A Logical Basis for Reasoning with Default Rules

Abstract

This thesis is an investigation into the foundations of reasoning with default rules as presented by Reiter in his seminal 1980 article: `A Logic for Default Reasoning'. In being such, it opens up with a critical appraisal of the logical underpinnings of Reiter's presentation of the main elements of reasoning with default rules. More precisely, following Reiter's presentation, it discusses the concept of a default rule in comparison with that of a rule of inference, the concept of an extension in comparison with that of a theory, and the concept of `being a consequence of' for reasoning with default rules. Contrary to the commonly perceived view, the argument put forth is that such a context does not provide sensible logical foundation for reasoning with default rules. As a result, this thesis argues for an alternative interpretation to what is captured by default rules, what is captured by extensions, and what `being a consequence of' for reasoning with default rules amounts to. In particular, it proposes to treat default rules as premiss-like objects standing for assertions made tentatively, to treat extensions as interpretation structures of a syntactical kind, and to bring the concept of `being a consequence of' for reasoning with default rules into the foreground by formulating a suitable notion of an entailment relation and its ensuing logical system. Accounting for the fact that in any logical system it is important to have at hand mechanisms for formulating proofs and for structuring large theories, this thesis presents a tableaux based proof calculus for reasoning with default rules and it explores some mappings notions related to the structuring of default presentations, i.e., presentations in the context of reasoning with default rules.