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

  • Ian Hodkinson
  • Angelo Montanari
  • Guido Sciavicco
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5213)

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.

Keywords

Modal Logic Temporal Logic Relation Algebra Derivation Tree Standard Rule 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Ian Hodkinson
    • 1
  • Angelo Montanari
    • 2
  • Guido Sciavicco
    • 3
  1. 1.Department of ComputingImperial College London(UK)
  2. 2.Department of Mathematics and Computer ScienceUniversity of Udine(Italy)
  3. 3.Department of Information Engineering and CommunicationsUniversity of MurciaMurcia(Spain)

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