Tableau-based decision procedure for non-Fregean logic of sentential identity

Sentential Calculus with Identity (SCI) is an extension of classical propositional logic, featuring a new connective of identity between formulas. In SCI two formulas are said to be identical if they share the same denotation. In the semantics of the logic, truth values are distinguished from denotations, hence the identity connective is strictly stronger than classical equivalence. In this paper we present a sound, complete, and terminating algorithm deciding the satisfiability of SCI-formulas, based on labelled tableaux. To the best of our knowledge, it is the first implemented decision procedure for SCI which runs in NP, i.e., is complexity-optimal. The obtained complexity bound is a result of dividing derivation rules in the algorithm into two sets: decomposition and equality rules, whose interplay yields derivation trees with branches of polynomial length with respect to the size of the investigated formula. We describe an implementation of the procedure and compare its performance with implementations of other calculi for SCI (for which, however, the termination results were not established). We show possible refinements of our algorithm and discuss the possibility of extending it to other non-Fregean logics

A Qualitative Spatio-Temporal Framework Based on Point Algebra

International audienc

Reasoning on Relations, Modalities, and Sets

This survey discusses the interplay among unquantified re- lational logics, propositional modal logics, and set theories. To set up a common ground, cross-translation methods among languages commonly used to work with relations, modalities, and sets, are revisited. This pa- per also reports on many experiments aimed at providing automated support for reasoning based on the calculus of dyadic relations