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Model Theory and Proof Theory of Coalgebraic Predicate Logic [article]

Tadeusz Litak, Dirk Pattinson, Katsuhiko Sano, Lutz Schröder
<span title="2018-03-03">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Basic model-theoretic constructions and results, in particular ultraproducts, obtain for the two classes that allow completeness---and in some cases beyond that.  ...  We discuss axiomatization and completeness results for several natural classes of such logics. Moreover, we show that an entirely general completeness result is not possible.  ...  We are also grateful to the editors of the Festschrift honoring Jiří Adámek for making us return to this material, and to Jiří himself for decades of broadening the frontiers of category theory and coalgebra  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1701.03773v3">arXiv:1701.03773v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/zu2zqndv4rb67e4wtsdyotylem">fatcat:zu2zqndv4rb67e4wtsdyotylem</a> </span>
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A logical framework combining model and proof theory

FLORIAN RABE
<span title="2013-03-01">2013</span> <i title="Cambridge University Press (CUP)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/jdpukxfslnfmradqb65llq43na" style="color: black;">Mathematical Structures in Computer Science</a> </i> &nbsp;
In particular, our framework takes a balanced approach between model theory and proof theory and permits the representation of logics in a way that comprises all major ingredients of a logic: syntax, models  ...  , satisfaction, judgments, and proofs.  ...  proofs and variable binding as expressions.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1017/s0960129512000424">doi:10.1017/s0960129512000424</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/b5trekjxdbb6bpickgqtzw4fiu">fatcat:b5trekjxdbb6bpickgqtzw4fiu</a> </span>
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Sabotage Modal Logic: Some Model and Proof Theoretic Aspects [chapter]

Guillaume Aucher, Johan van Benthem, Davide Grossi
<span title="">2015</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 investigate some model and proof theoretic aspects of sabotage modal logic.  ...  The second contribution is to provide a sound and complete tableau method for sabotage modal logic.  ...  For this research Davide Grossi was supported in part by NWO (VENI grant 639.021.816), and in part by EPSRC (grant EP/M015815/1).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-662-48561-3_1">doi:10.1007/978-3-662-48561-3_1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/y4y5hac6vffilh2ua3cu6zte4e">fatcat:y4y5hac6vffilh2ua3cu6zte4e</a> </span>
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LLF_ P: a logical framework for modeling external evidence, side conditions, and proof irrelevance using monads [article]

Furio Honsell, Luigi Liquori, Petar Maksimovic, Ivan Scagnetto
<span title="2017-06-30">2017</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We discuss encodings in LLF_ P of call-by-value λ-calculi, Hoare's Logic, and Fitch-Prawitz Naive Set Theory.  ...  These monads capture various possible proof attitudes in establishing the judgment of the object logic encoded by an LF type.  ...  Namely such variables can λ-bind only objects and Π-bind only types, i.e. terms of kind Type. In particular families are never λ-abstracted and kinds are never Π-bound by such variables.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1702.07214v2">arXiv:1702.07214v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6p3l2yfo2rey3ogapurqax7oaq">fatcat:6p3l2yfo2rey3ogapurqax7oaq</a> </span>
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Proof Search and Counter Model of Positive Minimal Predicate Logic

Tao Xue, Qichao Xuan
<span title="">2008</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/uy5mv2ncw5eahkdx47hkrglxmm" style="color: black;">Electronical Notes in Theoretical Computer Science</a> </i> &nbsp;
The algorithm returns a deduction tree, and hence a proof, when the formula is provable, and a counter-model will be constructed when the formula is unprovable.  ...  This paper presents an algorithm of proof search for positive formulas in minimal predicate logic. It is based on the LJB deduction system introduced in[2].  ...  Acknowledgement The authors thank Professor Jiang Ying a lot for many helpful advices for the subject, and thank the anonymous referees whose suggestions have helped improving the paper a lot.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.entcs.2008.04.055">doi:10.1016/j.entcs.2008.04.055</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ozcsngimnbdllmrlwiigeuomoy">fatcat:ozcsngimnbdllmrlwiigeuomoy</a> </span>
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Binding modalities

Sergei N. Artemov, Tatiana Yavorskaya (Sidon)
<span title="2013-10-07">2013</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;
FOS4 * extends first-order S4 and is the natural forgetful projection of the first-order logic of proofs FOLP.  ...  We introduce the first-order logic FOS4 * in which modalities can bind individual variables and, in particular, can directly represent both de re and de dicto modalities.  ...  Furthermore, the proof of Lemma 2 relies on transitivity axiom B2 and hence does not work for logics without transitivity, e.g., binding modalities versions of first-order logics K or T which, however,  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1093/logcom/ext017">doi:10.1093/logcom/ext017</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/tvm4izts2vbfnmz3bhd6ocm2ji">fatcat:tvm4izts2vbfnmz3bhd6ocm2ji</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190217145723/http://pdfs.semanticscholar.org/05d5/9ba283103dfabd3902e815a5cbc27fbcf6a9.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/05/d5/05d59ba283103dfabd3902e815a5cbc27fbcf6a9.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1093/logcom/ext017"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> oup.com </button> </a>

Binding in Nominal Equational Logic

Ranald Clouston
<span title="">2010</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/uy5mv2ncw5eahkdx47hkrglxmm" style="color: black;">Electronical Notes in Theoretical Computer Science</a> </i> &nbsp;
Clouston and Pitts's Nominal Equational Logic presented a formalism for this style of reasoning in which support for name binding was implicit.  ...  This paper extends this logic to offer explicit support for binding and then demonstrates that such an extension does not in fact add expressivity.  ...  Suppose that Σ is a binding NEL-signature and that M is a T (Σ)- Proof.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.entcs.2010.08.016">doi:10.1016/j.entcs.2010.08.016</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lfn3t3zmbzgdtna6m6pkz4z464">fatcat:lfn3t3zmbzgdtna6m6pkz4z464</a> </span>
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Correctness Proofs of Distributed Termination Algorithms [chapter]

Krzysztof R. Apt
<span title="">1985</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/g52a5nuvcvf7bi2ewpblkwh6qa" style="color: black;">Logics and Models of Concurrent Systems</a> </i> &nbsp;
A very simple proof method is proposed and applied to show correctness of a solution to the problem.  ...  It allows us to reason about liveness properties of temporal logic (see, e.g., Manna and Pnueli [12]) using a new notion of weak total correctness. J is a global invariant of S.  ...  Delporte-Gallet and A. Pnueli for their interesting and helpful discussions on the subject of this paper. Also, we are grateful to all three referees for their detailed reports.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-82453-1_6">doi:10.1007/978-3-642-82453-1_6</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/nato/Apt84.html">dblp:conf/nato/Apt84</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ij3u5rbxxjco3b73sn5rqkpeom">fatcat:ij3u5rbxxjco3b73sn5rqkpeom</a> </span>
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Binding logics in art

Sílvia Pinto, Moisés de Lemos Martins
<span title="2017-06-21">2017</span> <i title="Centro de Estudos de Comunicacao e Sociedade, Universidade Minho"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ppf25vy6fvba5okemzccwrp5ju" style="color: black;">Revista Comunicação e Sociedade</a> </i> &nbsp;
However, the thesis "Binding Logics in Art", as such, remains original and unpublished.  ...  From a historical perspective, we will attempt to show the evolution of art in three main binding logics: art as a magical activity (also in relation to index logic); art as mimesis; and art as language  ...  the public, contain the signs of a rupture and renewal with regard to a set of bindings to the other, to life, death, history or time, which we will call "binding logics".  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.17231/comsoc.31(2017).2617">doi:10.17231/comsoc.31(2017).2617</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/e73kdbsttfg37iuv6caprkxlre">fatcat:e73kdbsttfg37iuv6caprkxlre</a> </span>
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Variable Binding Term Operators

John Corcoran, William Hatcher, John Herring
<span title="">1972</span> <i title="Wiley"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/i3o5mtpiobamthfymhgizjecem" style="color: black;">Mathematical Logic Quarterly</a> </i> &nbsp;
The soundness and completeness proofs for logic with identity and vbtos given below exploit the analogy.  ...  The proof of completeness of logic wit,h identity can be obtained from completeness of logic without identity by showing that every model of the theory got by taking the added schemes as proper axioms  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1002/malq.19720181202">doi:10.1002/malq.19720181202</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qn24q3dknbcm3nngbkpqqqxdom">fatcat:qn24q3dknbcm3nngbkpqqqxdom</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20171009163127/https://philpapers.org/archive/CORVBT.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/0b/03/0b03ba1677b98a562826ca7730b7181e87f18689.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1002/malq.19720181202"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> wiley.com </button> </a>

Program logic without binding is decidable

V. R. Pratt
<span title="">1981</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2qaxtqe2rfgjnfefqcokcnzelq" style="color: black;">Proceedings of the 8th ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL &#39;81</a> </i> &nbsp;
When the "binding mechanisms" of assignment, quantification, and  ...  ., and Pnuefi, A., Finite Models for Deterministic Samet, and R.  ...  to the current value of e, the quantifier 3X can be thought of as nondctenninistically binding x to an arbitrarily chosen value, and the procedure dctinition proc fo =~can be thought of as binding f to  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/567532.567550">doi:10.1145/567532.567550</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/popl/Pratt81.html">dblp:conf/popl/Pratt81</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lieamm6q3fdwtcey4ihmqqpuha">fatcat:lieamm6q3fdwtcey4ihmqqpuha</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190217032713/https://static.aminer.org/pdf/20170130/pdfs/popl/lgm9oudut42kaethsqyzl8f5mqzdvwxi.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/38/ae/38ae1edb30eea38485a272607a01f2b4da514cb0.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/567532.567550"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

Nominal (Universal) Algebra: Equational Logic with Names and Binding

M. J. Gabbay, A. Mathijssen
<span title="2009-07-05">2009</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 investigate proof-theoretical properties, we provide a sound and complete semantics in nominal sets, and we compare and contrast our design decisions with other possibilities leading to similar systems  ...  In this paper we make the case for extending the logic of equality with meta-variables and capture-avoidance constraints, to obtain 'nominal algebra'.  ...  Modulo this caveat it seems to us that nominal algebra, compared with nominal equational logic, is simpler and more compact, and that it may offer easier syntax, semantics, and proofs for mathematical  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1093/logcom/exp033">doi:10.1093/logcom/exp033</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/r3baopstzzdelcm3ieus2itvoe">fatcat:r3baopstzzdelcm3ieus2itvoe</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20160913195100/http://www.gabbay.org.uk/papers/nomuae.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/2c/ec/2cecfcfd89db6d6c046736719104e571f927288e.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1093/logcom/exp033"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> oup.com </button> </a>

Combining Proof and Model-checking to Validate Reconfigurable Architectures

Arnaud Lanoix, Julien Dormoy, Olga Kouchnarenko
<span title="">2011</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/uy5mv2ncw5eahkdx47hkrglxmm" style="color: black;">Electronical Notes in Theoretical Computer Science</a> </i> &nbsp;
As architectural constraints involve first-order formulae, and a behavioural semantics of reconfigurations gives rise to infinite state systems, we propose to associate proof and model-checking within  ...  Second, given linear temporal logic formulae expressing the desirable dynamic behaviour of the system, we validate reconfigurable system architectures by using bounded model-checking tools supporting the  ...  Proof-based Approach: the B Method B is a formal software development method used to model systems and to reason about their development [1] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.entcs.2011.11.011">doi:10.1016/j.entcs.2011.11.011</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ekqt54ds7nczxfs7lha347yhze">fatcat:ekqt54ds7nczxfs7lha347yhze</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170927032703/http://publisher-connector.core.ac.uk/resourcesync/data/elsevier/pdf/4a8/aHR0cDovL2FwaS5lbHNldmllci5jb20vY29udGVudC9hcnRpY2xlL3BpaS9zMTU3MTA2NjExMTAwMTYwNQ%3D%3D.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/6a/f6/6af6ed55149da2b0f2639538b7c8628d701bd2ad.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.entcs.2011.11.011"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> elsevier.com </button> </a>

Undecidability of a Very Simple Modal Logic with Binding [article]

Guillaume Hoffmann
<span title="2015-08-14">2015</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
This work enriches the series of existing results of undecidability of modal logics with binders, which started with Hybrid Logics and continued with Memory Logics.  ...  We show undecidability of the satisfiability problem of what is arguably the simplest non-sub-Boolean modal logic with an implicit notion of binding.  ...  Undecidability of B( r , k )-sat We adapt the proof of [8] , where the tiling problem [11] is encoded into a description logic with the down-arrow binder, one nominal, and one relation.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1508.03630v1">arXiv:1508.03630v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/p5ndbpkhpvfmrnzhyz4ozd4tci">fatcat:p5ndbpkhpvfmrnzhyz4ozd4tci</a> </span>
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Focusing on Binding and Computation

Daniel R. Licata, Noam Zeilberger, Robert Harper
<span title="">2008</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/zw5e5duxvbdsthglbdpw3xoqae" style="color: black;">Logic in Computer Science</a> </i> &nbsp;
Variable binding is a prevalent feature of the syntax and proof theory of many logical systems.  ...  We present this logic as a focused sequent calculus in which the definitions of atoms are open-ended, and can be varied by means of logical connectives.  ...  Acknowledgements We thank Frank Pfenning, Karl Crary, Jason Reed, Rob Simmons, Neel Krishnaswami, William Lovas, Arbob Ahmad, Brigitte Pientka, and Ken Shan for discussions about the work presented here  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/lics.2008.48">doi:10.1109/lics.2008.48</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/lics/LicataZH08.html">dblp:conf/lics/LicataZH08</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/x5dyuxrurrgdjepcat5k2wdiee">fatcat:x5dyuxrurrgdjepcat5k2wdiee</a> </span>
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