Talk given at the Workshop on Tableau-systems (Brussels), and at the ILIAS-seminar (Luxembourg).

Abstract The traditional idea that logic is specially relevant for reasoning stems from the fact that logic is often conceived as an absolute normative constraint on what we should and should not believe (a synchronous constraint) and as an infallible guide for what we should (or may) come to believe in view of what we already believe (a diachronic constraint). This view is threathened by the existence of rational failures of deductive cogency; belief-states that do not conform to what logic would require, but that are never- theless more rational than any revised belief-state that would be deductively cogent.

The suggestion that belief-states that are not deductively cogent can still be rational depends itself on the view that logical norms like consistency or deductive closure can sometimes be overruled by extra-logical norms. The latter clearly poses a problem for views that grant logic a special role in reasoning. (The underlying idea is that the special role of logic is inconsistent with the presumed defeasible character of logical norms.)

There are many ways of coping with these insights.

1. One can just accept the conclusion that the received view about logic is wrong,

2. one can deny the existence of rational failures of deductive cogency, or

3. one can revise what we mean by logic and/or how we understand it's role in reasoning.

I'm only interested in the last type of response.

In particular, I'd like to focus on strategies that (a) rely on the use of non-classical logics, (b) claim that logic can be used to formalise defeasible reasoning forms, and (c) propose a logical model of belief and belief-revision. While each of these three strategies reduces the gap between logic and reasoning, and even share some of their formal resources, a unified philosophical account of such proposals is still missing.

My aim in this talk is relatively modest. I only want to develop a minimal model that integrates the crucial features of sub-classical logics, with models of belief that rely on defeasible reasoning and allow for belief-revision. The upshot is to distill an account of the special role of logic in reasoning that is consistent with our best formal (logical) models of belief.

The proposed account combines a modal reconstruction of adaptive consequence relations (Allo, 2013b) with a suggestion to adopt the finer distinctions of different types of group-knowledge (and belief) to model single-agent knowledge (and belief) (Allo, 2013a) and a formal model of belief-merge through communication (Baltag & Smets, 2013).