Abstract
Reasoning about change is a central issue in research on human and robot planning. We study an approach to reasoning about action and change in a dynamic logic setting and provide a solution to problems which are related to the Frame problem. Unlike most work on the frame problem the logic described in this paper is monotonic. It (implicitly) allows for the occurrence of actions of multiple agents by introducing non-stationary notions of waiting and test. The need to state a large number of “frame axioms” is alleviated by introducing a concept of chronological preservation to dynamic logic. As a side effect, this concept permits the encoding of temporal properties in a natural way. We compare the relative merits of our approach and non-monotonic approaches as regards different aspects of the frame problem. Technically, we show that the resulting extended systems of propositional dynamic logic preserve (weak) completeness, finite model property and decidability.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Baker, A.B., 1991, “Nonmonotonic reasoning in the framework of situation calculus,” Artificial Intelligence 49, 5–23.
Chellas, B.F., 1980, Modal Logic: An Introduction, Cambridge: Cambridge University Press.
Etherington, D.W., Kraus, S. and Perlis, D., 1991, “Nonmonotonicity and the scope of reasoning,” Artificial Intelligence 52, 221–261.
Fine, K. and Schurz, G., 1996, “Transfer theorems for stratified multimodal logics,” pp. 169–213 in Logic and Reality. Essays in Pure and Applied Logic. In Memory of Arthur Prior, J. Copeland, ed., Oxford: Oxford University Press.
Fischer, M.J. and Ladner, R.E., 1979, “Propositional dynamic logic of regular programs,” Journal of Computer and System Sciences 18, 194–211.
Gargov, G. and Passy, S., 1990, “A note on boolean modal logic,” pp. 299–309 in Proceedings of the Summer School and Conference on Mathematical Logic, P.P. Petkov, ed., Plenum Press, New York and London.
Gargov, G., Passy, S. and Tinchev, T., 1987, “Modal environment for boolean speculation,” pp. 253–263 in Proceedings of an Advanced International Summer School and Conference on Mathematical Logic and Its Applications, 1986, D.G. Skordev, ed., Plenum Press, New York and London.
Georgeff, M.P., 1987a, “Many agents are better than one,” pp. 59–79 in Proceedings of the 1987 Workshop on the Frame Problem in Artificial Intelligence, F.M. Brown, ed., Lawrence, KS: Morgan Kaufmann Publishers, Inc.
Georgeff, M.P., 1987b, “Planning,” Annual Review of Computer Science 2, 359–400.
Ginsberg, M.L., 1991, “Computational considerations in reasoning about action,” pp. 250–261 in Proceedings of the Second International Conference on Principles of Knowledge Representation and Reasoning, J. Allen, R. Fikes and E. Sandevall, eds., Cambridge, MA: Morgan Kaufmann Publishers.
Ginsberg, M.L. and Smith, D.E., 1988a, “Reasoning about actions I: A possible worlds approach,” Artificial Intelligence 35, 165–195.
Ginsberg, M.L. and Smith, D.E., 1988b, “Reasoning about actions II: The qualification problem,” Artificial Intelligence 35, 311–342.
Goldblatt, R., 1987, Logics of Time and Computation, Center for the Study of Language and Information Lecture Notes 7, Leland Stanford Junior University, Stanford.
Goranko, V. and Passy, V., 1992, “Using the universal modality: Gains and questions,” Journal of Logic and Computation 2(1), 5–30.
Hanks, St. and McDermott, D., 1987, “Nonmonotonic logic and temporal projection,” Artificial Intelligence 33, 379–412.
Harel, D., 1984, “Dynamic logic,” pp. 497–604 in Handbook of Philosophical Logic. II: Extensions of Classical Logic, D. Gabbay and F. Guenthner, eds., Boston, MA: Reidel.
Harel, D., 1987, Algorithmics. The Spirit of Computing, Workingham, England and Reading, MA: Addison-Wesley Publishing Company.
Harel, D., Kozen, D. and Parikh, R., 1982, “Process logic: Expressiveness, decidability, completeness,” Journal of Computer and System Sciences 25, 144–170.
Hughes, G.E. and Cresswell, M.J., 1984, A Comparison to Modal Logic, London, New York: Methuen & Methuen.
Katsuno, H. and Mendelzon, A.O., 1991, “Propositional knowledge base revision and minimal change,” Artificial Intelligence 52, 263–294.
Kautz, H.A., 1982, “A first-order dynamic logic for planning,” Technical report, Computer Systems Research Group (CSRG), University of Toronto.
Lifschitz, V., 1987, “Formal theories of action,” pp. 410–432 in Readings in Nonmonotonic Reasoning, M.L. Ginsberg, ed., Los Altos, CA: Morgan Kaufmann Publishers.
Makinson, D., 1993, “Five faces of minimality,” Studia Logica 52, 339–379.
Manna, Z., Paltrinieri, M. and Waldinger, R., 1993, “Temporal planning,” pp. 37–41 in Workshop on Reasoning about Action and Change at IJCAI-93, Chambéry, France.
Manna, Z. and Waldinger, R., 1980, “A deductive approach to program synthesis,” pp. 141–172 in Readings in Artificial Intelligence, B.L. Webber and N.J. Nilsson, eds., Los Altos, CA: Morgan Kaufmann Publishers, 1981. Originally published in 1980.
McCarthy, J. and Hayes, P.J., 19, “Some philosophical problems from the standpoint of artificial intelligence,” pp. 431–450 in Readings in Artificial Intelligence, B.L. Webber and N.J. Nilsson, eds., Los Altos, CA: Morgan Kaufmann Publishers, 1981. Originally published in 1969.
Miller, B. and Shanahan, M., 1994, ‘Narratives in the situation calculus,” Journal of Logic and Computation 4(5), 513–530.
Moore, R.C., 1985, “A formal theory of knowledge and action,” pp. 317–358 in Formal Theories of the Commonsense World, J.R. Hobbs and R.C. Moore, eds., Norwood, NJ: Ablex Publishing Corporation.
Morreau, M., 1992, “Planning from first principles,” pp. 204–219 in Belief Revision, P. Gärdenfors, ed., Cambridge: Cambridge University Press.
Passy, S. and Tinchev, T., 1991, “An essay in combinatory dynamic logic,” Information and Computation 93, 263–332.
Pnueli, A., 1981, “The temporal semantics of concurrent programs,” Theoretical Computer Science 13, 45–60.
Pratt, V.R., 1976, “Semantical considerations on Floyd-Hoare logic,” pp. 109–121 in Proceedings of the 17th Annual IEEE Symposium on Foundations of Computer Science, 1976.
Pratt, V.R., 1978, “A practical decision method for propositional dynamic logic,” pp. 326–337 in Proceedings 10th Annual Association for Computing Machinery (ACM) Symposium on Theory of Computing.
Pratt, V.R., 1980, “Applications of modal logic to programming,” Studia Logica 39, 257–274.
Reiter, R., 1980, “A logic for default reasoning,” Artificial Intelligence 13, 81–132.
Reiter, R., 1991, “The frame problem in the situation calculus: A simple solution (sometimes) and a completeness result for goal regression,” pp. 359–380 in Artificial Intelligence and Mathematical Theory of Computation. Papers in Honor of John McCarthy, V. Lifschitz, ed., Boston, New York: Academic Press.
Rosenschein, S.J., 1981, “Plan synthesis: A logical perspective,” pp. 331–337 in Proceedings of the Seventh International Joint Conference of Artificial Intelligence, Vancouver.
Schubert, L., 1990, “Monotonic solution of the frame problem in the situation calculus: An efficient method for worlds with fully specified action,” in Knowledge Representation and Defeasible Reasoning, H.E. Kyburg Jr., R.P. Loui and G.N. Carlson, eds., Dordrecht, Boston, London: Kluwer Academic Publishers.
Schurz, G., 1994, “Probabilistic justification of default reasoning,” pp. 248–259 in KI-94, 18th German Annual Conference on Artificial Intelligence: Advances in Artificial Intelligence, B. Nebel and L. Dreschler-Ficher, eds., Springer-Verlag.
Segerberg, K., 1980, “Applying modal logic,” Studia Logica 39, 275–295.
Segerberg, K., 1982, “A completeness theorem in the modal logic of programs,” pp. 31–46 in Universal Algebra and Applications, T. Traczyk, ed., Warsaw: Banach Center Publications.
Shoham, Y., 1988, Reasoning about Change. Time and Causation from the Standpoint of Artificial Intelligence. Cambridge, MA and London, England: The MIT Press.
Stephan, W. and Biundo, S., 1993, “A new logical framework for deductive planning,” pp. 32–38 in Proceedings of the Thirteenth Joint Conference on Artificial Intelligence ICJAI-93, Chambéry, France.
Waldinger, R., 1977, “Achieving several goals simultaneously,” pp. 250–271 in Readings in Artificial Intelligence, B.L. Webber and N.J. Nilsson, eds., Los Altos, CA: Morgan Kaufmann, 1981. Originally published in 1977.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Prendinger, H., Schurz, G. Reasoning about action and change. J Logic Lang Inf 5, 209–245 (1996). https://doi.org/10.1007/BF00173701
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00173701