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A SIMPLE ALGORITHM FOR DEDUCTION

Part of: General logic

Published online by Cambridge University Press:  09 March 2010

BILL WHITEN
BILL WHITEN*
Affiliation:
The University of Queensland, SMI, JKMRC, Brisbane 4072, Australia (email: [email protected])
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Abstract

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It is shown that a simple deduction engine can be developed for a propositional logic that follows the normal rules of classical logic in symbolic form, but the description of what is known about a proposition uses two numeric state variables that conveniently describe unknown and inconsistent, as well as true and false. Partly true and partly false can be included in deductions. The multi-valued logic is easily understood as the state variables relate directly to true and false. The deduction engine provides a convenient standard method for handling multiple or complicated logical relations. It is particularly convenient when the deduction can start with different propositions being given initial values of true or false. It extends Horn clause based deduction for propositional logic to arbitrary clauses. The logic system used has potential applications in many areas. A comparison with propositional logic makes the paper self-contained.

Keywords

deductionclassical propositional logictwo-variable logicsimple algorithm

MSC classification

Secondary: 03B05: Classical propositional logic 03B53: Paraconsistent logics 03B70: Logic in computer science
Type
Research Article
Information
The ANZIAM Journal , Volume 51 , Issue 1 , July 2009 , pp. 102 - 122
Copyright
Copyright © Australian Mathematical Society 2010

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