Propositional sequence-calculi for inconsistent systems.

Sequent calculi for bi-intuitionistic propositional logic

Bi-intuitionistic logic is the conservative extension of intuitionistic logic with a connective dual to implication. It is sometimes presented as a symmetric constructive subsystem of classical logic. In this talk, we compare three sequent calculi for bi-intuitionistic propositional logic: (1) a basic standard-style sequent calculus that restricts the premises of implication-right and exclusion...

Undecidable problems for propositional calculi with implication

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 few recognizing problems such as recognizing derivations, extensions, completeness, and axiomatizations. The main result of this paper is to prove that the problem of recognizing extensions is undecidable for e...

On Sequent Calculi for Intuitionistic Propositional Logic

The well-known Dyckoff’s 1992 calculus/procedure for intuitionistic propositional logic is considered and analyzed. It is shown that the calculus is Kripke complete and the procedure in fact works in polynomial space. Then a multi-conclusion intuitionistic calculus is introduced, obtained by adding one new rule to known calculi. A simple proof of Kripke completeness and polynomial-space decidab...

Referential Matrix Semantics for Propositional Calculi

Let L be a propositional language, and let F1, . . . , Fn be all propositional connectives it involves. We shall denote the set of all formulas of L as L, and identify L with the algebra of formulas (L,F1, . . . , Fn) freely generated by the propositional letters p1, . . . , pi, . . .. Assume that T is a non-empty set of indices (points of reference, possible worlds) and assume that a certain s...

A Two-Tiered Propositional Framework for Handling Multisource Inconsistent Information