A conditional logic for defeasible beliefs

摘要

This paper provides a framework for representing beliefs by distinguishing between (i) the defeasible principles of a belief system, (ii) the propositions that are beyond reasonable doubt in a belief state, and (iii) the propositions ‘favored’ on the basis of defeasible principles and those propositions that are beyond reasonable doubt. Defeasible principles are interpreted semantically by means of a Lewis-style ranking of worlds (without the assumption that the actual world is among the ‘innermost’, or most highly ranked, worlds). The ‘favored closure’ (F-closure) of a set of defeasible principles and reasonable propositions is non-monotonic. Yet, given the concept of ‘pruning’ the default ranking relative to a set of worlds (determined by what is beyond reasonable doubt in a particular belief state) we provide a formal characterization of the conditions under which in inference to a favored conclusion on the basis of defeasible rules and reasonable propositions, is warranted. The adequacy of our representation of defeasible principles can be tested by considering a number of valid formulas that we list. We show that our concept of defeasible principle parallels but is not identical to the concept of ‘relatively high conditional probability’. An example of application of the formal language and semantics is given, and the final parts of the paper contain u