We present a mathematical approach to defeasible reasoning. This approach is based on the notion of specificity introduced by Poole and the theory of warrant presented by Pollock. We combine the ideas of the two. This main contribution of this paper is a precise well-defined system which exhibits correct behavior when applied to the benchmark examples in the literature. We prove that an order relation can be introduced among equivalence classes under the equi-specificity relation. We also prove a theorem that ensures the termination of the process of finding the justified facts. Two more lemmas define a reduced search... Read Read
Logical models of arguement formalize commonsense reasoning while taking process and computation seriously. This survey discusses the main ideas that characterize different logical models of argument. It presents the formal features of a few features of a few main approaches to the modeling of argumentation. We trace the evolution of argumentation from the mid-1980s, when argument systems emerged as an alternative to nonmonotonic formalisms based on classical logic, to the present, as argument in embedded in different complex systems for real-world applications, and allow more formal work to be done in different areas, such as AI and Law, case-based reasoning and negotiation among intelligent agents.
Ronatd Loui is a groduale sludent ol the Universiiy t^f Rochesler sludying cognidVe science and oJgorilhms. His mtjsl receni operations research ivork ivas on network (opology design for
This paper investigates the appropriateness of formal dialectics as a basis for nonmonotonic reasoning and defeasible reasoning that takes computational limits seriously. Rules that can come into conflict should be regarded as policies, which are inputs to deliberative processes. Dialectical protocols are appropriate for such deliberations when resources are bounded and search is serial.AI, it is claimed here, is now perfectly positioned to correct many misconceptions about reasoning that have resulted from mathematical logic's enormous success in this century: among them, (1) that all reasons are demonstrative, (2) that rational belief is constrained, not constructed, and (3) that process and disputation are not essential to reasoning. AI mainly provides new impetus to formalize the alternative (but older) conception of reasoning, and AI provides mechanisms with which to create compelling formalism that describes the control of processes.The technical contributions here are: the partial justification of dialectic based on controlling search; the observation that nonmonotonic reasoning can be subsumed under certain kinds of dialectics; the portrayal of inference in knowledge bases as policy reasoning; the review of logics of dialogue and proposed extensions; and the preformal and initial formal discussion of aspects and variations of dialectical systems with nondemonstrative reasons.
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