An Algorithm to Compute Circumscription

Abstract McCarthy's theory of circumscription appears to be the most powerful among various formalizations of nonmonotonic reasoning designed to handle incomplete and negative information in knowledge representation systems. In this paper we describe a query answering algorithm for circumscriptive theories. The Closed-World Assumption (CWA) and its generalizations, the Generalized Closed-World Assumption (GCWA) and the Extended Closed-World Assumption (ECWA), can be considered as special forms of circumscription. Consequently, our algorithm also applies to answering queries in theories using the Closed-World Assumption and its generalizations. Similarly, since prioritized circumscription is equivalent to a conjunction of (parallel) circumscriptions, our algorithm can be used to answer queries in theories circumscribed by prioritized circumscription.

[1]  Teodor C. Przymusinski.  Query Answering in Circumscriptive and Closed-World Theories , 1986, AAAI.

[2]  Jack Minker,et al.  Logic and Databases: A Deductive Approach , 1984, CSUR.

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

[4]  John Grant,et al.  Answering Queries in Indefinite Databases and the Null Value Problem , 1986, Adv. Comput. Res..

[5]  Pierre Siegel,et al.  Saturation, Nonmonotonic Reasoning and the Closed-World Assumption , 1985, Artif. Intell..

[6]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

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

[8]  Raymond Reiter.  On Closed World Data Bases , 1977, Logic and Data Bases.

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

[10]  Adrian Walker,et al.  Towards a Theory of Declarative Knowledge , 1988, Foundations of Deductive Databases and Logic Programming..

[11]  Keith L. Clark,et al.  Negation as Failure , 1987, Logic and Data Bases.

[12]  Richard C. T. Lee,et al.  Symbolic logic and mechanical theorem proving , 1973, Computer science classics.

[13]  Vladimir Lifschitz,et al.  Pointwise circumscription , 1987 .

[14]  Raymond Reiter,et al.  Towards a Logical Reconstruction of Relational Database Theory , 1982, On Conceptual Modelling.

[15]  Alan van Gelser.  Negation as failure using tight derivations for general logic programs , 1989 .

[16]  Raymond Reiter,et al.  A Logic for Default Reasoning , 1987, Artif. Intell..

[17]  Robert C. Moore.  Semantical Considerations on Nonmonotonic Logic , 1985, IJCAI.

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

[19]  Drew McDermott,et al.  Non-Monotonic Logic I , 1987, Artif. Intell..

[20]  Robert E. Mercer,et al.  On the adequacy of predicate circumscription for closed‐world reasoning , 1985, Comput. Intell..

[21]  Jack Minker,et al.  On Indefinite Databases and the Closed World Assumption , 1987, CADE.

[22]  Teodor C. Przymusinski,et al.  A decidable query answering algorithm for circumscriptive theories , 1986, ISMIS '86.

[23]  Michael Gelfond,et al.  Negation as Failure: Careful Closure Procedure , 1986, Artif. Intell..

[24]  Vladimir Lifschitz,et al.  Closed-World Databases and Circumscription , 1987, Artif. Intell..

[25]  Teodor C. Przymusinski,et al.  The extended closed world assumption and its relationship to parallel circumscription , 1985, PODS '86.