More on Representation Theory for Default Logic

AbstractIn this paper, we investigate the representability of a family of theories as the set of extensions of a default theory. First, we present both new necessary conditions and sufficient ones for the representability by means of general default theories, which improves on similar results known before. Second, we show that one always obtains representable families by eliminating countably many theories from a representable family. Finally, we construct two examples of denumerable, representable families; one is not supercompactly nonincluding, and the other consists of mutually inconsistent theories but fails to be represented by a normal default theory

Reasoning with Inconsistent Information

In this thesis we are concerned with developing formal and representational mechanisms for reasoning with inconsistent information. Strictly speaking there are two conceptually distinct senses in which we are interested in reasoning with inconsistent information. In one sense, we are interested in using logical deduction to draw inferences in a symbolic system. More specifically, we are interested in mechanisms that can continue to perform deduction in a reasonable manner despite the threat of inconsistencies as a direct result of errors or misrepresentations. So in this sense we are interested in inconsistency-tolerant or paraconsistent deduction. … ¶ In this thesis we adopt a novel framework to unify both logic-as-deduction and logic-as-representation approaches to reasoning with inconsistent information. …

Representation Theory for Default Logic

Default logic can be regarded as a mechanism to represent families of belief sets of a reasoning agent. As such, it is inherently second-order. In this paper, we study the problem of representability of a family of theories as the set of extensions of a default theory. We give a complete solution to the problem of representability by means of default theories with finite set of defaults, and by means of normal default theories. We obtain partial results on representability by arbitrary (infinite, nonnormal) default theories. We construct examples of denumerable families of non-including theories that are not representable. We also study the concept of equivalence between default theories

Representation Theory for Default Logic

Default logic can be regarded as a mechanism to represent families of belief sets of a reasoning agent. As such, it is inherently second-order. In this paper, we study the problem of representability of a family of theories as the set of extensions of a default theory. We give a complete solution to the representability by means of normal default theories. We obtain partial results on representability by arbitrary default theories. In particular, we construct examples of denumerable families of nonincluding theories that are not representable. We also study the concept of equivalence between default theories. We show that for every normal default theory there exists a normal prerequisitefree theory with the same set of extensions. We derive a representation result connecting normal default logic with a version of CWA.