Hua, S. (1995). A New Approach to Cumulative Default Logic. Technical Report LiTH-IDA-R-95-22, Department of Computer and Information Science, Linköping University, Sweden. (bibtex),
Abstract: Cumulativity has been widely recognized as a desirable property of the logics for defeasible reasoning. The previous approaches to cumulative default logics are mainly concerned with the applicability conditions for defaults, rather than with the underlying, deductive system of the default extensions. This paper presents a new approach to cumulative default logic, by identifying more constructive underlying deductive systems. We show that cumulativity can be guaranteed if the semantic structures of the default extensions satisfy the properties of the coherence spaces. Based on this result, we investigate two variants of cumulative default logic. The first variant is that based on the conjunctive logic a non-classical (two-valued) propositional logic that can be examined as intuitionistic logic without the disjunction and implication connectives. The second, which is the more interesting one from the proof-theoretic point of view, is that based on linear logic another non-classical logic that can be examined as sequent calculus without the structural rules of weakning and contraction . The semantics for the latter variant of cumulative default logic seems to coincide rather nicely with the semantics for cumulative default logic based on coherent semantic structures presented in this paper. This brings us closer to a more constructive formalization of cumulative default reasoning, and eventually to an implementation of the cumulative default logic.
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