Temporal reasoning in the situation calculus

A fundamental problem in Knowledge Representation is the design of a logical language to express theories about actions and change. One of the most prominent proposals for such a language is John McCarthy's situation calculus, a formalism which views situations as branching towards the future. The situation calculus has been criticized for imposing severe representational limitations. For example, actions cannot be concurrent, properties change discreetly, etc. In this thesis we show that many of these limitations can be overcome. Our work builds upon the discrete situation calculus and on Reiter's montonic solution to the frame problem. A limitation of Reiter's approach is that it does not allow for state constraints. However, Lin and Reiter have made progress by providing a correctness criterion by which one can determine if an axiomatization can be said to solve the frame problem for theories that include state constraints. In this thesis we extend Lin and Reiter's work on the ramification problem by providing mechanisms to deal with theories of action that include binary state constraints and/or stratified definitions. Furthermore, we show how to extend the situation calculus to deal with a wider range of representational issues. In particular, we provide an approach to represent determinate knowledge about the future. Also, we extend the situation calculus to deal with concurrent actions. This problem is addressed by separating the problem into a precondition interaction problem and an effect interaction problem. Moreover, we present an enriched ontology of the situation calculus that allows the representation of knowledge about continuous properties of the world. We introduce the notion of a natural event, which is the result of a process governed by the laws of nature. Finally, we show that the situation calculus provides a better logical foundation for reasoning about actions and time than some other popular temporal logics.

[1]  John McCarthy,et al.  Programs with common sense , 1960 .

[2]  Richard C. Holt.  Structured concurrent programming with operating systems applications , 1978 .

[3]  John McCarthy,et al.  Circumscription - A Form of Non-Monotonic Reasoning , 1980, Artif. Intell..

[4]  John McCarthy,et al.  SOME PHILOSOPHICAL PROBLEMS FROM THE STANDPOINT OF ARTI CIAL INTELLIGENCE , 1987 .

[5]  James F. Allen,et al.  Planning Using a Temporal World Model , 1983, IJCAI.

[6]  James F. Allen.  Maintaining knowledge about temporal intervals , 1983, CACM.

[7]  James F. Allen.  Towards a General Theory of Action and Time , 1984, Artif. Intell..

[8]  John McCarthy,et al.  Applications of Circumscription to Formalizing Common Sense Knowledge , 1987, NMR.

[9]  Vladimir Lifschitz,et al.  Computing Circumscription , 1985, IJCAI.

[10]  Patrick J. Hayes,et al.  A Common-Sense Theory of Time , 1985, IJCAI.

[11]  David W. Etherington,et al.  Reasoning with incomplete information: investigations of non-monotonic reasoning , 1986 .

[12]  Henry A. Kautz.  The Logic of Persistence , 1986, AAAI.

[13]  Drew McDermott,et al.  Nonmonotonic Logic and Temporal Projection , 1987, Artif. Intell..

[14]  Michael Georgeff,et al.  MANY AGENTS ARE BETTER THAN ONE , 1987 .

[15]  V. Lifschitz.  Formal theories of action , 1987 .

[16]  Edwin P. D. Pednault,et al.  Synthesizing plans that contain actions with context‐dependent effects 1 , 1988, Comput. Intell..

[17]  Teodor C. Przymusinski.  On the Declarative Semantics of Deductive Databases and Logic Programs , 1988, Foundations of Deductive Databases and Logic Programming..

[18]  Erik Sandewall,et al.  Filter Preferential Entailment for the Logic of Action in Almost Continuous Worlds , 1989, IJCAI.

[19]  Erik Sandewall,et al.  Combining Logic and Differential Equations for Describing Real-World Systems , 1989, KR.

[20]  Patrick J. Hayes,et al.  Moments and points in an interval‐based temporal logic , 1989, Comput. Intell..

[21]  Vladimir Lifschitz,et al.  Miracles in Formal Theories of Action , 1989, Artif. Intell..

[22]  Josh Tenenbergy,et al.  A Non-reiied Temporal Logic , 1989 .

[23]  Andrew B. Baker,et al.  A Simple Solution to the Yale Shooting Problem , 1989, KR.

[24]  Murray Shanahan,et al.  Representing Continuous Change in the Event Calculus , 1990, ECAI.

[25]  Antony Galton,et al.  A Critical Examination of Allen's Theory of Action and Time , 1990, Artif. Intell..

[26]  Vladimir Lifschitz,et al.  Toward a Metatheory of Action , 1991, KR.

[27]  Fangzhen Lin,et al.  Provably Correct Theories of Action (Preliminary Report) , 1991, AAAI.

[28]  Manny Rayner,et al.  On the Applicability of Nonmonotonic Logic to Formal Reasoning in Continuous Time , 1991, Artif. Intell..

[29]  Andrew B. Baker,et al.  Nonmonotonic Reasoning in the Framework of Situation Calculus , 1991, Artif. Intell..

[30]  Michael Gelfond,et al.  What are the Limitations of the Situation Calculus? , 1991, Automated Reasoning: Essays in Honor of Woody Bledsoe.

[31]  J. M. Larrazabal,et al.  Reasoning about change , 1991 .

[32]  Raymond Reiter,et al.  The Frame Problem in the Situation Calculus: A Simple Solution (Sometimes) and a Completeness Result for Goal Regression , 1991, Artificial and Mathematical Theory of Computation.

[33]  Robert A. Kowalski,et al.  Database Updates in the Event Calculus , 1992, J. Log. Program..

[34]  Raymond Reiter,et al.  Proving Properties of States in the Situation Calculus , 1993, Artif. Intell..

[35]  Murray Shanahan,et al.  Narratives in the Situation Calculus , 1994, J. Log. Comput..

[36]  Fangzhen Lin,et al.  State Constraints Revisited , 1994, J. Log. Comput..

[37]  Fangzhen Lin,et al.  Provably correct theories of action , 1991, JACM.

[38]  Raymond Reiter,et al.  On Specifying Database Updates , 1995, J. Log. Program..