Non-finite Axiomatizability and Undecidability of Interval Temporal Logics with C, D, and T
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.
KeywordsModal Logic Temporal Logic Relation Algebra Derivation Tree Standard Rule
Unable to display preview. Download preview PDF.
- 1.Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge University Press, Cambridge (2002)Google Scholar
- 4.Bresolin, D., Goranko, V., Montanari, A., Sala, P.: Tableau-based Decision Procedure for the Logic of Proper Subinterval Structures over Dense Orderings. In: Areces, C., Demri, S. (eds.) Proceedings of M4M-5: 5th International Workshop on Methods for Modalities, pp. 335–351 (2007)Google Scholar
- 7.Bresolin, D., Goranko, V., Montanari, A., Sciavicco, G.: Propositional interval neighborhood logics: Expressiveness, decidability, and undecidable extensions. Technical Report 05, Department of Mathematics and Computer Science, University of Udine, Italy (2008)Google Scholar
- 11.Gabbay, D.M.: An irreflexive lemma with applications to axiomatization on linear frames. In: Aspects of Philosophical Logic, pp. 67–89 (1981)Google Scholar
- 22.Moszkowski, B.: Reasoning about digital circuits. Tech. rep. stan-cs-83-970, Dept. of Computer Science, Stanford University, Stanford, CA (1983)Google Scholar
- 23.Roy, S., Sciavicco, G.: Completeness of chop. In: Guesguen, H.W., Ligozat, G., Rodriguez, R.V. (eds.) Proc. IJCAI 2007, pp. 90–95 (2007)Google Scholar