An explication of reasoning in multiple inheritance systems through non-monotonic horn clause logic

Abstract In this paper we present a new approach to explicate the IS-A link and the inheritance of properties down through IS-A links. We introduce the syntactic category of common nouns intended to represent kinds (or prototypes) of objects. We describe two sentence-forming operations: the attribution of membership of kinds to objects or objects of a certain kind, and the attribution of properties to objects or objects of a certain kind. We then argue that the inferential behavior of sentences is different depending on how the sentence was formed. Although the attribution of membership in a kind will always hold true for any instance, the attribution of a property may be overridden. We explicate the inferential behavior of these sentences in non-monotonic logic and present the proof theory and semantics for this non-monotonic logic.

[1]  Ronald J. Brachman,et al.  What IS-A Is and Isn't: An Analysis of Taxonomic Links in Semantic Networks , 1983, Computer.

[2]  David S. Touretzky,et al.  A Clash of Intuitions: The Current State of Nonmonotonic Multiple Inheritance Systems , 1987, IJCAI.

[3]  Krzysztof R. Apt,et al.  Contributions to the Theory of Logic Programming , 1982, JACM.

[4]  Tony Hoare,et al.  Hierarchical Program Structures , 1972 .

[5]  Raymond Reiter,et al.  On Inheritance Hierarchies With Exceptions , 1983, AAAI.

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

[7]  Alan Borning,et al.  Multiple Inheritance in Smalltalk-BO , 1982, AAAI.

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

[9]  Daniel G. Bobrow,et al.  On Overview of KRL, a Knowledge Representation Language , 1976, Cogn. Sci..

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

[11]  Marvin Minsky,et al.  A framework for representing knowledge , 1974 .

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

[13]  David W. Etherington.  Formalizing Nonmonotonic Reasoning Systems , 1987, Artif. Intell..

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

[15]  Drew McDermott,et al.  Nonmonotonic Logic II: Nonmonotonic Modal Theories , 1982, JACM.

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

[17]  Dov M. Gabbay,et al.  Intuitonistic Basis for Non-Monotonic Logic , 1982, CADE.

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

[19]  John Mylopoulos,et al.  A language facility for designing database-intensive applications , 1980, TODS.

[20]  Mark S. Fox,et al.  On Inheritance in Knowledge Representation , 1979, IJCAI.

[21]  David S. Touretzky,et al.  A Skeptical Theory of Inheritance in Nonmonotonic Semantic Networks , 1987, Artif. Intell..

[22]  R. Gill.  The Logic of Common Nouns. , 1982 .

[23]  J. Lloyd.  Foundations of Logic Programming , 1984, Symbolic Computation.

[24]  John Mylopoulos,et al.  Generalization/Specialization as a Basis for Software Specification , 1982, On Conceptual Modelling.

[25]  David Robson,et al.  Smalltalk-80: The Language and Its Implementation , 1983 .

[26]  David S. Touretzky,et al.  The Mathematics of Inheritance Systems , 1984 .

[27]  John Mylopoulos,et al.  A language facility for designing interactive database-intensive applications , 1978, SIGMOD '78.

[28]  E. Sandewall,et al.  Nonmonotonic inference rules for multiple inheritance with exceptions , 1986, Proceedings of the IEEE.