Are Tableaux an Improvement on Truth-Tables? Cut-Free proofs and Bivalence (1992)
| Citations: | 10 - 0 self |
BibTeX
@MISC{D'Agostino92aretableaux,
author = {Marcello D'Agostino},
title = {Are Tableaux an Improvement on Truth-Tables? Cut-Free proofs and Bivalence},
year = {1992}
}
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Abstract
We show that Smullyan's analytic tableaux cannot p-simulate the truth-tables. We identify the cause of this computational breakdown and relate it to an underlying semantic difficulty which is common to the whole tradition originating in Gentzen's sequent calculus, namely the dissonance between cut-free proofs and the Principle of Bivalence. Finally we discuss some ways in which this principle can be built into a tableau-like method without affecting its "analytic" nature. 1 Introduction The truth-table method, introduced by Wittgenstein in his Tractatus LogicoPhilosophicus, provides a decision procedure for propositional logic which is immediately implementable on a machine. However this time-honoured method is usually mentioned only to be immediately dismissed because of its incurable inefficiency. The well-known tableau method (which is closely related to Gentzen's cut-free sequent calculus) is commonly regarded as a "shortcut" in testing the logical validity of complex propositions...
