Course 3

Unifying Defeasible Reasoning: Adaptive Logics

Diderik Batens
University of Ghent


Most actual reasoning is defeasible and all knowledge ultimately results from de- feasible reasoning. The latter is clearly distinct from deductive reasoning, in technical respects as well as in philosophical respects. Defeasible reasoning forms display often an external dynamics (non-monotonicity) and always an internal dynamics. The internal dynamics results from the absence of a positive test—the consequence set need not be recursively enumerable.

Crucial is the so-called standard format. The pursued thesis is that every sensible defeasible reasoning form is characterized by an adaptive logic in standard format. The logics have a selection semantics and a dynamic proof theory, which explicates the reasoning process. A strong point of the approach is that the metatheory is studied for the whole domain at once rather than for each logic separately.

At the predicative level, defeasible reasoning forms have very weak decidability properties. This required the development of dynamic proofs, of which usual (static) proofs are a special case.

Adaptive logics offer precise an formal characterizations of methods. While their origin lies with methods for handling inconsistency, there are many results on other methods (inductive generalization, abduction and explanation, erotetic logic, etc.). Most of these require ampliative adaptive logics. It was shown that adaptive logics are also interesting for defining complex mathematical theories. While the weakness of decidability proper- ties also affects classical theories, adaptive logics engender theories that are up to Pi-1-1 complex and of which the non-triviality is provable by finitary means.

The course will offer a survey of the program and elucidate technical and philosophical results. Innovative aspects will be emphasized. Special attention will go to relations with results from the Brazilian school, especially the Cn-logics of Newton da Costa and LFIs.