Formalized meta-theory of sequent calculi for linear logics
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TL;DR: This work formalized textbook proofs of the meta-theory of sequent calculi for linear logic in Abella using only elementary reasoning principles, which makes the proof techniques fairly portable to other formal reasoning systems.
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About: This article is published in Theoretical Computer Science. The article was published on 16 Aug 2019. and is currently open access. The article focuses on the topics: Sequent & Linear logic.
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References
Logic Programming with Focusing Proofs in Linear Logic
TL;DR: It is shown that the syntactic restriction induced by LinLog is not performed at the cost of any expressive power: a mapping from full linear logic to LinLog, preserving focusing proofs, and analogous to the normalization to clausal form for classical logic, is presented.
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Structural cut elimination
Frank Pfenning
- 26 Jun 1995
TL;DR: New proofs of cut elimination for intuitionistic, classical and linear sequent calculi are presented, avoiding the explicit use of multi-sets and termination measures on sequent derivations.
111
•Proceedings Article
Label-free Modular Systems for Classical and Intuitionistic Modal Logics
Sonia Marin,Lutz Straßburger +1 more
- 05 Aug 2014
TL;DR: This paper shows for each of the modal axioms d, t, b, 4, and 5 an equivalent set of inference rules in a nested sequent system, such that, when added to the basic system for themodal logic K, the resulting system admits cut elimination.
•Journal Article
A framework for specifying, prototyping, and reasoning about computational systems
Gopalan Nadathur,Andrew Gacek +1 more
TL;DR: An interactive, tactic-style theorem prover called Abella is described that realizes the reasoning logic and embodies the use of lemmas in proofs and also provides intuitively well-motivated tactics for inductive and co-inductive reasoning.
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Structural Focalization
Robert J. Simmons
- 08 Sep 2014
TL;DR: A focused sequent calculus for propositional intuitionistic logic is presented and the proof of identity expansion, which establishes internal completeness, is a major contribution of this work.
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