Adaptive logics using the minimal abnormality strategy are $$\Pi^1_1$$ -complex

Abstract

In this article complexity results for adaptive logics using the minimal abnormality strategy are presented. It is proven here that the consequence set of some recursive premise sets is 1 1 -complete. So, the complexity results in (Horsten and Welch, Synthese 158:41-60, 2007) are mistaken for adaptive logics using the minimal abnormality strategy.

Adaptive Logics as a Necessary Tool for Relative Rationality: Including a Section on Logical Pluralism

“…This might especially be the case in 'provisional' stages of those theories, in which lots of theoretical problems are still to be solved by means of defeasible reasoning forms. 25 If such a situation obtains, one may still devise deductive logics but their application will be restricted if not empty and their use spurious.…”

“…For such theories Cn L (Γ ) is not in general semi-recursive-it may be up to Π 1 1 -complex-see [25]. The reasons for introducing adaptive theories is that the world may be so complex that it cannot be captured by semi-recursive theories.…”

Hierarchic adaptive logics

“…However, they have hitherto lagged behind flat adaptive logics, when it comes to the investigation of their universal properties. Now that our picture of flat adaptive logics has been clarified in several studies [3,7,6,10,18], it has become time to turn to the combined logics, with the aid of the metatheory of the flat logics themselves.…”

On Possibilities and Thought Experiments

“…Interestingly, final derivability may be defined by: if and only if any extension of the proof in which the line is marked may be further extended in such a way that the line is unmarked. Final derivability is computationally complex (in general Π 1 1 for the Minimal Abnormality strategy; see [27] but assess this in terms of what is said in the last footnote). Nevertheless, there are procedures that form criteria for final derivability-see [6] and forthcoming work by Peter Verdée.…”