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Deriving Inverse Operators for Modal Logic [chapter]

Michell Guzmán, Salim Perchy, Camilo Rueda, Frank D. Valencia
<span title="">2016</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;
We shall use spatial constraint systems to give an abstract characterization of the notion of normality in modal logic and to derive right inverse/reverse operators for modal languages.  ...  We shall apply our results to existing modal languages such as the weakest normal modal logic, Hennessy-Milner logic, and linear-time temporal logic.  ...  In previous work [13] the authors derived an inverse modality but only for the specific case of a logic of belief.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-46750-4_13">doi:10.1007/978-3-319-46750-4_13</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/v3arqrxk4fbfhbinp6s2egb2rm">fatcat:v3arqrxk4fbfhbinp6s2egb2rm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190219031626/http://pdfs.semanticscholar.org/179c/683ffc2e752397975fb57581843557c7b038.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/17/9c/179c683ffc2e752397975fb57581843557c7b038.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-319-46750-4_13"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Characterizing right inverses for spatial constraint systems with applications to modal logic

Michell Guzmán, Salim Perchy, Camilo Rueda, Frank D. Valencia
<span title="">2018</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/elaf5sq7lfdxfdejhkqbtz6qoq" style="color: black;">Theoretical Computer Science</a> </i> &nbsp;
In this paper spatial constraint systems are used to give an abstract characterization of the notion of normality in modal logic and to derive right inverse/reverse operators for modal languages.  ...  We shall also be interested in inverse modalities. An operator −1 i is a (right) inverse modality for i if the formula i −1 i φ is logically equivalent to φ.  ...  In particular, we prove that there is no reverse modality for the box operator of the logic system K nor for the always operator of LTL and we also derive existing inverse modalities for the next operator  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.tcs.2018.05.022">doi:10.1016/j.tcs.2018.05.022</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jv3tihyc4zcepja5u5jkyrqddy">fatcat:jv3tihyc4zcepja5u5jkyrqddy</a> </span>
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Proof‐theoretic semantics of natural deduction based on inversion

Ernst Zimmermann
<span title="2021-12-05">2021</span> <i title="Wiley"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/mjsahkkkg5bgzc2w6tnuukxthm" style="color: black;">Theoria</a> </i> &nbsp;
Such an inversion-extending Prawitz' concept of inversion-gives the following theorem: Inversion for two rules of operator q (intro rule, elim rule) exists iff a reduction of a maximum formula for q exists  ...  The article presents a full proof-theoretic semantics for natural deduction based on an extended inversion principle: the elimination rule for an operator q may invert the introduction rule for q, but  ...  Inversion will be defined by pairs of derivations-one pair for every operator.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1111/theo.12375">doi:10.1111/theo.12375</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jznnnobzubdhhnstvtulxc3ery">fatcat:jznnnobzubdhhnstvtulxc3ery</a> </span>
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On the Expressiveness of Spatial Constraint Systems

Michell Guzmán, Frank D. Valencia, Marc Herbstritt
<span title="2016-11-07">2016</span> <i > <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/lp3a6vqizfdbvlneh2os4i6swe" style="color: black;">International Conference on Logic Programming</a> </i> &nbsp;
Then, we present our preliminary results on the representation of modal behaviour by using spatial constraint systems.  ...  In this paper we shall report on our progress using spatial constraint system as an abstract representation of modal and epistemic behaviour.  ...  The formulae of a modal logic are those of propositional logic extended with modal operators.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/oasics.iclp.2016.16">doi:10.4230/oasics.iclp.2016.16</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/iclp/GuzmanV16.html">dblp:conf/iclp/GuzmanV16</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5o5cujxuczga7aemjce3ull3ji">fatcat:5o5cujxuczga7aemjce3ull3ji</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20220120062337/https://drops.dagstuhl.de/opus/volltexte/2016/6746/pdf/OASIcs-ICLP-2016-16.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/6d/1b/6d1b184464a4689481fbb98d60f9acfc8c694316.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/oasics.iclp.2016.16"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Generic Modal Cut Elimination Applied to Conditional Logics

Dirk Pattinson, Lutz Schröder, Martin Giese
<span title="2011-03-17">2011</span> <i title="Logical Methods in Computer Science e.V."> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/c67srop7pbe3nciquoxzy3d6pm" style="color: black;">Logical Methods in Computer Science</a> </i> &nbsp;
We develop a general criterion for cut elimination in sequent calculi for propositional modal logics, which rests on absorption of cut, contraction, weakening and inversion by the purely modal part of  ...  Our criterion applies also to a wide variety of logics outside the realm of normal modal logic. We give extensive example instantiations of our framework to various conditional logics.  ...  For the modal logics K, K4 and T , we fix the modal signature Λ = { } consisting of a single modal operator with arity one.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2168/lmcs-7(1:4)2011">doi:10.2168/lmcs-7(1:4)2011</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/rd74qvbhpzb73j5qdzb6ubqwva">fatcat:rd74qvbhpzb73j5qdzb6ubqwva</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20150910200228/http://www.doc.ic.ac.uk/~dirk/Publications/tableaux2009.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/08/11/0811106ed3f5fef520bff79d053d9b24177c73ed.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2168/lmcs-7(1:4)2011"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Generic Modal Cut Elimination Applied to Conditional Logics [chapter]

Dirk Pattinson, Lutz Schröder
<span title="">2009</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 develop a general criterion for cut elimination in sequent calculi for propositional modal logics, which rests on absorption of cut, contraction, weakening and inversion by the purely modal part of  ...  Our criterion applies also to a wide variety of logics outside the realm of normal modal logic. We give extensive example instantiations of our framework to various conditional logics.  ...  For the modal logics K, K4 and T , we fix the modal signature Λ = { } consisting of a single modal operator with arity one.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-02716-1_21">doi:10.1007/978-3-642-02716-1_21</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2hjph7e7d5f7dirskrhwoajhmi">fatcat:2hjph7e7d5f7dirskrhwoajhmi</a> </span>
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Strong Completeness of Coalgebraic Modal Logics

Lutz Schröder, Dirk Pattinson, Marc Herbstritt
<span title="2009-02-19">2009</span> <i > <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/npfxqbtrtjcmndol3ijtu4shem" style="color: black;">Symposium on Theoretical Aspects of Computer Science</a> </i> &nbsp;
In modal logic, completeness proofs come in two flavours: weak completeness, i.e. derivability of all universally valid formulas, is often proved using finite model constructions, and strong completeness  ...  While the canonical model construction is well understood for Kripke semantics, non-normal modal logics often present subtle difficulties -up to the point that canonical models may fail to exist, as is  ...  The similarity type Λ K of standard modal logic consists of a single unary operator 2. 2.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/lipics.stacs.2009.1855">doi:10.4230/lipics.stacs.2009.1855</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/stacs/SchroderP09.html">dblp:conf/stacs/SchroderP09</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/sv2bh5sdnvgwhpfj7mlfp2rajm">fatcat:sv2bh5sdnvgwhpfj7mlfp2rajm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170705073727/http://users.cecs.anu.edu.au/%7Edpattinson/Publications/stacs2009.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/64/c8/64c8e6429558cb8d11da92a19ae688718a67abda.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4230/lipics.stacs.2009.1855"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Strong Completeness of Coalgebraic Modal Logics [article]

Lutz Schröder, Dirk Pattinson
<span title="2009-02-12">2009</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
While the canonical model construction is well understood for Kripke semantics, non-normal modal logics often present subtle difficulties - up to the point that canonical models may fail to exist, as is  ...  In particular, we prove strong completeness of graded modal logic with finite multiplicities, and of the modal logic of exact probabilities.  ...  The similarity type Λ K of standard modal logic consists of a single unary operator 2. 2.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/0902.2072v1">arXiv:0902.2072v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5u4f747r2rf27ovqzoacaaud2e">fatcat:5u4f747r2rf27ovqzoacaaud2e</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-0902.2072/0902.2072.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> File Archive [PDF] </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/0902.2072v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Page 24 of Mathematical Reviews Vol. , Issue 2002A [page]

<span title="">2002</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Applications to the cardi- nality of countermodels, the inversion of rules and the derivability yf L6b rules are given.” For the entire collection see MR 2001g:03008 } George F.  ...  Logic Comput. 11 (2001), no. 1, 85-106 A satisfiability algorithm in PSpace is given for the graded modal logic GR(Kg).  ... 
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Page 17 of Mathematical Reviews Vol. , Issue 98A [page]

<span title="">1998</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
modal logic systems into resolution-based rules for (complete) modal systems, such as S4.  ...  What is the expressive power of the modal language in terms of first- order logic? 2. Is there a finite derivation system for the set of formulas valid in the given class of multi-dimensional frames?  ... 
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Propositional Logics Complexity and the Sub-Formula Property

Edward Hermann Haeusler
<span title="2015-04-10">2015</span> <i title="Open Publishing Association"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/qzezkwolyvf33pglm2jldjklca" style="color: black;">Electronic Proceedings in Theoretical Computer Science</a> </i> &nbsp;
The sub-formula principle for a deductive system for a logic L states that whenever F1,...  ...  In this work we extend Statman result and show that any propositional (possibly modal) structural logic satisfying a particular formulation of the sub-formula principle is in PSPACE.  ...  We remenber that we call operator any propositional connective or modality. We consider that the logic L has a finite set {c 1 , . . . , c k } of operators.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.4204/eptcs.179.1">doi:10.4204/eptcs.179.1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pnkjfdf7gvcwjnkbuspnpoezzy">fatcat:pnkjfdf7gvcwjnkbuspnpoezzy</a> </span>
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Page 4684 of Mathematical Reviews Vol. , Issue 97H [page]

<span title="">1997</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Against that background, the author investigates re- lational structures for systems with three modal operators: the Priorian P and F and the possibility operator >.  ...  presents a Gentzen sys- tem L;LBQ, which contains *:’ as the main (though not the only) structural connective, the sentential constant ‘t’, truth and fal- sity operators (‘T’ and ‘F’), inversion rules  ... 
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Termination of derivations for minimal tense logic

Regimantas Pliuškevičius
<span title="2009-12-20">2009</span> <i title="Vilnius University Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/fnhdacj4cvhopimej2u4vvaxsy" style="color: black;">Lietuvos matematikos rinkinys</a> </i> &nbsp;
In the paper a method for elimination of loop checking in backward proof search for minimal tense logic Kt is proposed.  ...  To obtain termination of derivation indices and marks are used instead of history.  ...  Since the logic K t can be regarded as some prototype for temporal logic with past operator and for dynamic logic with inverse operator, this logic is interesting to Computer Science and Artificial Intelligence  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.15388/lmr.2009.47">doi:10.15388/lmr.2009.47</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ayxa4ypgn5hota6k4vr7uhebki">fatcat:ayxa4ypgn5hota6k4vr7uhebki</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200526011251/https://www.journals.vu.lt/LMR/article/download/17975/17136" 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/60/30/603028e390dd248943cb42cd3961fb0b3f3f3fd1.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.15388/lmr.2009.47"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Uniform provability realization of intuitionistic logic, modality and λ-terms

Sergei N. Artemov
<span title="">1999</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;
This question turned out to be a part of the more general problem of the intended realization for G odel's modal logic of provability S4 which w as open since 1933.  ...  In addition, LP subsumes the -calculus, modal -calculus, combinatory logic and provides a uniform provability realization of modality a n d -terms.  ...  These operations subsume the simply typed -calculus together with the modal logic S4, a n d t h us the entire modal -calculus ( 4], 18]).  ... 
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An algebraic view of space/belief and extrusion/utterance for concurrency/epistemic logic

Stefan Haar, Salim Perchy, Camilo Rueda, Frank Valencia
<span title="">2015</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/mht6wa2vdbg7dn6n6lws4hpzti" style="color: black;">Proceedings of the 17th International Symposium on Principles and Practice of Declarative Programming - PPDP &#39;15</a> </i> &nbsp;
From a computational point of view the new operators provide for process/information extrusion, a central concept in formalisms for mobile communication.  ...  We enrich spatial constraint systems with operators to specify information and processes moving from a space to another.  ...  Acknowledgements We would like to thank Moreno Falaschi, Thomas Given-Wilson, Michell Guzman, Sophia Knight and Carlos Olarte for their insights and discussions on some preliminary ideas of this work.  ... 
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