The Situation and State Calculus versus Branching Temporal Logic
The situation calculus (SC) is a formalism for reasoning about action. Within SC, the notion of state of a given situation is usually characterized by the set of fluents that hold in that situation. However, this concept is insufficient for system specification. To overcome this limitation, an extension of SC is proposed, the situation and state calculus (SSC), where the concept of state is primitive, just like actions, situations and fluents. SSC is then compared with a branching temporal logic (BTL). A representation of BTL in SSC is defined and shown to establish a sound and complete encoding.
KeywordsTemporal Logic Natural Transformation Linear Temporal Logic Predicate Symbol Interpretation Structure
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- 2.H. Ehrig and B. Mahr. Fundamentals of Algebraic Specification 1: Initial Semantics, volume 6 of EATCS Monographs on Theoretical Computer Science. Springer-Verlag, New York, N.Y., 1985.Google Scholar
- 8.J. McCarthy and P. Hayes. Some philosophical problems from the standpoint of artificial intelligence. In B. Meltzer and D. Michie, editors, Machine Intelligence 4, pages 463–502. Edinburgh University Press, Scotland, 1969.Google Scholar
- 9.J. Meseguer. General logics. In H.-D. Ebbinghaus et al, editor, Proc. Logic Colloquium’ 87. North-Holland, 1989.Google Scholar
- 12.J. Ramos. The situation and state calculus. In A. Drewery, G.-J. Kruijff and R. Zuber, editors, Proceedings of the Second ESSLLI Student Session, 1997.Google Scholar
- 13.R. Reiter. The frame problem in the situation calculus: a simple solution (sometimes) and a completeness result for goal regression. In V. Lifschitz, editor, Artificial Intelligence and Mathematical Theory of Computation: Papers in Honor of John McCarthy, pages 359–380. Academic Press, San Diego, CA, 1991.CrossRefGoogle Scholar
- 17.C. Stirling. Modal and temporal logics. In S. Abramsky, D. Gabbay, and T. Maibaum, editors, Handbook of Logic in Computer Science. Volume 2. Background: Computational Structures, pages 477–563. Oxford University Press, 1992.Google Scholar
- 20.A. Zanardo, B. Barcellan, and M. Reynolds. Non-denability of the class of complete bundled trees. The Logic Journal of IGPL. To appear.Google Scholar