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A solution of the uniform word problem for ortholattices

Published online by Cambridge University Press:  27 May 2010

ANDREA MEINANDER
ANDREA MEINANDER*
Affiliation:
Department of Philosophy, University of Helsinki, P.O. box 24, FIN-00014, Helsinki, Finland Email: andrea.meinander@helsinki.fi
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Abstract

The uniform word problem for finitely presented ortholattices is shown to be solvable through a method of terminating proof search. The axioms of ortholattices are all Harrop formulas, and thus can be expressed in natural deduction style as single succedent rules. A system of natural deduction style rules for orthologic is given as an extension of the system for lattices presented by Negri and von Plato. By considering formal derivations of atomic formulas from a finite number of given atomic formulas, it is shown that proof search is bounded, and thus that the question of derivability of any atomic formula from any finite set of given atomic formulas is decidable.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 20 , Issue 4 , August 2010 , pp. 625 - 638
Copyright
Copyright © Cambridge University Press 2010

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