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From axioms to synthetic inference rules via focusing

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Focusing is a general technique that was designed to improve proof search, but has since become increasingly relevant in structural proof theory. The essential idea is to identify and merge the non-deterministic choices in a proof. A focused proof is then given by the alternation of phases where invertible rules are applied eagerly (bottom-up) and phases where the other rules are confined and controlled. The focusing theorem, which asserts the completeness of focused proofs, delivers strong representational benefits. For instance, by ignoring the internal structure of the phases one obtains a well-behaved notion of ‘synthetic rule’ (e.g. they commute with cut-reduction steps).

In this talk, we will present a careful study of a family of synthetic rules, the bipoles, giving a fresh view to an old problem: how to incorporate inference rules corresponding to axioms into proof systems for classical and intuitionistic logics. As different synthetic inference rules can be produced for the same axiom, we in fact unify and generalise previous approaches for transforming axioms into rules.

=== Zoom Details ===

Topic: Sonia Marin – Theory Seminar, 12/11/2021 Time: Nov 12, 2021 01:45 PM London

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This talk is part of the Theoretical computer science seminar series.

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