Yes fellows, most human reasoning is complex

Abstract

This paper answers the philosophical contentions defended in Horsten and Welch (2007, Synthese, 158, 41-60). It contains a description of the standard format of adaptive logics, analyses the notion of dynamic proof required by those logics, discusses the means to turn such proofs into demonstrations, and argues that, notwithstanding their formal complexity, adaptive logics are important because they explicate an abundance of reasoning forms that occur frequently, both in scientific contexts and in common sense contexts.

Strong, universal and provably non-trivial set theory by means of adaptive logic

“…Adaptive logics are excellent tools to formalize defeasible reasoning (cf. [2], [4], [3] and [1] for some general formal and philosophical introductions to AL). A large amount of very different types of defeasible reasoning have been characterized by means of an adaptive logic: abductive reasoning, inductive reasoning, inconsistency corrective reasoning, reasoning with vagueness, reasoning with ambiguity, reasoning about compatibility, question raising, coping with theories where statements are only plausibly true, diagnosis, causal discovery, belief merging and default reasoning.…”

Hierarchic adaptive logics

“…Of course, it is required that the justification of every line only refers to preceding lines in the proof. 6 Definition 7 A is finally derived from Γ on line l of a stage s iff (i) A is the second element of line l, (ii) line l is unmarked at stage s, and (iii) every extension of the stage in which line l is marked may be further extended in such a way that line l is unmarked again.…”

“…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.…”

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

“…Although they would probably see this result as an even bigger problem for adaptive logics, I insist that a very complex consequence set is not problematic for this type of logics. In Batens et al (2007) Horsten and Welch's negative reflections on their complexity results are criticized. However, there is more.…”