New arguments for adaptive logics as unifying frame for the defeasible handling of inconsistency

Diderik Batens

pp. 101-122

in: Koji Tanaka, Francesco Berto, Edwin D. Mares, Francesco Paoli (eds), Paraconsistency, Berlin, Springer, 2013

Abstract

Nearly all popular reasoning forms that handle inconsistencies in a defeasible way have been characterised in terms of inconsistency-adaptive logics in standard format. This format has great advantages, which are explained in the first two sections. This suggests that inconsistency-adaptive logics form a suitable unifying framework for handling such reasoning forms. I shall present four new arguments in favour of this suggestion. (1);Identifying equivalent premise sets proceeds along familiar lines and is much easier than for many other formats. (2);Inconsistency-adaptive logics offer maximally consistent interpretations by themselves, without requiring tinkering from their user. (3);Characterization in terms of inconsistency-adaptive logics offers easy extensions and variations (a fascinating new type of example will be given). (4);Inconsistency-adaptive logics allow for axiomatisations that identify a set of isomorphic models and enable one to describe inconsistent models in an unambiguous way.