Non-finite Axiomatizability and Undecidability of Interval Temporal Logics with C, D, and T

Authors:
Ian Hodkinson;Angelo Montanari;Guido Sciavicco
Affiliations:
Department of Computing, Imperial College London, (UK);Department of Mathematics and Computer Science, University of Udine, (Italy);Department of Information Engineering and Communications, University of Murcia, Murcia, (Spain)
Venue:
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
Year:
2008

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Abstract

Interval logics are an important area of computer science. Although attention has been mainly focused on unary operators, an early work by Venema (1991) introduced an expressively complete interval logic language called CDT, based on binary operators, which has many potential applications and a strong theoretical interest. Many very natural questions about CDT and its fragments, such as (non-)finite axiomatizability and (un-)decidability, are still open (as a matter of fact, only a few undecidability results, including the undecidability of CDT, are known). In this paper, we answer most of these questions, showing that almost all fragments of CDT, containing at least one binary operator, are neither finitely axiomatizable with standard rules nor decidable. A few cases remain open.