A Mathematical Treatment of Defeasible Reasoning and its Implementation

In this dissertation I present a formal approach to defeasible reasoning. This mathematical approach is based on the notion of specificity introduced by Poole and the general theory of warrant as presented by Pollock. General background information on the subject of Nonmonotonic Reasoning is presented and some of the shortcomings of existing systems are analyzed. We believe that the approach presented here represents a definite improvement over past systems. The main contribution of this thesis is a formally precise, elegant, clean, well-defined system which exhibits a correct behavior when applied to the benchmark examples in the literature. Model-theoretic semantical issues have been addressed. The investigation on the theoretical issues has aided the study of how this kind of reasoner can be realized on a computer. An interpreter of a restricted language, an extension of Horn clauses with defeasible rules, has been implemented. Finally, the implementation details are discussed.

[1]  Drew McDermott,et al.  Nonmonotonic Logic and Temporal Projection , 1987, Artif. Intell..

[2]  David Poole,et al.  A Logical Framework for Default Reasoning , 1988, Artif. Intell..

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

[4]  James P. Delgrande,et al.  An Approach to Default Reasoning Based on a First-Order Conditional Logic: Revised Report , 1987, Artif. Intell..

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

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

[7]  Richmond H. Thomason,et al.  Default Reasoning and the Logic of Theory Perturbation , 1984, Non-Monotonic Reasoning.

[8]  Leon Sterling,et al.  The Art of Prolog , 1987, IEEE Expert.

[9]  David Poole,et al.  On the Comparison of Theories: Preferring the Most Specific Explanation , 1985, IJCAI.

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

[11]  John L. Pollock,et al.  Defeasible Reasoning , 2020, Synthese Library.

[12]  Hector Geffner,et al.  A Framework for Reasoning with Defaults , 1990 .

[13]  Ronald Prescott Loui,et al.  Defeat among arguments: a system of defeasible inference , 1987, Comput. Intell..

[14]  B. Sauphanor.  The logical foundations of statistical inference , 1974 .

[15]  Eric Neufeld,et al.  Probabilsitic semantics and defaults , 2013, UAI.