Talk by Andrea Sabatini

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.

Teams Link

Anyone who is interested is welcome to join.

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