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predicate calculus

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: (more…)

Project Sherlock

Working as part of Vulcan’s Project Halo[1], Automata is applying a natural language understanding system that translates carefully formulated sentences into formal logic so as to answer questions that typically require deeper knowledge and inference than demonstrated by Watson.

The objective over the next three quarters is to acquire enough knowledge from the 9th edition of Campbell’s Biology textbook to demonstrate three things.

  • First, that the resulting system answers, for example, biology advanced placement (AP) exam questions more competently than existing systems (e.g., Aura[2] or Inquire[3]).
  • Second, that knowledge from certain parts of the textbook is effectively translated from English into formal knowledge with sufficient breadth and depth of coverage and semantics.
  • Third, that the knowledge acquisition process proves efficacious and accessible to less than highly skilled knowledge engineers so as to accelerate knowledge acquisition beyond 2012.

Included in the second of these is a substantial ontology of background knowledge expected of students in order to comprehend the selected parts of the textbook using a combination of OWL, logic, and English sentences from sources other than the textbook.

Automata is hiring logicians, linguists, and biologists to work as consultants, contracts, or employees for:

  • Interactive tree-banking and word-sense disambiguation of several thousand sentences.[4]
  • Extending its lexical ontology and a broad-coverage grammar of English with additional vocabulary and deeper semantics, especially concerning cellular biology and related scientific knowledge including chemistry, physics, and math.
  • Maturing its upper and middle ontology of domain independent knowledge using OWL in combination with various other technologies, including description logic, first-order logic, high-order logic, modal logic, and defeasible logic.[5]
  • Enhancing its platform for text-driven knowledge engineering towards a collaborative wiki-like architecture for self-aware content in scientific education and biomedical applications.

Terms of engagement are flexible; ranging from small units of work to full-time employment.  We are based in Pittsburgh, Pennsylvania and Vulcan is headquartered in Seattle, Washington, but the team is distributed across the country and overseas.

Please contact Paul Haley by e-mail to his first name at this domain.

[1] Vulcan:; Project Halo:
Video introduction/overview :

[2] Aura:

[3] Inquire:

[4] tree-banking and WSD: and

[5] e.g., SILK ( ) and SBVR (

The $50 Business Rule

Work on acquiring knowledge about science has estimated the cost of encoding knowledge in question answering or problem solving systems at $10,000 per page of relevant textbooks. Regrettably, such estimates are also consistent with the commercial experience of many business rules adopters. The cost of capturing and automating hundreds or thousands of business rules is typically several hundred dollars per rule. The labor costs alone for a implementing several hundred rules too often exceed $100,000.

The fact that most rule adopters face costs exceeding $200 per rule is even more discouraging when this cost does not include the cost of eliciting or harvesting functional requirements or policies but is just the cost of translating such content into the more technical expressions understood by business rules management systems (BRMS) or business rule engines (BRE).

I recommend against adopting any business rule approach that cannot limit the cost of automating elicited or harvested content to less than $100 per rule given a few hundred rules. In fact, Automata provides fixed price services consistent with the following graph using an approach similar to the one I developed at Haley Systems.

Cost per Harvested or Elicited Rule