Semantics for a useful fragment of the situation calculus

In a recent paper, we presented a new logic called ES for reasoning about the knowledge, action, and perception of an agent. Although formulated using modal operators, we argued that the language was in fact a dialect of the situation calculus but with the situation terms suppressed. This allowed us to develop a clean and workable semantics for the language without piggybacking on the generic Tarski semantics for first-order logic. In this paper, we reconsider the relation between ES and the situation calculus and show how to map sentences of ES into the situation calculus. We argue that the fragment of the situation calculus represented by ES is rich enough to handle the basic action theories defined by Reiter as well as Golog. Finally, we show that in the full second-order version of ES, almost all of the situation calculus can be accommodated.

[1]  Max J. Cresswell,et al.  A New Introduction to Modal Logic , 1998 .

[2]  Hector J. Levesque,et al.  GOLOG: A Logic Programming Language for Dynamic Domains , 1997, J. Log. Program..

[3]  Ray Reiter,et al.  On knowledge-based programming with sensing in the situation calculus , 2001, ACM Trans. Comput. Log..

[4]  Dov M. Gabbay,et al.  Handbook of Philosophical Logic , 2002 .

[5]  Andreas Herzig,et al.  Formalizing Action and Change in Modal Logic I: the frame problem , 1999, J. Log. Comput..

[6]  Gerhard Lakemeyer,et al.  Situations, Si! Situation Terms, No! , 2004, KR.

[7]  Dominique Longin,et al.  A Logic for Planning under Partial Observability , 2000, AAAI/IAAI.

[8]  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.

[9]  Gerhard Lakemeyer,et al.  The logic of knowledge bases , 2000 .

[10]  E. Sandewall.  Features and fluents (vol. 1): the representation of knowledge about dynamical systems , 1995 .

[11]  Hector J. Levesque,et al.  Foundations for the Situation Calculus , 1998, Electron. Trans. Artif. Intell..

[12]  Hector J. Levesque,et al.  Knowledge, action, and the frame problem , 2003, Artif. Intell..

[13]  Robert Demolombe,et al.  Belief Change: from Situation Calculus to Modal Logic , 2003, J. Appl. Non Class. Logics.

[14]  Herbert B. Enderton,et al.  A mathematical introduction to logic , 1972 .

[15]  Alex M. Andrew,et al.  Knowledge in Action: Logical Foundations for Specifying and Implementing Dynamical Systems , 2002 .

[16]  G. E. Hughes,et al.  An introduction to modal logic, 2e éd., 1 vol , 1973 .

[17]  Raymond Reiter,et al.  Knowledge in Action: Logical Foundations for Specifying and Implementing Dynamical Systems , 2001 .

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

[19]  Maarten Marx,et al.  Situation Calculus as Hybrid Logic: First Steps , 2001, EPIA.

[20]  Vaughan R. Pratt,et al.  SEMANTICAL CONSIDERATIONS ON FLOYD-HOARE LOGIC , 1976, FOCS 1976.

[21]  Bernhard Beckert,et al.  Dynamic Logic , 2007, The KeY Approach.

[22]  Vaughan R. Pratt,et al.  Semantical consideration on floyo-hoare logic , 1976, 17th Annual Symposium on Foundations of Computer Science (sfcs 1976).

[23]  Michael Gelfond,et al.  Representing Action and Change by Logic Programs , 1993, J. Log. Program..