The next talk of our seminar series will be given by Andrea Sabatini (Scuola Normale Superiore) via Teams (please, see details below) on Monday, May 6th, starting from 12:30 CET. Here it is the title and abstract of his talk:
Title: Proofs and refutations: a structural approach to nonmonotonic reasoning
Abstract: In this talk I will present a novel proof-theoretic approach to nonmonotonic reasoning, which is based on the combination of sequents and antisequents — i.e., sequents for unprovability — into suitable Gentzen-style calculi.
In the first part, I introduce hybrid hypersequent calculi for propositional default logics, where distinct extra-logical rules directly capture default rules, and parallel composition of sequents and antisequents formalizes contrary updating on the conclusions of extra-logical rules. I show that hybrid hypersequent calculi enjoy good structural properties, and that specific calculi are sound and weakly complete with respect to credulous consequence based on Lukaszewicz extensions. Moreover, I define a hypersequent-based decision method for skeptical consequence which circumvents the need for early computation of all extensions.
In the second part, I explore abductive reasoning — i.e., the search for the missing premise in an “unsaturated” deductive inference — by means of a hybrid sequent calculus for classical propositional logic. I define a procedure for identifying the set of analytic hypotheses that a rational agent would be expected to select as explanans. In particular, I show that this set may not include the deductively minimal hypothesis due to the presence of redundant information: on this basis, I propose a deductive criterion for differentiating between the best explanans candidates and other hypotheses. Additionally, I establish that the hypersequent-based decision procedure for skeptical consequence assesses provability against finite sequences of abductive inferences.
Finally, I sketch applications of this proof-theoretic approach to Reiter’s default logic and base-generate AGM revision.
Anyone who is interested is welcome to join.
