to CFOs and in financial analysis at commercial banks and by the capital markets.  As for CRM, you don’t have to go far beyond FOAF to get the benefits of linked data and entity analytics.  So much more functionality would emerge than any vendor can provide or maintain, such as in mash-ups using open technology and linked data, if CRM was ontological.  (Mash-ups demonstrate that creativity is very powerful when unleashed.)

So, unless the vendors agree on an ontology for CRM or unless XBRL shifts from data modeling (e.g., XML schema definitions) to semantics, users are either doomed to redundant investments or trans-enterprise collaborative development of ontology is needed.  (I would not hold my breath on the former!)  I am ignoring a third alternative for the moment, which is that a technology startup or a professional organization gains significant traction or market leadership in providing such an ontology as a product or service offering.  On the other hand, given the size of commercial ontologies such as these, even such a disruptive innovator will need to overcome the collaboration bottleneck with respect to ontology, which is my focus here.

The most promising approach for models that are common across enterprises may be to develop them using a wiki, as in Wikipedia.  Certainly, some collaborative platform that exists “outside the firewall” is necessary.  But we need this platform to avoid the problems of spam and nuisance editors that plague Wikipedia and other completely open platforms.  We want to embrace the web’s lack of authority but we don’t want our platform to be completely egalitarian.  We want the community to direct itself to a collective objective, which is ontology worthy of broad enterprise adoption.

Ontologies as standards

If we are successful, completely open standards – the ontologies themselves – will be defined without committees.  There are challenges to be sure, but it seems possible that such ontological standards are within reach, driven by those who will derive the most benefit: enterprise consumers.  There are things we need from ontology in order for it to be an enterprise worth standard, however.  For one thing, we need version control.  An enterprise cannot use an ontology that changes at the whim of a Wikipedia editor.

Take Semantic MediaWiki, for example.  If we use SMW as a platform for collaborative ontology and we adopt that ontology in resources that our CRM or financial systems make available as linked data, what happens when someone deletes or renames a concept that we use?

The solution is not as simple as making a copy of the ontology at a moment in time.  Don’t forget that people from around the world are editing at every hour.  Asking the world to stop for a snapshot won’t work.  Nor will asking the world to unanimously agree that every concept in an ontology is right and final, at least for this version.  No, more sophisticated change management is needed.

All this should sound familiar to enterprise architects. We hold our models increasingly tightly as we approach a release.  And then they are fixed in stone until the next release.  We avoid the challenges of collaboration above.  We share at first and gradually take control.  It works.

But this approach won’t work across enterprises and is doomed to redundant investment within the enterprise.  It may be tough to sell across enterprises but there is definite value and ROI if the collaboration can overcome the issues of change management.

Unfortunately, ontology standards and platforms simply don’t address this problem yet.  Chalk this up as another bridge for semantic technology to cross in order to cross the chasm.  Some ideas for crossing that bridge follow.

Social semantics

We need the collaborative platform to allow convergence towards a stable ontology.  At the very least, we need to converge on some parts of the ontology.  If the community never “finally” agrees on even a single concept or property a standard will certainly not be born.  Fortunately, social media and change management may combine to address this problem.

Consider, for example, that social media ubiquitously support voting and rating functionality, whether five stars, thumbs up or down, dig it or favorite.  We can use this kind of functionality within the wiki to gauge the quality of content.  We can also take collective opinions on the need for elaboration.  There are other possibilities and details concerning voting and rating.  Among them are important details about aggregate opinions versus individual opinions. 

Wiki communities

In the context of a wiki supporting enterprises, there might be a taxonomy of organizations, groups, and projects, each of which define a community for which voting or rating might be tracked.  A community is a collection of individuals where those collections are organized taxonomically.  Most wikis have only a single community that anyone can join, including anonymously.  Within this community there might be individuals with different roles who can perform certain operations that typical users may not.  A more general notion might define communities as requiring permission for an individual or community to join.  The privilege to grant membership might be given to those who play an administrative role for the community.  And the level of privilege or permission granted to an individual could use the voting and rating functionality described above. 

Wiki democracy

As mentioned above, authority is not a natural phenomenon in open societies, such as the web.  Respect may be earned, but authority must be given, not taken.  The obvious technique for giving authority is by voting (possibly including a veto mechanism).  For example, a community may adopt the policy of extending the role of administrator along with its privileges to the top quartile of rated members.  Or, the community might follow a normal nomination and election process.  Or the community might elect a president or board of directors to whom it delegates the assignment of roles to community members.

Wiki citizens

Unfortunately, there are people who will be disruptive or cheat in any system.  Unchecked, they will post commercials or vote more than once for or against matters for various reasons.  So, it is important to know who is eligible to vote and ensure that there is a most one vote per citizen and that enough citizens vote on specific matters of governance.

It’s nice to have the template of Democracy so well established in the world.  Let’s use it.

Freeze-free releases

Now, with wiki democracy and communities, we have the basis for controlling release cycles.  Communities can configure their democracy, especially with regard to membership and the roles assigned to members.  More specifically, they decide the governance process by which versions are gradually stabilized.  They do this by assigning privileges or permissions to individuals, roles, or sub-communities.  These privileges or permissions allow them to “freeze” parts of the ontology.  But we cannot really allow the wiki (or its ontology) to be frozen.  Rather, we mark particular versions of parts of the ontology as being frozen with respect to a target release for our community.  Then, when we have frozen all parts of the ontology that our community needs in its ontology, we extract those versions into a release.  Other communities are unaffected by our release cycle.

The wiki might even show a community view of its content.  That is, it might show the versions of the ontology (and related wiki content) that is consistent with a community view.  Two different individuals might see two distinct views for the same pages.  Each might see the version of content that was frozen for their next release or the current content for parts that are not frozen for their community.

The careful IT reader might at this point be wondering about forks and other change management functionality.  I do not want to try to address such issues here, but I would welcome your comments and suggestions, especially if you think merges are important.  I would argue that forks are to be avoided.  They might be frozen for the practical reasons described here, but we need individual communities to converge with the entire community over time.

Bureaucracy

As the enterprise –worthy ontology underlying the collaborative platform grows and matures the electorate will inevitably demand more stability in what will become the core or upper ontology common to most enterprises.  Perhaps an amendment to the constitution will be offered and adopted by super-majority.  And a new community will form at the top of the taxonomy with permission to govern aspects and versions of parts of the ontology delegated to it by the electorate.  When this happens, the chasm will have been crossed.  Or, perhaps the wiki would start with such a board of directors acting as a senate or superior court, if you will.

(See bureaucrats and recent elections at Wikipedia for further insight on practices and possibilities.)

Permissions

The bureaucracy will want to effectively freeze certain parts of the ontology for all communities other than itself.  Even while frozen however, the upper ontology might still receive votes, ratings, and annotations (which is an important and substantial topic in itself).  The mechanism for enforcing this is familiar to almost anyone who would use such a wiki: permissions.  The typical approach is to map types of users to things they can or cannot do with, to, or on a particular thing (and to support inheritance between things as appropriate).  For example, Revelytix supports some of what I have described for communities as well as role-based permissions in Knoodl, its semantic wiki.

Convergence

As the modifications to the content concerning a part of the ontology diminish, it is either becoming less relevant or more stable.  Voting or rating can determine which.  Combined with voting and rating information, version control helps identify parts of the ontology that are (close to being) ready for inclusion in a “frozen” version.

On the other hand, volatility in votes, ratings, and versions indicates potential controversy.  Wiki democracy can govern controversy.  For example, the electorate can dictate or delegate the definition of policies concerning limits and resolution of controversy. 

More practically, if membership in the wiki is limited to people with a vested interest in the emergent and continuous use of the resulting ontology, such as by authentication and other policies, such as nomination and formal acceptance, many of the problems experienced by Wikipedia can be effectively eliminated.

Both of these approaches are becoming increasing common in popular wikis.

Authority

Social media demonstrate a variety of techniques for gauging authority, whether globally or per community, generally using voting and rating, but in some cases more objectively.  In addition, communities, particularly where they correspond to organizations, may explicitly delegate authority concerning their operations without “resorting” to democracy.  The wiki should support both kinds of authority, but it can leverage the former (within or across communities) in gauging the quality of content or to resolve controversy.

With appropriate views of the ontology, people can see what parts of the ontology have many positive or negative votes or ratings filtered by community and level of authority and ranked by volatility.  Additional criteria that may help assess the stability and adequacy of ontological knowledge (e.g., concepts, whether categories, collections, or individuals, and properties) are certainly possible and we solicit your ideas and suggestions.

Private Content

Our interest is in deriving enterprise benefits.  We believe that semantics offers significant benefits within enterprises.  These are most widely recognized in the areas of data governance and integration but will become increasingly relevant in business process management, enterprise knowledge management, and policy automation.  And we are looking forward to leveraging increased understanding of enterprise objectives, in business intelligence and enterprise performance management (e.g., leveraging XBRL for CFOs).

Enterprises who define their business processes, policies, and objectives semantically want their business process models (BPMN), their semantics of business vocabulary and rules (SBVR) and business motivation model (BMM) to be closely related to the ontology wiki.  In effect, they want a wiki within their firewall that is seamlessly integrated with the extended enterprise ontology wiki. They want control over their contributions to the community. 

In the extreme, enterprises want to host their own wiki as inheriting from the version of the external wiki that their community is working with and towards.  As they edit their content they want careful control over what will be published to the broader community and what will be retained as proprietary.  If there is a firewall between their wiki and the global wiki, they want to ensure that none of their proprietary content penetrates the firewall.

This is an extended effect of permissions that interacts with an inheritance scheme between a taxonomy of two wikis.  Although this inheritance can be generalized to support a taxonomy of wikis rooted globally but extended internally, the typical use case is inheritance from one external wiki to one internal wiki.  This permissions and inheritance mechanism should support overrides and exclusions such that the enterprise can prefer its own definitions which improve or conflict with the global wiki without disclosing them to the broader community.

Collaborative Protege

Although it does not provide wiki functionality, Collaborative Protégé addresses many of the issues discussed above.  For example, the following shows Protégé’s support for an extensible set of annotations.

Protégé uses annotations to encode version information, which is cumbersome but stays within the framework of using an RDF representation.  The following shows that even fine-grained constructs, such as annotations, are maintained with author and date/time information:

Note that the changes tab would show the history for a specific object in the ontology.  Protégé also supports proposals and voting or rating within a discussion forum metaphor:

Workflow support is planned for future versions of Collaborative Protégé.

Overall, Protégé is a good tool for the ontological aspects but insufficient when compared to the blog, wiki, content management, and discussion forum functionality common across the social, read-write web.  Unfortunately, as with other platforms discussed below, it does not yet go far enough with regard to communities, permissions, and inheritance (or other mappings) between federated ontologies.

Semantic MediaWiki

Semantic MediaWiki (SMW) has the virtue of facilitating evolutionary consensus on what concepts and relations between them mean by allowing authors to converge on a few paragraphs of text.  SMW pages may correspond to ontological objects, such as concepts or properties and links between SMW pages may correspond to ontological properties.

SMW is an extension of MediaWiki, the platform used for Wikipedia.  MediaWiki has adequate version control functionality but ignores conflicting edits; the last writer wins.  This may be fine, in practice but other wikis provide automatic locking with timeouts to avoid conflicting edits.

Conflicting edits can be particularly important when modifying ontological structure, especially where inheritance is involved, as in SMW.  Furthermore SMW content is more technical to edit than editing MediaWiki content, which is also technical.  Although SMW provides an adequate backbone for merging ontology with wiki content, its unstructured approach to editing and collaboration may prove inadequate for convergent ontological development.

MediaWiki supports limited group functionality (i.e., Bureaucrats, Administrators and Everyone) with correspondingly little support for permissions, consequently SMW falls short with regard to communities and convergence.

Content Management Systems

CMS, such as Drupal, can provide wiki-like functionality in addition to blog and other functionality which may prove attractive and useful to a community.  Drupal also provides discussion forum functionality.  Although MediaWiki provides discussion pages, the thread functionality provided by Drupal and other systems (including Protégé) is much more suitable for collaborative development.  Drupal also allows content to be edited in a more structured manner and to be more flexibly and dynamically composed.

Blogs

Wiki articles typically correspond to specific topics, as in an encyclopedia.  WordPress and TypePad articles are more free-form, while content management systems are best suited for on-line publications, including magazines and newspapers.

In a blog, the discussion is typically more in-line with the content than a wiki’s discussion or “talk” pages.  Many blogs support threaded commentary as in a more full-fledge discussion forum platform.   Blog-like commentary has been adopted in content management but is generally more limited in its presentation, such as when an article is viewed individually at

The wiki metaphor aligns better with the conceptual structure of an ontology.  This is demonstrated, for example, in the Semantic MediaWiki extension of MediaWiki (SMW).  The primary principle underlying SMW is that the ontology is documented by a page per concept or property.  Conceptually, the categories of MediaWiki become classes in an SMW ontology and the classes of the ontology correspond to MediaWiki categories.  Instances within the ontology also have their own pages.

Social Networks

Social networks, such as Facebook and Twine, for example, facilitate interpersonal communication, groups, interest tracking, and content or contact rankings and recommendations.  Clearly, such features should be considered extensions of a collaborative ontology platform.  Among them the ranking is most important, as discussed above.

Bookmarking

Services that originally provided bookmarking services, such as Digg, have evolved into social networks.  Nonetheless, their initial functionality was to provide tagging of bookmarks that would otherwise have remained unorganized within web browsers.  The tags assigned to bookmarks are typically less formal than ontological classification.  Some such services surreptitiously organize user tags and content ontologically, however.  Some argue that such ontological structure enables better recommendation, search, and browsing functionality.

In a platform for collaborative ontology development, it makes sense to support explicit tagging using ontological concepts.  Adding a tag would correspond to choosing (or defining) a concept in the ontology.  If in a wiki presentation, the pages for concepts could have a region or tab for bookmarks that use the category.  Moreover, semantic pivoting and drill-down could be supported, as is common in semantic web applications.  As with other content, bookmarks could be openly shared or limited to communities or individuals.

A Foundation for Semantic Collaboration

We are investigating platforms and formulating requirements for such a collaborative platform for developing and maintaining extended enterprise ontologies.  We will be writing further on this area in the future but welcome your thoughts and interests in the meantime.

1. Reasoning at a point within a [business] process
2. Reasoning about events that occur over time.
3. Reasoning about a [business] process (as in deciding what comes next)
4. Reasoning about and across different states (as in planning)

Enterprise decision management (EDM) addresses the first.  Complex event processing (CEP) is concerned with the second.  In theory, EDM could address the third but it does not in practice.  This third item includes  the issue of governing and defining workflow or event-driven business processes rather than point decisions within such business processes. 

Business applications of rules have not advanced to include the fourth item.  That is to say, business has yet to significantly leverage reasoning or problem solving techniques that are common in artificial intelligence.  For example, artificially intelligent question and answer systems, which are being developed for  the semantic web,  can do more than retrieve data – they perform inference.  Commercial database and business intelligence queries are typically much less intelligent, which presents a number of opportunities that I don’t want to go into here but would happy to discuss with interested parties.  The point here is that business does not use reasoning much at all, let alone to search across the potential ramifications of alternative decisions or courses of action before making or taking one.  Think of playing chess or a soccer-playing robot planning how to advance the ball on goal.  Why shouldn’t business strategies or tactical business decisions benefit from a little simulated look-ahead along with a lot of inference and evaluation?

Even though I have recently become more interested in the fourth of these areas, I expect the audience at the business rules forum to be most interested in the first two points above.  There will also be some who have enough experience with complex business processes, which are common in larger enterprises.  These folks will be interested in the third item.  Only the most advanced applications, such as in biochemical process planning, will be interested in the fourth.  I don’t expect many of them to attend!

The notion of enterprise decision management (EDM) is focused on point decision making within a business process.  For enterprises that are concerned with governing business processes, a model of the process itself must be available to the business rules that govern its operation.  I’ve written elsewhere about the need for an ontology of events and processes in order to effectively integrate business process management (BPM) with business rules.  Here, and in the workshop, I intend to get a little more specific about the requirements, what is lacking in current standards and offerings, and what we’re trying to do about it.

As I’ve written previously, the distinction between business process management (BPM) and CEP is not well principled but arises from somewhat arbitrary, historically distinct emphases on technology and market segmentation.  Any modern business process system must handle events and discussing events processing without considering processes is a limiting perspective.

Most people would intuitively agree that events trigger business processes.  For example, a business receiving a payment or a letter from a customer or vendor is an event that triggers the process of crediting and depositing that payment or considering and responding to that letter  Hopefully, we are moving beyond academic arguments about the distinction.  (I am ignoring here the algorithmic applications of streaming event processing as in trading in the capital markets.)

So, in current BPM, which should include CEP capabilities, we want decision management that is less ignorant about where it is in a business process and that is aware of events that trigger processing.  That is, we want policies that talk about the state of a business process and the occurrence of events.  The surprising thing is that current business rules management systems (BRMS) and related standards are of no help.  Tools from the leading business rule management system (BRMS) vendors, including Oracle and IBM / Ilog, have no intrinsic understanding of processes, events, or time.  And, outside their integrated BRMS, tools from BPM vendors don’t let us “talk” about anything.  They help us structure flows and code, but they rely on integrated BRMS to manage rules.  The rules include the policies, in which the business “talks”.  The BRMS is where English sentences (or something that increasing looks like English) are managed as the enterprise repository of policy. 

Note that there is nothing special about English.  It’s just easier to read than “natural language”.  Another limitation of current policy management systems is their lack of language independence, which requires automatic translation, which is much simpler if the sentences are unambiguously interpreted with logical rigor, but I digress from the point of this missive…

Some examples will help here.  Suppose we check the credit of an applicant at various points within the collection of processes that constitute how our enterprise conducts business.  We might have policies that are concerned with how we consider or act based on credit information in originating a loan (or policy) versus in renewing  or re-pricing one.  In effect, our policies want to talk not just about evaluating credit or pricing risk, but to do so in the context of a larger business process.  To be more specific, business policies that sound like, “if evaluating credit in the course of pricing a renewal…” or “if evaluating credit while considering a new policy…” are quite natural.  These statements define or govern the business process.  They also talk about where the decision is being made within a business process.  

• BRMS need to understand the context of the business process in order to make context-sensitive decisions.
• BPM needs to tell the BRMS what it is going on from the top-down for the BRMS to understand the context of a decision.

So, we need the BRMS to be told things like:

• I am considering a new applicant.
• I am considering the renewal of a contract.

In these statements, the pronoun “I” is the overall enterprise system contemplating its own actions.  If you find that awkward, just substitute “while”  to obtain what you might “say” in a business policy.  Ideally, the language your policy management system would not be overly stilted but would understand any of:

• while considering…
• during consideration of …
• if considering…
• if an … is being considered for…

and so on.  Otherwise, users will find authoring such statements cumbersome.  Reading and understanding English, even if it is a bit stilted, is easy for people.  We’re built to communicate, after all.

Now consider what you would want to say if you were writing policies that involved events.  In this case, the event has already occurred, such as “we received a letter from a customer…”.  You do not want to say, “if I am receiving a letter from a customer…” (which could only be true for an instant that passes quickly unless it was stated as “… I will be receiving…”).  But if we can only refer to events in past tense, how do we talk about a current event that needs to be handled versus another event that we have already handled?

Many business to consumer (B2C) applications, such as pharmacy benefits have this problem, for example.  To a pharmacy benefit manager (PBM), like Medco or Express Scripts, the swiping of an insurance card at a retail pharmacy is an event to be processed.  Any individual beneficiary has a history of such requests.  We can try to model the current one as a request and the prior ones as transactions, but this becomes awkward for less formal or technical people who want to talk about how many requests someone has submitted over a period of time, for example.  The truth is that there is a history of requests per beneficiary and technical limitations should not obscure this fact.  We should be able to distinguish the current request from prior requests, as in the following:

• a request that has not been processed is current or pending
• if processing a request…
• if a request for … is being considered…

Note that “request” is a deverbal noun, which is to say that the root form is the verb (in this case “to request”).  A request is a reference to an act of requesting that may be in any tense.  The sentences above reflect this in the use of an additional verb that carries the tense.  Of course, this is all completely natural since every sentence has a verb.

The most dangerous expression might be:

• if … requests …

and yet this is the form that almost all BRMS would handle today!  This is dangerous because it is too ambiguous about when the request occurred.  It would be better to say:

• when … requests …

provided that the system understands that, unlike “if”, “when” involves time, but even “when” is less than ideal since an event has always occurred in the past by the time it is processed.  On the other hand, we might define when a request occurs as in:

• a request occurs from the time it is received until it receives a final response.

This assumes that “when” combined with a verb in present perfect tense means during the period of time in which the process referenced by the verb continues.  And this is an important point:

• An event can be an occurrence of a process.
• An event may have a duration.
• “When” may refer to an interval of time.

Events are not necessarily processes, but may refer to instantaneous points in time, such as in the following:

• When a request is received…
• When the processing of a request begins…

but these uses of “when” refer to a point in time before any action can be taken in response to the event, therefore the sentences should only conclude with statements of implied, necessary, or modal logic and should not include any statement of action. Of course, a competent BPM/CEP/BRMS would understand all this and advise the author of a policy that suggests taking action in the past.

As we proceed through these examples our intuition should be building the understanding of the first three points made above.  Processes and events and reasoning about or over time are completely intertwined in nature and separating them between BPM and CEP and BRMS systems is completely artificial and hopelessly limiting.

So what is the solution?  I suggest it is a knowledge management  system that understands the following:

• 1. Policies that use tense.
• 2. Policies that refer to events using deverbal nouns.
• 3. Policies that refer to occurrences of processes as events.
• 4. Policies that refer to potential action using future tense, possibly by way of modals.
• 5. Policies that refer to occurrences of processes using verbs such as “begin”, “end”, “start”, etc.
• 6. Policies that refer to occurrences of process using words like “during”, “while” and “when”
• 7. Policies that refer to events using prepositions like “by”, “before”, “after”, and “when”

The natural language technology to parse such sentences is widely available using many approaches.  I am happy to discuss that with interested parties.  The second step that needs to be addressed is transforming the logical interpretation of such sentences derived from the natural language system into the underlying execution architecture, which includes a process engine and a rules engine that must be appropriately integrated.  That integration involves the informing of the BRMS about the state of the business process and the actions that may be taken which may be expressed as processes in the BPMS.  I’ve written elsewhere about this in more detail and am also happy to discuss it in more detail with BPM or CEP practitioners, product managers and architects.

Understanding events and occurrences of processes as events adds a great deal of power to policy management.  It allows statements of policy to reference and consider the context of business processes.  It allows statements of policy to reference and consider how to handle events in the context of business processes.  And, if it is done with adequate natural language understanding, it accomplishes this integration of BPM and CEP within a single policy management system.

Although I had hoped to cover the fourth point made first above here, I now prefer to conclude with a brief discussion about reasoning over time.  I will strive to cover reasoning about potential states of a process another day.  It is interesting but rigorous material that requires (in my opinion) architectural support that is lacking from current rules engines, whether production rule or logically based, even if the situational or event calculi are good formalisms.

Reasoning over time is pervasive in CEP.  In the pharmacy benefits management domain, for example, coverage is commonly limited based on the history of transactions.  For example, a policy might limit the amount of refills over a period of time.  This involves aggregation over a number of events, each of which is the result of handling a prior request.

Very few knowledge or policy management systems understand that transactions are processes, occurrences of which can be viewed as events.  For example, is “order” an noun or a verb in your enterprise applications?  Our technology has biased us to thinking about objects, which drives our modeling towards nouns and away from verbs.  Our technology biases us against modeling events and processes well!  And it shows up, insidiously sapping productivity and accessibility.

The lack of ontology of process and event in current BRMS not only precludes the kind of integrated BPM and CEP I am discussing here, it also limits the ability of current BRMS to automate policies that consider what has happened in making decisions in the present.  For example, a statement like:

• if a medicine has a maximum therapeutic dosage over a period that is less than the total dosage of that medicine requested by a member over the same period then…

is beyond the capabilities of current offerings.  Authority understood some grammar about time but did not understand that events, such as a request, occurred in any deep sense.  So it could automate a sentence like:

• if the total dosage of a medicine requested by a member on a date within the last 90 days exceeds the maximum quarterly therapeutic quarterly dosage for the medicine then…

but understanding why it understands one sentence and not the other is too much for many authors to tolerate, let  alone understand.  The essential reason is that we sold the company before extending Authority’s ontology to include events and revising its parser to understand that both verbs and their deverbal nouns referred to events (including occurences of processes).

The bottom line here is that a quantum leap in natural language processing of business rules is needed.  Fortunately, this is not a quantum leap for natural language processing itself.  It is well-established that sentences are parsed into representations of events in which noun phrases play semantic roles, such as the following:

• agent or counteragent
• donor or beneficiary
• patient or “experiencer”
• causer
• instrument
• locative or time
• source or destination

where quite a few prepositions relate to more refined aspects of time and location, such as at, on, during, by, before, after, in and so on.   The critical thing for processes and events is that they occur in time.

Realizing this quantum leap in policy management and knowledge automation is really pretty simple.  Take an approach such as Authority and extend its core, upper ontology with the semantic roles and the concepts of events and processes.  Then extend its relation-centric parsing with even-centric parsing (both are needed).  A few more steps, notably handling metonymy, and the next generation of knowledge management and automation that provides the integrated understanding of time, events, and processes discussed here becomes a reality.

That’s what we’re patiently working towards.  And we’re doing it in as engine-independent a manner as practical so that we can leverage standards like RIF and SBVR.  It’s all about the knowledge.

Finally, we are looking for collaborators who would like to learn more or help, and, perhaps, get involved in leveraging the solution or its underlying technology.

David Karger of MIT’s AI lab challenged the panel from the audience by asserting that the data people posted on the web is much more important than any ontology that might define what that data means.  This set off a bit of a firestorm.  There was consensus that data itself is critically important, if not central.  For the most part, panelists were aghast at the notion that spreadsheets of data would be useless to computers unless the meaning of its headings, for example, were related to concepts defined by reference to ontology those computers understood. 

With respectful deference, the panel and audience yielded.  Sir Tim Berners-Lee took the floor.

The issue of semantics briefly faded from the discussion.  Utility seemed to be the crux of the matter.  Sir Tim illustrated how even the smallest bit of semantics (i.e., meaning by reference) added to a spreadsheet allowed others to quickly and incrementally, almost continuously add value to published data.  He did this by way of example, discussing mash-ups of bicycle accident, traffic, and map data by different people over the course of a day or so after someone first published the bicycle accident data.  Most interesting to me, however, was his concluding point: simply identifying what something is by reference to an existing semantic web concept makes data much more immediately consumable, useful and valuable.  For example, simply identifying that a column is a longitude using RDF adds a lot of value.   Yes, I realize mash-ups are old, and linked data is well known, but his point was delivered in such a straightforward and compelling manner that the argument simply passed.  He put  a lot of experts eyes back on the ball.

Sir Tim reiterated this point an hour or so later at a meet-up of meet-ups.  His consistent, critical point was that lightweight use of ontology realizes a great deal of value.  Simply using RDF to anchor the semantics of linked data, without substantial ontology development, makes data much more useful to humans.  And with regard to enterprises, he discussed how eleven (yes, he said 11) different concepts are enough to address most of the semantic needs of various enterprises (i.e., their relational database models).  Of course, they will receive more value from reusing existing ontology, extended according to their needs.  His point was that the small step of simply linking data with open web semantics using only the most widely adopted RDF identifiers is a huge step forward for the semantic web and the benefits its technologies can bring to individuals and enterprises.  Full-fledged ontology is important for deeper functionality and long-term visions, but simply using concepts from existing ontology can be a huge step forward.

I started to use Radar Networks’ Twine at the invitation of CEO Nova Spivak after writing this earlier this year (also see this). I enjoyed it for a while, especially because a lot of technology folks were hooking up with each other, especially the semantic web community, on Twine. But I found it  tedious to work through beta issues and to be bothered with recommendations or news about who was saying or bookmarking things about what. (I should have turned off the emails sooner!)

I was disappointed that Twine was taking an apparently folksonomic approach to tagging. It was as if Radar Networks was riding semantic web buzz without really embracing it openly or sharing the momentum that the invite-only community was investing in.  That may not sound fair – I believe that there are semantics in the back room, but that’s how it felt and it’s still the way it looks.  But probably the worst part is the process that you have to go through to add a bookmark – which is the whole point, of course!  (I ultimately sacrificed popup blockers, but the process still seems laborious compared to other alternatives.)

I stumbled across Zigtag almost accidentally while working for a VC firm with a portfolio of semantic startups. What I like most about Zigtag is that they make it obvious that they are building an ontology of tags and encourage users to select semantic tags (i.e., concepts) rather than folksonomic “words”.  They also provide tools for managing tags that allow you to move smoothly and incrementally from a folksonomic to a more semantic approach.

The key to the semantic approach for Zigtag is that shared tags are just that – they are more precise than strings.  They are not only words – they have definitions.

Unfortunately, like Twine, Zigtag’s ontological model remains hidden.

My initial experience with Zigtag resulted in immediate jubilation.  The Firefox plug-in works for me.  It lets me type in tags with nice completion and recommendations from the tags that others have defined.  Within 15 minutes I was writing to compliment Zigtag on a practical, elegant approach to the semantic bookmarking problem.  I liked it much better than Twine right off the bat – and despite its book-market, I like Twine a lot!  Within a few minutes I had an email from their founder, Reg Cheramy.  An hour later we were talking.  We talked about his early meeting with Michael Arrington, how his work compares to bulletin board or discussion forum emphasis in Twine , how he facilitates semantic tagging given a very large ontology and vocabulary, and so on.

Whether Reg took my advice to emphasize groups more or was already headed in that direction is unclear, but Zigtag now has group functionality that seems as good as (and in some ways better) than Twine’s.  If you go to Zigtag the web site, you can find groups to join, but unlike Twine’s web site, Zigtag does not recommend groups for you based on your interests.  I’m not sure this is a problem, though.  Recommendations can be distracting.  Nonetheless, if people want recommendations for more than content, it would be a simple step for Zigtag given the fact that they already recommend content that others have bookmarked.

I’m not too concerned with recommendations, even of content, so I cannot comment on Zigtag versus Twine on that front.  Generally, there is plenty of RSS and recommendation noise to go around.  I prefer the linked approach to finding information rather than searching and I don’t expect recommendations to become excellent in the near term.  For more on this, you might want to check out the recent news  about Vulcan’s EVRI investment at Webware or ReadWriteWeb.

I like to use Zigtag from the sidebar in Firefox.  Actually, I owe Reg additional thanks for, in effect, causing me to abandon Internet Explorer for Firefox.     I use it primarily to organize my bookmarks semantically and across machines.  For those that want to do the same, you might also be interested in Mitch Kapor’s Foxmarks.

I’m fine with finding groups on my own and I like seeing people and what they tend to tag, too.  Now that I know they are available on the web site, though, I want them in the sidebar.   The fact that they are indirect on the web site, not presented in the sidebar, and not proactively recommended probably explains why there are relatively few (especially compared to Twine).  It would be nice, for example,  to see groups and people organized along with bookmarks according to how heavily they use tags as I pivot through various facets.

So, on a feature basis, I like Zigtag more than Twine for two primary reasons:

1. Zigtag’s Firefox plug-in is a great user interface while Twine’s book-market is awkward in every sense that matters to me.
2. Zigtag emphasizes and leverages shared tagging of tags that have clearly documented interpretations  Twine is too folksonomic.

The picture shown in this post shows that Zigtag already “knows” a lot about semantics.  Part of the reason is that they must have a roomful of people watching for  tags that people enter that are not defined.  Quite a few of the tags I’ve added have become defined within hours (sometimes minutes) of when I enter them.  We’ll see how this scales up, but I like it – a lot.

The key question for both these sites is:

Are you going to share your ontology?  If not, why not?  If so, when or why not now?

Note that I am not suggesting they should. But if they have a reason not to, it would be nice to understand that.

It also would be nice to know whether the effort I expend on either site will be lost if they are acquired or I want to switch.  That’s how it looks at Twine today.

Zigtag exports my bookmarks.  I can get them from or over to Delicious, no problem.  But I want their semantics, too.  I would really appreciate preservation of the text, preferably the semantics of my tags.  Perhaps if my bookmarks were simply output as an OWL referencing their ontology?  At least then I could move without losing the effort that I have put into them, whether folksonomic or semantic.  I also want to know if their ontology is are any good and, if so, I’d appreciate export to OWL so that I could use bookmarks for other purposes that interest me.

The background issue of data portability, for bookmarks, social networks, and other personal profile data is huge.

If I had OWL export and an open ontology, I would be less worried about my investment in Zigtag or Twine.  Consider Techcrunch’s recent comments:

Zigtag’s biggest obstacle is the slew of other social bookmarking sites already available (…). The semantic tagging feature is fairly unique, but its appeal is still untested, especially against automated semantic taggers like Twine. Frankly, a lot of people are just going to stick with the simple but effective Delicious interface.

It’s hard to argue with the first sentence, but the second seems harsh.  Twine is getting credit that it may not deserve.  Also, Zigtag recommends tags, too.  But the third sentence is a problem for Zigtag as well as Twine, although the latter benefits from superior PR.

Another question, of course, is how Zigtag and Twine will fare once they try to make money.  Radar Networks has stated that Twine will start running ads by the end of the year.  Zigtag has made no public announcements.  Delicious selectively advertises (e.g., on search pages), perhaps to feed intelligence to Yahoo’s advertising network.  The advertisements are so selective that the value of other book-marking sites may be limited to the intelligence that they provide to established advertising networks.  If so, this will hold down valuations and slow innovation.  We’ll see, but obviously, I hope not..

• Understanding events and processes takes time
• Oracle should teach Siebel CRM about location and money
• Ontology of time in progress – amounts needed  

The core principle here is that software needs to have a common core of understanding that makes sense to most people and across almost every application.  These are the concepts of Pareto’s 80/20 Principle.  A concept like building could easily be out, but concepts like money and time (and whatever it takes to really understand money and time) are in.  Location, including distance, is in.  Luminousity could be out, but probably not if color is in.  Charge and current could be out, but not if electricity or magnetism is in.  The cutoff is less scientific than practical, but what is in has to be deeply consistent and completely rational (i.e., logically rigorous).^[2]

Angle is in

It took working with a team that is getting software to pass AP tests in physics, chemistry, and other areas (e.g., biology and economics) for me to realize that the physicists and chemists who defined the the International System of Units overlooked something fundamental not only to math and physics, but to our integration of language with visual perception. 

It turns out that understanding angles can be just as important – and is just as primitive – as understanding distance.  Consider longitude and latitude, for example.  And if you’re trying to get a computer to get college credit by passing the advanced placement test for Physics , then you need to understand angular momentum. 

Surprisingly, distance is among the SI units, but angle is not!^[1]

Getting computers to understand angles involves circles and fractions, which bring a few other concepts into our upper ontology, such as diameter, circumference, arcs, and denominators and numerators.  Curiously, angles are primitive and yet they are intrinsically fractions of circles.

A piece of a pie could be an eighth or a sixth of the whole pie.  The angle of either such piece would be 30 or 45 degrees, since there are 360 degrees in a circle (assuming the pie is round).

What is an angle?

Here’s what Wikipedia has to say on the matter:

In geometry and trigonometry, an angle (in full, plane angle) is the figure formed by two rays sharing a common endpoint, called the vertex of the angle. The magnitude of the angle is the “amount of rotation” that separates the two rays, and can be measured by considering the length of circular arc swept out when one ray is rotated about the vertex to coincide with the other (see “Measuring angles”, below). Where there is no possibility of confusion, the term “angle” is used interchangeably for both the geometric configuration itself and for its angular magnitude (which is simply a numerical quantity).

And another definition says:

A shape formed by two rays sharing a common endpoint or two lines that intersect. An angle has one vertex and two sides.

So before we are done with all this our ontology will have to include fundamental geometry, including rays, endpoints, vertices, length (which we’ve previously covered), lines, and intersection.  Here we are going to deal with nothing more than how angles are measured and pi.

Angles are measured in degrees or radians.  Radians may seem strange at first but they are harmless.  The ratio of a circle’s circumference to its diameter is the same, regardless of its radius (which is half its diameter, of course).  This is really no big surprise, since the ratio of a square’s circumference to the length of its sides is constant, too.  Unlike a square, where the ratio is the number of sides (i.e., 4), the ratio of the circumference of a circle to its diameter is an irrational number, called pi. 

Is pi a fraction?

Most of us know that pi is approximately 3.1415.  It is also true that the digits after the decimal point continue forever without a repeating pattern.  Numbers that cannot be expressed with a mantissa that is either finite or repeating are called irrational numbers.  If a real number is not irrational then it is rational.  There are also complex numbers that mix real and imaginary numbers (involving the square root of negative one), but we’ll skip those for now, OK?

Rational numbers are not irrational

Rational numbers are normal fractions, one integer over another.  Any rational number that is not equal to an integer has either a limited mantissa or a repeating pattern.  For example, the mantissa of ½ is a single digit, as in 0.5.  The mantissa of ¼ is two digits, as in 0.25.  The mantissa of 1/3 is an infinite number of digits, all of which are 3, as in 0.33333….  The mantissa of 1/7 is a little more interesting.  It is a repeating pattern of 6 digits, as in 0. 142857142857142857142857142857142857…

So our ontology of numbers includes both rational numbers (i.e., fractions) and irrational numbers and pi is an irrational number.  But recall that rational numbers and irrational numbers are disjoint.  That is, a fraction cannot be an irrational number.  So pi cannot be a fraction!

Ratios are not fractions

Fractions are the ratio of one integer to another.  Not all ratios are between integers, however.  In fact, some ratios are between amounts, such as an amount of distance per an amount of time (e.g., miles or kilometers per hour).

Pi is not a fraction because the circumference of a circle is not an integer.  But more generally, a fraction is a ratio but not all ratios are fractions.

Angular units

An angle of one radian covers an arc of circle that is equal to the circle’s radius in length.  Since the diameter is twice the radius in length and the circumference of a circle is pi times its diameter, there are 2 times pi radians in a circle.

A degree is also an angle.  More precisely, there are 360 degrees in a circle.  And each degree equals 60 seconds of an arc.  And each second of arc has 60 minutes.  Thus, a second of arc is 1/3600^th of a circle.

Acute and other angles

So, a radian is a little more than 57° and both a radian a degree are acute angles.  All of these units of angle are therefore acute, which means that they are less than a right angle (which is 90°).  An angle of 180° is called a straight angle and an angle between a right angle and a straight angle is called an obtuse angle.  And an angle that is more than a straight angle is called a reflex angle (they are commonly used to express a heading or bearing).

Pi at last

So, pi is a positive, irrational number and the ratio of any circle’s circumference to its diameter, as shown below.

Note that e is Napier’s constant – the base of the natural logarithm (i.e., ln(x) = log_e(x)).  It is another positive, irrational number that is distinct from pi.  These are, practically speaking, the only two irrational numbers most people will ever come across in math or physics.  In fact, most people know pi but never use it.  Relatively few know or use e, but you need to know the natural logarithm in mathematics class or if you hope to get college credit for physics with high marks on the AP test.