Much of what passes for knowledge about the world is defeasible, or can be mistaken. Our perceptions and premises can never be certain, we are forced to jump to conclusions in the presence of incomplete information, and we have to cut our deliberations short when our environment closes in. For this reason, any theory of artificial intelligence requires at its heart a theory of default reasoning, the process of reaching plausible, but uncertain, conclusions; and a theory of belief revision, the process of retracting and adding certain beliefs as information becomes available.
In this thesis, we will address both of these problems from a logical point of view. We will provide a semantic account of these processes and develop conditional logics to represent and reason with default or normative statements, about normal or typical states of affairs, and statements of belief revision. The conditional logics will be based on standard modal systems, and the possible worlds approach will provide a uniform framework for the development of a number of such systems.
Within this framework, we will compare the two types of reasoning, determining that they are remarkably similar processes at a formal level of analysis. We will also show how a number of disparate types of reasoning may be analyzed within these modal systems, and to a large extent unified. These include normative default reasoning, probabilistic default reasoning, autoepistemic reasoning, belief revision, subjunctive, hypothetical or counterfactual reasoning, and abduction.
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