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Article . 2014
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https://dx.doi.org/10.1184/r1/...
Other literature type . 2002
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https://dx.doi.org/10.1184/r1/...
Other literature type . 2002
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https://dx.doi.org/10.48550/ar...
Article . 2011
License: arXiv Non-Exclusive Distribution
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Article . 2018
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DBLP
Article . 2018
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Structural Focalization

Structural focalization
Authors: Robert J. Simmons;

Structural Focalization

Abstract

Focusing, introduced by Jean-Marc Andreoli in the context of classical linear logic [Andreoli 1992], defines a normal form for sequent calculus derivations that cuts down on the number of possible derivations by eagerly applying invertible rules and grouping sequences of non-invertible rules. A focused sequent calculus is defined relative to some nonfocused sequent calculus; focalization is the property that every nonfocused derivation can be transformed into a focused derivation. In this article, we present a focused sequent calculus for propositional intuitionistic logic and prove the focalization property relative to a standard presentation of propositional intuitionistic logic. Compared to existing approaches, the proof is quite concise, depending only on the internal soundness and completeness of the focused logic. In turn, both of these properties can be established (and mechanically verified) by structural induction in the style of Pfenning's structural cut elimination without the need for any tedious and repetitious invertibility lemmas. The proof of cut admissibility for the focused system, which establishes internal soundness, is not particularly novel. The proof of identity expansion, which establishes internal completeness, is a major contribution of this work.

Related Organizations
Keywords

focusing, FOS: Computer and information sciences, Computer Science - Logic in Computer Science, intuitionstic logic, Structure of proofs, polarized logic, proof search, cut admissibility, Logic in Computer Science (cs.LO), normalization, proof terms, identity expansion, F.4.1, 89999 Information and Computing Sciences not elsewhere classified, Cut-elimination and normal-form theorems, 03F05, 03F07, 03F65, Subsystems of classical logic (including intuitionistic logic)

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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!
18
Top 10%
Top 10%
Top 10%
Green
bronze