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A Constraint Sequent Calculus for First-Order Logic with Linear Integer Arithmetic [chapter]

Philipp Rümmer
<span title="">2008</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
As a possible answer, we introduce a sequent calculus that combines ideas from free-variable constraint tableaux with the Omega quantifier elimination procedure.  ...  From the former method, our calculus inherits the concept of generating constraints that describe valuations of free variables for which a formula is satisfied.  ...  with unknown constraint, a proof procedure will first apply analytic rules to the antecedent and succedent and build a proof tree, similarly as in a normal Gentzen-style sequent calculus.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-89439-1_20">doi:10.1007/978-3-540-89439-1_20</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/faq7ytyz4jgwtdkx6sdjovqjse">fatcat:faq7ytyz4jgwtdkx6sdjovqjse</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170829004508/http://www.cse.chalmers.se/~philipp/constrainedSequents.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/cd/e5/cde5cae4ff4a43e10f41ea078abdd788001542e3.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-89439-1_20"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

A constraint sequent calculus

J.-L. Lassez, K. McAloon
<i title="IEEE Comput. Soc. Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/cnybbxuptncftdgxtodn5edz7m" style="color: black;">[1990] Proceedings. Fifth Annual IEEE Symposium on Logic in Computer Science</a> </i> &nbsp;
As a consequence, completeness theorems involving positive and negative constraints can be proven in a general setting for constraint propagation.  ...  Constraints play an important role in programming languages and in OR and AI work.  ...  If a constraint sequent calculus is admissible, admits a negatable cover and has a canonical form map on positive constraint sets which preserves negatable constraints then the calculus is called regular  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/lics.1990.113733">doi:10.1109/lics.1990.113733</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/lics/LassezM90.html">dblp:conf/lics/LassezM90</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2ahice2775hsdivzqmzcutfu4y">fatcat:2ahice2775hsdivzqmzcutfu4y</a> </span>
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Sequoia: A Playground for Logicians [chapter]

Giselle Reis, Zan Naeem, Mohammed Hashim
<span title="">2020</span> <i title="Springer International Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
Sequent calculus is a pervasive technique for studying logics and their properties due to the regularity of rules, proofs, and metaproperty proofs across logics.  ...  Sequoia is a web-based application for specifying sequent calculi and performing basic reasoning about them.  ...  Given a tree, a constraint list, and a set of rules, a selected rule can be applied to an open sequent in the tree to produce a new tree and constraints with the appropriate updates.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-030-51054-1_32">doi:10.1007/978-3-030-51054-1_32</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jjpuhsits5d6vgluspitladqrm">fatcat:jjpuhsits5d6vgluspitladqrm</a> </span>
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A sequent calculus for skeptical Default Logic [chapter]

P. A. Bonatti, N. Olivetti
<span title="">1997</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
In this paper, we contribute to the proof-theory of Reiter's Default Logic by introducing a sequent calculus for skeptical reasoning.  ...  The main features of this calculus are simplicity and regularity, and the fact that proofs can be surprisingly concise and, in many cases, involve only a small part of the default theory.  ...  Tiomkin 39] introduced an anti-sequent calculus, complete w.r.t. nite models, that can be used in place of the anti-sequent calculus adopted here.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/bfb0027408">doi:10.1007/bfb0027408</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/n2l37vevs5d4xk5dfukmzkdmfm">fatcat:n2l37vevs5d4xk5dfukmzkdmfm</a> </span>
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Saturation Up to Redundancy for Tableau and Sequent Calculi [chapter]

Martin Giese
<span title="">2006</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
., which is not easily done with a standard Hintikka-style completeness proof.  ...  We discuss an adaptation of the technique of saturation up to redundancy, as introduced by Bachmair and Ganzinger [1], to tableau and sequent calculi for classical first-order logic.  ...  A tableau for a semi-sequent calculus is a tree where each node is labeled with a semi-sequent.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/11916277_13">doi:10.1007/11916277_13</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hikznevwxjbphcerkwmk4yovxi">fatcat:hikznevwxjbphcerkwmk4yovxi</a> </span>
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Page 220 of Computational Linguistics Vol. 25, Issue 2 [page]

<span title="">1999</span> <i title="MIT Press Journals"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_computational-linguistics" style="color: black;">Computational Linguistics </a> </i> &nbsp;
Computational Linguistics Volume 25, Number 2 proofnets: for each proof of a sequent | I in the one-sided sequent calculus for mullti- plicative linear logic, there is a corresponding proofnet whose conclusions  ...  To every proof z of a sequent + [ in the one-sided sequent calculus for multiplicative noncommutative linear logic, we can associate (by induction on the construction of the proof 7) a noncommutative proofnet  ... 
<span class="external-identifiers"> </span>
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Proof complexity of propositional default logic

Olaf Beyersdorff, Arne Meier, Sebastian Müller, Michael Thomas, Heribert Vollmer
<span title="2011-07-03">2011</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/3egevcnserbbni4tcigsztdici" style="color: black;">Archive for Mathematical Logic</a> </i> &nbsp;
Definition A credulous default sequent Σ; Γ| ∼∆ consists of a set Σ of provability constraints, a default theory Γ, and a set ∆ of propositional sentences.  ...  The Credulous Default Calculus Default Logic Results Proof Systems and Bounds for Default Logic Summary Definition A provability constraint is of the form Lα or ¬Lα with a formula α.  ...  The Residual Calculus Default Logic Results Proof Systems and Bounds for Default Logic Summary Definition A residual rule is a default rule α γ without justification.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00153-011-0245-8">doi:10.1007/s00153-011-0245-8</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pzkiv6j53rgy7erqomv75t5yfm">fatcat:pzkiv6j53rgy7erqomv75t5yfm</a> </span>
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A labelled sequent calculus for BBI: proof theory and proof search

Zhé Hóu, Rajeev Goré, Alwen Tiu
<span title="2015-06-09">2015</span> <i title="Oxford University Press (OUP)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/crzmi3qeiramtlvcrfycib3qg4" style="color: black;">Journal of Logic and Computation</a> </i> &nbsp;
We present a labelled sequent calculus for Boolean BI (BBI), a classical variant of the logic of Bunched Implication. The calculus is simple, sound, complete, and enjoys cut-elimination.  ...  Based on this, we demonstrate a free variable calculus that deals with the structural rules lazily in a constraint system.  ...  Oddly, the formula ¬( * ∧ A ∧ (B * ¬(C− * ( * → A)))), which is valid in BBI ND , is very hard to prove in the display calculus and Park et al.'s method. We ran this formula using Park et al.'  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1093/logcom/exv033">doi:10.1093/logcom/exv033</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hqj7fskkrravhn3b4spgqk3acm">fatcat:hqj7fskkrravhn3b4spgqk3acm</a> </span>
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A Labelled Sequent Calculus for BBI: Proof Theory and Proof Search [chapter]

Zhé Hóu, Alwen Tiu, Rajeev Goré
<span title="">2013</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
We present a labelled sequent calculus for Boolean BI (BBI), a classical variant of the logic of Bunched Implication. The calculus is simple, sound, complete, and enjoys cut-elimination.  ...  Based on this, we demonstrate a free variable calculus that deals with the structural rules lazily in a constraint system.  ...  Oddly, the formula ¬( * ∧ A ∧ (B * ¬(C− * ( * → A)))), which is valid in BBI ND , is very hard to prove in the display calculus and Park et al.'s method. We ran this formula using Park et al.'  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-40537-2_16">doi:10.1007/978-3-642-40537-2_16</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qog3quiafjbd3mmye666gwa6bq">fatcat:qog3quiafjbd3mmye666gwa6bq</a> </span>
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Proof Complexity of Propositional Default Logic [chapter]

Olaf Beyersdorff, Arne Meier, Sebastian Müller, Michael Thomas, Heribert Vollmer
<span title="">2010</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
In this paper we examine these calculi from a proof-complexity perspective.  ...  In 2002, Bonatti and Olivetti introduced several sequent calculi for credulous and skeptical reasoning in propositional default logic.  ...  Acknowledgement The first author wishes to thank Neil Thapen for interesting discussions on the topic of this paper during a research visit to Prague.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-14186-7_5">doi:10.1007/978-3-642-14186-7_5</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/m3j2j4evynb33ljd25w4ot234e">fatcat:m3j2j4evynb33ljd25w4ot234e</a> </span>
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A sequent calculus for circumscription [chapter]

P. A. Bonatti, N. Olivetti
<span title="">1997</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
In this paper, we introduce a sequent calculus CIRC for propositional Circumscription.  ...  Among the novelties of the calculus, we mention that CIRC is analytic and comprises an axiomatic rejection method, which allows for a fully detailed formalization of the nonmonotonic aspects of inference  ...  The calculus makes use of classical sequents and antisequents, and special sequents of the form: ; ?`P ; where ? and are sets of formulas, and is a set of atoms called constraints.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/bfb0028009">doi:10.1007/bfb0028009</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5zwp67y2kfckxb7w74wmfk4kni">fatcat:5zwp67y2kfckxb7w74wmfk4kni</a> </span>
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A Hybrid Linear Logic for Constrained Transition Systems [article]

Joelle Despeyroux
<span title="2016-03-08">2016</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The logic has a focused cut-free sequent calculus that can be used to internalize the rules of particular constrained transition systems; we illustrate this with an adequate encoding of the synchronous  ...  We propose a general modal extension of intuitionistic linear logic where logical truth is indexed by constraints and hybrid connectives combine constraint reasoning with logical reasoning.  ...  Thanks also go to Nicolas Champagnat, Luc Pronzato and André Hirschowitz who helped us understand the algebraic nature of stochastic constraints.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1603.02641v1">arXiv:1603.02641v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ik7kx7jz5zc7zm3bmejbaylwdy">fatcat:ik7kx7jz5zc7zm3bmejbaylwdy</a> </span>
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A Hybrid Linear Logic for Constrained Transition Systems

Joëlle Despeyroux, Kaustuv Chaudhuri, Marc Herbstritt
<span title="2014-07-15">2014</span> <i > <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/bg7eff2ccngt5gat6bipkw45b4" style="color: black;">Types for Proofs and Programs</a> </i> &nbsp;
a focused cut-free sequent calculus that can be used to internalize the rules of particular constrained transition systems; we illustrate this with an adequate encoding of the synchronous stochastic pi-calculus  ...  We propose a general modal extension of intuitionistic linear logic where logical truth is indexed by constraints and hybrid connectives combine constraint reasoning with logical reasoning.The logic has  ...  Thanks also go to Nicolas Champagnat, Luc Pronzato and André Hirschowitz who helped us understand the algebraic nature of stochastic constraints.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/lipics.types.2013.150">doi:10.4230/lipics.types.2013.150</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/types/DespeyrouxC13.html">dblp:conf/types/DespeyrouxC13</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/t7wm6k4j6zbrzkzff7sdqeckqe">fatcat:t7wm6k4j6zbrzkzff7sdqeckqe</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20181101225958/https://hal.inria.fr/hal-01285039/document" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/e1/ac/e1ac42f8f079a3cd40da25efa58c93f83127f3f8.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/lipics.types.2013.150"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Parsing as natural deduction

Esther König
<span title="">1989</span> <i title="Association for Computational Linguistics"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5n6volmnonf5tn6xputi5f2t3e" style="color: black;">Proceedings of the 27th annual meeting on Association for Computational Linguistics -</a> </i> &nbsp;
Lambek Calculus (LC) constitutes an example for a natural deduction 1 style parsing method.  ...  The original Lambek Calculus, when it is used as a parser/theorem prover, has the undesirable property of allowing for the derivation of more than one proof for a reading of a sentence, in the general  ...  Acknowledgements The research reported in this paper is supported by the LILOG project, and a doctoral fellowship, both from IBM Deutschland GmbH, and by the Esprit Basic Research Action Project 3175 (  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3115/981623.981656">doi:10.3115/981623.981656</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/acl/Konig89.html">dblp:conf/acl/Konig89</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/umppk7m3nzaj7gzjsflniojkgu">fatcat:umppk7m3nzaj7gzjsflniojkgu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170922060726/http://www.aclweb.org/anthology/P89-1033" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/3f/bf/3fbf3ac92afd7cb1c7a653cedcfbeebca970ca31.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3115/981623.981656"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Proof-search in intuitionistic logic based on constraint satisfaction [chapter]

Andrei Voronkov
<span title="">1996</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
We characterize provability in intuitionistic predicate logic in terms of derivation skeletons and constraints and study the problem of instantiations of a skeleton to valid derivations.  ...  We prove that for two di erent notions of a skeleton the problem is respectively polynomial and NP-complete.  ...  Calculus LJ c The calculus LJ c derives constrained sequents: De nition 3. (Constrained sequent) A constrained sequent is an expression S C where S is a sequent and C is a constraint.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-61208-4_20">doi:10.1007/3-540-61208-4_20</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2nsctsj5vfd3jfmm5wqeqyicki">fatcat:2nsctsj5vfd3jfmm5wqeqyicki</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190221002354/http://pdfs.semanticscholar.org/2bab/4ffb9b87bbef63dcf367364b16d57afb87c3.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/2b/ab/2bab4ffb9b87bbef63dcf367364b16d57afb87c3.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-61208-4_20"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>
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