Topic
Deep inference
About: Deep inference is a research topic. Over the lifetime, 143 publications have been published within this topic receiving 2768 citations.
Papers published on a yearly basis
Papers
TL;DR: A logical system, called BV, is introduced, which extends multiplicative linear logic by a noncommutative self-dual logical operator, and yields a modular proof of cut elimination.
Abstract: This article introduces a logical system, called BV, which extends multiplicative linear logic by a noncommutative self-dual logical operator. This extension is particularly challenging for the sequent calculus, and so far, it is not achieved therein. It becomes very natural in a new formalism, called the calculus of structures, which is the main contribution of this work. Structures are formulas subject to certain equational laws typical of sequents. The calculus of structures is obtained by generalizing the sequent calculus in such a way that a new top-down symmetry of derivations is observed, and it employs inference rules that rewrite inside structures at any depth. These properties, in addition to allowing the design of BV, yield a modular proof of cut elimination.
277 citations
TL;DR: A systematic set of cut-free axiomatisations for all the basic normal modal logics formed by some combination the axioms d, t, b, 4, 5, which stay very close to Gentzen’s sequent calculus.
Abstract: We see a systematic set of cut-free axiomatisations for all the basic normal modal logics formed by some combination the axioms d, t, b, 4, 5. They employ a form of deep inference but otherwise stay very close to Gentzen’s sequent calculus, in particular they enjoy a subformula property in the literal sense. No semantic notions are used inside the proof systems, in particular there is no use of labels. All their rules are invertible and the rules cut, weakening and contraction are admissible. All systems admit a straightforward terminating proof search procedure as well as a syntactic cut elimination procedure.
212 citations
Proceedings Article•
1 Jan 2006
TL;DR: In this article, a set of cut-free axiomatisations for all the basic normal modal logics formed by some combination of the axioms d, t, b, 4, 5 are presented.
Abstract: We see a systematic set of cut-free axiomatisations for all the basic normal modal logics formed by some combination the axioms d, t, b, 4, 5. They employ a form of deep inference but otherwise stay very close to Gentzen’s sequent calculus, in particular they enjoy a subformula property in the literal sense. No semantic notions are used inside the proof systems, in particular there is no use of labels. All their rules are invertible and the rules cut, weakening and contraction are admissible. All systems admit a straightforward terminating proof search procedure as well as a syntactic cut elimination procedure.
144 citations
3 Dec 2001
TL;DR: The calculus of structures is a framework for specifying logical systems, which is similar to the one-sided sequent calculus but more general, and a system of inference rules for propositional classical logic is presented, with the main novelty that all the rules are local.
Abstract: The calculus of structures is a framework for specifying logical systems, which is similar to the one-sided sequent calculus but more general. We present a system of inference rules for propositional classical logic in this new framework and prove cut elimination for it. The system enjoys a decomposition theorem for derivations that is not available in the sequent calculus. The main novelty of our system is that all the rules are local: contraction, in particular, is reduced to atomic form. This should be interesting for distributed proof-search and also for complexity theory, since the computational cost of applying each rule is bounded.
142 citations
TL;DR: Certain enhanced systems of sequent calculi for tense logics are introduced, and their completeness with respect to Kripke-type semantics is proved.
Abstract: We introduce certain enhanced systems of sequent calculi for tense logics, and prove their completeness with respect to Kripke-type semantics.
139 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 7 |
| 2020 | 9 |
| 2019 | 12 |
| 2018 | 7 |
| 2017 | 10 |
| 2016 | 4 |