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. / Thesis / Doctor of Philosophy (PhD) / 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'. A first very general problem definition for this Ph.D. thesis is raised by the following question: Can reasoning with default rules, as presented in Reiter's seminal 1980 article: `A Logic for Default Reasoning', be understood as a logic for non-monotonic reasoning? This thesis presents a rationale for the formulation of such a question and a possible answer for it. On the more technical side, this thesis presents a proof calculus for a particular formulation of a logic for reasoning with default rules, as well as some mapping concepts for structuring presentations defined on this logic.

The inadequacy of the usual possible world semantics of modal languages when the meaning of 'belief' is attached to the modal operator is discussed. Three other approaches are then investigated. In the case of Moore's autoepistemic logic it becomes possible to compare an agent's beliefs to 'reality', which cannot be done directly in the possible world semantics. Levesque's semantics makes explicit in the object language the notion of 'this is all the information the agent has', which plays an important role in nonmonotonic reasoning. Both of these approaches deal with ideal reasoners. The third approach, Konolige's deduction model, is based on a semantics capable of describing the beliefs of one or more resourcebounded agents. Finally, the AGM postulates for belief revision are discussed. / Computer Science / M.Sc. (Computer Science)

The inadequacy of the usual possible world semantics of modal languages when the meaning of 'belief' is attached to the modal operator is discussed. Three other approaches are then investigated. In the case of Moore's autoepistemic logic it becomes possible to compare an agent's beliefs to 'reality', which cannot be done directly in the possible world semantics. Levesque's semantics makes explicit in the object language the notion of 'this is all the information the agent has', which plays an important role in nonmonotonic reasoning. Both of these approaches deal with ideal reasoners. The third approach, Konolige's deduction model, is based on a semantics capable of describing the beliefs of one or more resourcebounded agents. Finally, the AGM postulates for belief revision are discussed. / Computer Science / M.Sc. (Computer Science)