A Poly-Connexive Logic

The paper introduces a variant of connexive logic in which connexivity is extended from the interaction of negation with implication to the interaction of negation also with conjunction and disjunction. The logic is presented by two deductively equivalent methods: an axiomatic one and a natural-deduction one. Both are shown to be complete for a four-valued model theory

Rethinking inconsistent mathematics

This dissertation has two main goals. The first is to provide a practice-based analysis of the field of inconsistent mathematics: what motivates it? what role does logic have in it? what distinguishes it from classical mathematics? is it alternative or revolutionary? The second goal is to introduce and defend a new conception of inconsistent mathematics - queer incomaths - as a particularly effective answer to feminist critiques of classical logic and mathematics. This sets the stage for a genuine revolution in mathematics, insofar as it suggests the need for a shift in mainstream attitudes about the rolee of logic and ethics in the practice of mathematics

General Proof Theory. Celebrating 50 Years of Dag Prawitz's "Natural Deduction". Proceedings of the Conference held in Tübingen, 27-29 November 2015

General proof theory studies how proofs are structured and how they relate to each other, and not primarily what can be proved in particular formal systems. It has been developed within the framework of Gentzen-style proof theory, as well as in categorial proof theory. As Dag Prawitz's monograph "Natural Deduction" (1965) paved the way for this development (he also proposed the term "General Proof Theory"), it is most appropriate to use this topic to celebrate 50 years of this work. The conference took place 27-29 November, 2015 in Tübingen at the Department of Philosophy. The proceedings collect abstracts, slides and papers of the presentations given, as well as contributions from two speakers who were unable to attend

Beyond Logic. Proceedings of the Conference held in Cerisy-la-Salle, 22-27 May 2017

The project "Beyond Logic" is devoted to what hypothetical reasoning is all about when we go beyond the realm of "pure" logic into the world where logic is applied. As such extralogical areas we have chosen philosophy of science as an application within philosophy, informatics as an application within the formal sciences, and law as an application within the field of social interaction. The aim of the conference was to allow philosophers, logicians and computer scientists to present their work in connection with these three areas. The conference took place 22-27 May, 2017 in Cerisy-la-Salle at the Centre Culturel International de Cerisy. The proceedings collect abstracts, slides and papers of the presentations given, as well as a contribution from a speaker who was unable to attend