A simple algorithm for deduction

Bill Whiten

Abstract


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 a 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 proposition values 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.


doi:10.1017/S1446181109000352

Keywords


deduction, classical propositional logic, two-variable logic, simple algorithm



DOI: http://dx.doi.org/10.21914/anziamj.v51i0.2380



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.