An Analysis of Defeasible Inheritance Systems

We give a conceptual analysis of (defeasible or nonmonotonic) inheritance diagrams, and compare our analysis to the ”small/big sets” of preferential and related reasoning. In our analysis, we consider nodes as information sources and truth values, direct links as information, and valid paths as information channels and comparisons of truth values. This results in an upward chaining, split validity, off-path preclusion inheritance formalism. We show that the small/big sets of preferential reasoning have to be relativized if we want them to conform to inheritance theory, resulting in a more cautious approach, perhaps closer to actual human reasoning. Finally, we interpret inheritance diagrams as theories of prototypical reasoning, based on two distances: set difference, and information difference. We will also see that some of the major distinctions between inheritance formalisms are consequences of deeper and more general problems of treating conflicting information. AMS Classification: 68T27, 68T30

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

[2]  K. Schlechta.  Nonmonotonic Logics: Basic Concepts, Results, and Techniques , 1997 .

[3]  Arnon Avron,et al.  Cut-Free Ordinary Sequent Calculi for Logics Having Generalized Finite-Valued Semantics , 2007, Logica Universalis.

[4]  Krishnaprasad Thirunarayan,et al.  On the Declarative Semantics of Inheritance Networks , 1989, IJCAI.

[5]  Karl Schlechta.  Semantics for Defeasible Inheritance , 1990, ECAI.

[6]  KARL SCHLECHTA.  Directly Sceptical Inheritance Cannot Capture the Intersection of Extensions , 1993, J. Log. Comput..

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

[8]  Karl Schlechta,et al.  Filters and Partial Orders , 1997, Log. J. IGPL.

[9]  Karl Schlechta,et al.  Distance semantics for belief revision , 1996, Journal of Symbolic Logic.

[10]  Hector J. Levesque,et al.  The Tractability of Path-Based Inheritance , 1989, IJCAI.

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

[12]  Karl Schlechta,et al.  Defaults as Generalized Quantifiers , 1995, J. Log. Comput..

[13]  David S. Touretzky,et al.  Implicit Ordering of Defaults in Inheritance Systems , 1984, AAAI.

[14]  Leora Morgenstern,et al.  Inheritance Comes of Age: Applying Nonmonotonic Techniques to Problems in Industry , 1997, IJCAI.

[15]  Sarit Kraus,et al.  Nonmonotonic Reasoning, Preferential Models and Cumulative Logics , 1990, Artif. Intell..

[16]  Joseph Y. Halpern,et al.  Plausibility measures and default reasoning , 1996, JACM.

[17]  Krishnaprasad Thirunarayan,et al.  An Evidence-based Framework for a Theory of Inheritance , 1989, IJCAI.

[18]  Rachel Ben-Eliyahu-Zohary,et al.  A modal logic for subjective default reasoning , 2000, Artif. Intell..

[19]  Christopher. Thornton,et al.  Coherent Systems , 2007 .

[20]  Dov M. Gabbay,et al.  On the Logic of Information Flow , 1995, Log. J. IGPL.