A Logic Based Approach to the Static Analysis of Production Systems
In this paper we present an embedding of propositional production systems into μ-calculus, and first-order production systems into fixed-point logic, with the aim of using these logics for the static analysis of production systems with varying working memories. We encode properties such as termination and confluence in these logics, and briefly discuss which ones cannot be expressed, depending on the expressivity of the logic. We show how the embeddings can be used for reasoning over the production system, and use known results to obtain upper bounds for special cases. The strong correspondence between the structure of the models of the encodings and the runs of the production systems enables the straightforward modeling of properties of the system in the logic.
KeywordsProduction System Computation Tree Linear Temporal Logic Kripke Model Resolution Strategy
Unable to display preview. Download preview PDF.
- 2.Gurevich, Y., Shelah, S.: Fixed-point extensions of first-order logic. In: Symposium on Foundations of Computer Science, pp. 346–353 (1985)Google Scholar
- 5.McCarthy, J., Hayes, P.: Some philosophical problems from the standpoint of artificial intelligence. In: Meltzer, B., Michie, D. (eds.) Machine Intelligence, vol. 4, pp. 463–502. Edinburgh University press, Edinburgh (1969)Google Scholar
- 6.Baral, C., Lobo, J.: Characterizing production systems using logic programming and situation calculus, http://www.public.asu.edu/~cbaral/papers/char-prod-systems.ps
- 7.Kautz, H., Selman, B.: Planning as satisfiability. In: ECAI 1992: Proceedings of the 10th European Conference on Artificial Intelligence, New York, NY, USA, pp. 359–363. John Wiley & Sons, Inc., Chichester (1992)Google Scholar
- 9.Mattmller, R., Rintanen, J.: Planning for temporally extended goals as propositional satisfiability. In: Veloso, M. (ed.) Proceedings of the 20th International Joint Conference on Artificial Intelligence, Hyderabad, India, January 2007, pp. 1966–1971. AAAI Press, Menlo Park (2007)Google Scholar
- 11.De Giacomo, G., Lenzerini, M.: Pdl-based framework for reasoning about actions. In: AI*IA 1995: Proceedings of the 4th Congress of the Italian Association for Artificial Intelligence on Topics in Artificial Intelligence, London, UK, pp. 103–114. Springer, Heidelberg (1995)Google Scholar
- 15.Bailey, J., Dong, G., Ramamohanarao, K.: Decidability and undecidability results for the termination problem of active database rules. In: Proceedings of the 17th ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems, pp. 264–273 (1998)Google Scholar
- 17.Courcelle, B.: The expression of graph properties and graph transformations in monadic second-order logic, pp. 313–400. World Scientific, Singapore (1997)Google Scholar