A Hybrid Framework for Representing Uncertain Knowledge

This paper addresses the problem of bridging the gap between the fields of Knowledge Renresentation (KR) and Uncertain Reasoning (UR). The proposed solution consists of a framework for representing uncertain knowledge in which two components, one dealing with (categorical) knowledge and one dealing with uncertainty about this knowledge, are singled out. In this sense, the framework is "hybrid". This framework is characterized in both modeltheoretic and proof-theoretic terms. State of belief is represented by "belief sets", defined in terms of the "functional approach to knowledge representation" suggested by Levesque. Examples are given, using first order logic and (a minimal subset of) M-Krypton for the KR side, and a yes/no trivial case and Dempster-Shafer theory for the UR side.

[1]  Alessandro Saffiotti.  A Hybrid Belief System for Doubtful Agents , 1990, IPMU.

[2]  Joseph Y. Halpern,et al.  A Guide to the Modal Logics of Knowledge and Belief: Preliminary Draft , 1985, IJCAI.

[3]  Hector J. Levesque,et al.  An Essential Hybrid Reasoning System: Knowledge and Symbol Level Accounts of KRYPTON , 1985, IJCAI.

[4]  Petr Hájek,et al.  On Belief Functions , 1992, Advanced Topics in Artificial Intelligence.

[5]  Alessandro Saffiotti,et al.  An AI view of the treatment of uncertainty , 1987, The Knowledge Engineering Review.

[6]  Peter Schefe.  On foundations of reasoning with uncertain facts and vague concepts , 1980 .

[7]  E. Ruspini.  The Logical Foundations of Evidential Reasoning (revised) , 1987 .

[8]  Hector J. Levesque,et al.  Foundations of a Functional Approach to Knowledge Representation , 1984, Artif. Intell..

[9]  David J. Israel,et al.  Distinctions and Confusions: A Catalogue Raisonne , 1981, IJCAI.

[10]  Alessandro Saffiotti,et al.  Dialogue modelling in M-KRYPTON-a hybrid language for multiple believers , 1988, [1988] Proceedings. The Fourth Conference on Artificial Intelligence Applications.

[11]  L. A. Zedeh.  Knowledge representation in fuzzy logic , 1989 .

[12]  Hector J. Levesque,et al.  Competence in Knowledge Representation , 1982, AAAI.

[13]  Johan de Kleer,et al.  An Assumption-Based TMS , 1987, Artif. Intell..

[14]  Ronald Fagin,et al.  Uncertainty, belief, and probability 1 , 1991, IJCAI.

[15]  Philippe Smets.  Non-standard logics for automated reasoning , 1988 .

[16]  Lotfi A. Zadeh,et al.  Knowledge Representation in Fuzzy Logic , 1996, IEEE Trans. Knowl. Data Eng..

[17]  Malcolm C. Harrison,et al.  An analysis of four uncertainty calculi , 1988, IEEE Trans. Syst. Man Cybern..

[18]  Haim Gaifman,et al.  A Theory of Higher Order Probabilities , 1986, TARK.

[19]  Terence R. Thompson.  Parallel Formulation of Evidential-Reasoning Theories , 1985, IJCAI.

[20]  Kathryn B. Laskey,et al.  Assumptions, Beliefs and Probabilities , 1989, Artif. Intell..

[21]  Glenn Shafer,et al.  A Mathematical Theory of Evidence , 2020, A Mathematical Theory of Evidence.