Year: 2016
Type: article
Abstract: In this article, we deal with propositional calculi over a signature containing the classical implication → with the rules of modus ponens and substitution. For these calculi, we consider several decision problems such as recognition of derivations, extensions, completeness and axiomatizations. The main result of this article is that the problem of recognizing extensions is undecidable for every propositional calculus, and the problems of recognizing axiomatizations and completeness are undecidable for propositional calculi containing the axiom x→(y→x) . As a corollary, for all formulas A , the problem of derivability of A is undecidable.
Source: Logic Journal of IGPL
Author: Grigoriy V. Bokov
Institution: Lomonosov Moscow State University
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1607680367