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Is business logic too much for classical logic?

Business logic is not limited to mathematical logic, as in first-order predicate calculus.

Business logic commonly requires “aggregation” over sets of things, like summing the value of claims against a property to subtract it from the value of that property in order to determine the equity of the owner of that property.

  • The equity of the owner of a property in the property is the excess of the value of the property over the value of claims against it.

There are various ways of describing such extended forms of classical logic.  The most relevant to most enterprises is the relational algebra perspective, which is the base for relational databases and SQL.  Another is the notion of generalized quantifiers.

In either case, it is a practical matter to be able to capture such logic in a rigorous manner.  The example below shows how that can be accomplished using English, producing the following axiom in extended logic:

  • ∀(?x15)(property(?x15)→∀(?x10)(owner(of)(?x10,?x15)→∃(?x31)(value(of(?x15))(?x31)∧∑(?x44)(∀(?x49)(claim(against(?x15))(?x49)→value(of(?x49))(?x44))→∃(?x26)(excess(of(?x31))(over(?x44))(?x26)∧equity(in(?x15))(of(?x10))(?x26))))))

This logic can be realized in various ways, depending on the deployment platform, such as: Continue reading “Is business logic too much for classical logic?”

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Simply Logical English

This is not all that simple of an article, but it walks you through, from start to finish, how we get from English to logic. In particular, it shows how English sentences can be directly translated into formal logic for use with in automated reasoning with theorem provers, logic programs as simple as Prolog, and even into production rule systems.

There is a section in the middle that is a bit technical about the relationship between full logic and more limited systems (e.g., Prolog or production rule systems). You don’t have to appreciate the details, but we include them to avoid the impression of hand-waving

The examples here are trivial. You can find many and more complex examples throughout Automata’s web site.

Consider the sentence, “A cell has a nucleus.”:

Continue reading “Simply Logical English”

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Financial industry to define standards using defeasible logic and semantic web technologies

Last week, I attended the FIBO (Financial Business Industry Ontology) Technology Summit along with 60 others.

The effort is building an ontology of fundamental concepts in the financial services. As part of the effort, there is surprisingly clear understanding that for the resulting representation to be useful, there is a need for logical and rule-based functionality that does not fit within OWL (the web ontology language standard) or SWRL (a simple semantic web rule language). In discussing how to meet the reasoning and information processing needs of consumers of FIBO, there was surprisingly rapid agreement that the functionality of Flora-2 was most promising for use in defining and exemplifying the use of the emerging standard. Endorsers including Benjamin Grosof and myself, along with a team from SRI International. Others had a number of excellent questions, such as concerning open- vs. closed-world semantics, which are addressed by support for the well-founded semantics in Flora-2 and XSB.

Thanks go to Vulcan for making the improvements to Flora and XSB that have been developed in Project Halo available to all!

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Pedagogical applications of proofs of answers to questions

In Vulcan’s Project Halo, we developed means of extracting the structure of logical proofs that answer advanced placement (AP) questions in biology.  For example, the following shows a proof that separation of chromatids occurs during prophase.

textual explanation of entailment using the Linguist and SILK

This explanation was generated using capabilities of SILK built on those described in A SILK Graphical UI for Defeasible Reasoning, with a Biology Causal Process Example.  That paper gives more details on how the proof structures of questions answered in Project Sherlock are available for enhancing the suggested questions of Inquire (which is described in this post, which includes further references).  SILK justifications are produced using a number of higher-order axioms expressed using Flora‘s higher-order logic syntax, HiLog.  These meta rules determine which logical axioms can or do result in a literal.  (A literal is an positive or negative atomic formula, such as a fact, which can be true, false, or unknown.  Something is unknown if it is not proven as true or false.  For more details, you can read about the well-founded semantics, which is supported by XSB. Flora is implemented in XSB.)

Now how does all this relate to pedagogy in future derivatives of electronic learning software or textbooks, such as Inquire?

Well, here’s a use case: Continue reading “Pedagogical applications of proofs of answers to questions”