Adaptive strategies and finite-conditional premise sets

Abstract

The standard format of adaptive logics makes use of two so-called strategies: reliability and minimal abnormality. While these are fairly well-known and frequently applied, the question of whether and when the two strategies are equi-epressive has so far remained unaddressed.In this paper, we show that for a specific, yet significant class of premise sets, the consequence set of an adaptive logic that uses the minimal abnormality strategy can be expressed by another adaptive logic that uses the reliability strategy. The basic idea is that we close the set of abnormalities under conjunction. We show that the consequence sets obtained by both logics from a premise set Γ is identical if and only if Γ is finite-conditional. The latter property is specified in terms of a well-known characterization of minimal abnormality. In addition, we discuss other (stronger) properties of premise sets that have been considered in the literature, showing each of them to imply finite-conditionality.

Adaptive logics: a parametric approach

“…A direct proof for Theorem 4.10 is given in [29]. Here, we will see that it follows from more generic results concerning truth-functional connectives and their interplay with abnormalities.…”

“…Hence we may ask whether in general, ,m = ∧ ,r . We refer the interested reader to [29] for an in-depth discussion of this matter. 12 …”