On the Verification of Very Expressive Temporal Properties of Non-terminating Golog Programs

The agent programming language GOLOG and the underlying Situation Calculus have become popular means for the modelling and control of autonomous agents such as mobile robots. Although such agents' tasks are typically open-ended, little attention has been paid so far to the analysis of non-terminating GOLOG control programs. Recently we therefore introduced a logic that allows to express properties of Golog programs using operators from temporal logics while retaining the full first-order expressiveness of the Situation Calculus. Combining ideas from classical symbolic model checking with first-order theorem proving we presented a verification method for a restricted subclass of temporal properties. In this paper, we extend this work by considering arbitrary temporal formulas. Our algorithm is inspired by classical CTL* model checking, but introduces techniques to cope with arbitrary first-order quantification.

[1]  Scott Sanner,et al.  Practical solution techniques for first-order MDPs , 2009, Artif. Intell..

[2]  R. Reiter,et al.  Forget It ! , 1994 .

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

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

[5]  Gerard J. Holzmann,et al.  The SPIN Model Checker - primer and reference manual , 2003 .

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

[7]  Stephan Merz,et al.  Model Checking , 2000 .

[8]  Pierre Wolper,et al.  An Automata-Theoretic Approach to Automatic Program Verification (Preliminary Report) , 1986, LICS.

[9]  Hongkai Liu,et al.  Computing updates in description logics , 2009 .

[10]  Dov M. Gabbay,et al.  Quantifier Elimination in Second-Order Predicate Logic , 1992, KR.

[11]  Giuseppe De Giacomo,et al.  Situation Calculus Based Programs for Representing and Reasoning about Game Structures , 2010, KR.

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

[13]  Yilan Gu Model Checking Meets Theorem Proving : a Situation Calculus Based Approach , 2022 .

[14]  Michael Wooldridge,et al.  On the complexity of practical ATL model checking , 2006, AAMAS '06.

[15]  Gerhard Lakemeyer,et al.  A Logic for Non-Terminating Golog Programs , 2008, KR.

[16]  Gerhard Lakemeyer,et al.  The Situation Calculus: A Case for Modal Logic , 2010, J. Log. Lang. Inf..

[17]  Sofiène Tahar,et al.  First-Order LTL Model Checking Using MDGs , 2004, ATVA.

[18]  Marco Pistore,et al.  NuSMV 2: An OpenSource Tool for Symbolic Model Checking , 2002, CAV.

[19]  Hector J. Levesque,et al.  ConGolog, a concurrent programming language based on the situation calculus , 2000, Artif. Intell..