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DBLP
Conference object . 2023
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Focusing on Contraction.

Authors: A. Avellone; C. Fiorentini; A. Momigliano;

Focusing on Contraction.

Abstract

Focusing [1] is a proof-theoretic device to structure proof search in the sequent calculus: it provides a normal form to cut-free proofs in which the application of invertible and non-invertible inference rules is structured in two separate and disjoint phases. It is commonly believed that every “reasonable” sequent calculus has a natural focused version. Although stemming from proof-search considerations, focusing has not been thoroughly investigated in actual theorem proving, in particular w.r.t. termination, if not for the folk observations that only negative formulas need to be duplicated (or contracted if seen from the top down) in the focusing phase. We present a contraction-free (and hence terminating) focused proof system for multi-succedent propositional intuitionistic logic, which refines the G4ip calculus of Vorob’ev, Hudelmeier and Dyckhoff. We prove the completeness of the approach semantically and argue that this offers a viable alternative to other more syntactical means.

Country
Italy
Keywords

Intuitionistic logic, Automated theorem proving

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
Green