A Logic for Non-Terminating Golog Programs

Typical Golog programs for robot control are non-terminating. Analyzing such programs so far requires meta-theoretic arguments involving complex fix-point constructions. In this paper we propose a logic based on the situation calculus variant ES, which includes elements from branching time, dynamic and process logics and where the meaning of programs is modelled as possibly infinite sequences of actions. We show how properties of non-terminating programs can be formulated in the logic and, for a subset of it, how existing ideas from symbolic model checking in temporal logic can be applied to automatically verify program properties.

[1]  Adrian R. Pearce,et al.  Property Persistence in the Situation Calculus , 2007, IJCAI.

[2]  David Harel,et al.  Process Logic: Expressiveness, Decidability, Completeness , 1980, FOCS.

[3]  Jerzy Tiuryn,et al.  Dynamic logic , 2001, SIGA.

[4]  Yongmei Liu.  A hoare-style proof system for robot programs , 2002, AAAI/IAAI.

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

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

[7]  E. Allen Emerson,et al.  Temporal and Modal Logic , 1991, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[8]  Koen V. Hindriks,et al.  A verification framework for agent programming with declarative goals , 2007, J. Appl. Log..

[9]  Eugenia Ternovska,et al.  A model checker for verifying ConGolog programs , 2002, AAAI/IAAI.

[10]  Alfredo Gabaldon,et al.  Precondition Control and the Progression Algorithm , 2004, ICAPS.

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

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

[13]  Shin Nakajima,et al.  The SPIN Model Checker : Primer and Reference Manual , 2004 .

[14]  Donald Michie,et al.  Machine Intelligence 4 , 1970 .

[15]  Eugenia Ternovska,et al.  Reducing Inductive Definitions to Propositional Satisfiability , 2005, ICLP.

[16]  Hardi Hungar,et al.  First-Order-CTL Model Checking , 1998, FSTTCS.

[17]  Yde Venema,et al.  Dynamic Logic by David Harel, Dexter Kozen and Jerzy Tiuryn. The MIT Press, Cambridge, Massachusetts. Hardback: ISBN 0–262–08289–6, $50, xv + 459 pages , 2002, Theory and Practice of Logic Programming.

[18]  Gerhard Lakemeyer,et al.  Semantics for a useful fragment of the situation calculus , 2005, IJCAI.

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

[20]  Edmund M. Clarke,et al.  Symbolic Model Checking: 10^20 States and Beyond , 1990, Inf. Comput..

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

[22]  Nikola Bogunovic,et al.  Model checking procedures for infinite state systems , 2006, 13th Annual IEEE International Symposium and Workshop on Engineering of Computer-Based Systems (ECBS'06).

[23]  Edmund M. Clarke,et al.  Model Checking , 1999, Handbook of Automated Reasoning.

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

[25]  Marsha Chechik,et al.  Model-checking infinite state-space systems with fine-grained abstractions using SPIN , 2001, SPIN '01.