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relational algebra

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…)

“Only full page color ads can run on the back cover of the New York Times Magazine.”

A decade or so ago, we were debating how to educate Paul Allen’s artificial intelligence in a meeting at Vulcan headquarters in Seattle with researchers from IBM, Cycorp, SRI,  and other places.

We were talking about how to “engineer knowledge” from textbooks into formal systems like Cyc or Vulcan’s SILK inference engine (which we were developing at the time).   Although some progress had been made in prior years, the onus of acquiring knowledge using SRI’s Aura remained too high and the reasoning capabilities that resulted from Aura, which targeted University of Texas’ Knowledge Machine, were too limited to achieve Paul’s objective of a Digital Aristotle.  Unfortunately, this failure ultimately led to the end of Project Halo and the beginning of the Aristo project under Oren Etzioni’s leadership at the Allen Institute for Artificial Intelligence.

At that meeting, I brought up the idea of simply translating English into logic, as my former product called “Authorete” did.  (We renamed it before Haley Systems was acquired by Oracle, prior to the meeting.)

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