{"title":"Axiomatizing a Real-Valued Modal Logic","authors":"Denisa Diaconescu, G. Metcalfe, Laura Schnüriger","doi":"10.7892/BORIS.88009","DOIUrl":"https://doi.org/10.7892/BORIS.88009","url":null,"abstract":"A many-valued modal logic is introduced that combines the standard (crisp) Kripke frame semantics of the modal logic K with connectives interpreted locally as abelian group operations over the real numbers. A labelled tableau system and a sequent calculus admitting cut elimination are then defined for this logic and used to establish completeness of an axiomatic extension of the multiplicative fragment of abelian logic.","PeriodicalId":129696,"journal":{"name":"Advances in Modal Logic","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121898287","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Hennessy-Milner Property for Many-Valued Modal Logics","authors":"M. Marti, G. Metcalfe","doi":"10.7892/BORIS.59756","DOIUrl":"https://doi.org/10.7892/BORIS.59756","url":null,"abstract":"A Hennessy-Milner property, relating modal equivalence and bisimulations, is defined \u0000for many-valued modal logics that combine a local semantics based on a complete MTL-chain (a linearly ordered commutative integral residuated lattice) with crisp \u0000Kripke frames. A necessary and sufficient algebraic condition is then provided for the \u0000class of image-finite models of these logics to admit the Hennessy-Milner property. \u0000Complete characterizations are obtained in the case of many-valued modal logics \u0000based on BL-chains (divisible MTL-chains) that are finite or have universe [0,1], \u0000including crisp Lukasiewicz, Godel, and product modal logics.","PeriodicalId":129696,"journal":{"name":"Advances in Modal Logic","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127438930","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Complexity of Reasoning with Boolean Modal Logics","authors":"C. Lutz, U. Sattler","doi":"10.1142/9789812776471_0018","DOIUrl":"https://doi.org/10.1142/9789812776471_0018","url":null,"abstract":"Boolean Modal Logics extend multi-modal K by allowing the use of boolean operators to define complex relation terms. In this paper, we investigate the complexity of reasoning with various such logics. The main results are that (1) adding negation of modal parameters to K makes reasoning ExpTime-complete, which is shown by using an automata-theoretic approach, and that (2) adding atomic negation and conjunction to K even yields a NExpTime- complete logic, which is shown by a reduction of a variant of the domino problem. The last result is relativized by the fact that it depends on an infinite number of modal parameters to be available. If the number of modal parameters is bounded, full Boolean Modal Logic becomes ExpTime-complete. This is shown by a reduction to K enriched with the universal modality.","PeriodicalId":129696,"journal":{"name":"Advances in Modal Logic","volume":"68 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115946814","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Computing Minimal EL-unifiers is Hard","authors":"F. Baader, Stefan Borgwardt, Barbara Morawska","doi":"10.25368/2022.187","DOIUrl":"https://doi.org/10.25368/2022.187","url":null,"abstract":"Unification has been investigated both in modal logics and in description logics, albeit with different motivations. In description logics, unification can be used to detect redundancies in ontologies. In this context, it is not sufficient to decide unifiability, one must also compute appropriate unifiers and present them to the user. For the description logic EL, which is used to define several large biomedical ontologies, deciding unifiability is an NP-complete problem. It is known that every solvable EL-unification problem has a minimal unifier, and that every minimal unifier is a local unifier. Existing unification algorithms for EL compute all minimal unifiers, but additionally (all or some) non-minimal local unifiers. Computing only the minimal unifiers would be better since there are considerably less minimal unifiers than local ones, and their size is usually also quite small. In this paper we investigate the question whether the known algorithms for EL-unification can be modified such that they compute exactly the minimal unifiers without changing the complexity and the basic nature of the algorithms. Basically, the answer we give to this question is negative.","PeriodicalId":129696,"journal":{"name":"Advances in Modal Logic","volume":"108 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130710545","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A canonical model construction for intuitionistic distributed knowledge","authors":"Gerhard Jäger, M. Marti","doi":"10.7892/BORIS.94867","DOIUrl":"https://doi.org/10.7892/BORIS.94867","url":null,"abstract":"Intuitionistic epistemic logic is an active research field. However, so far no consensus has been reached what the correct form of intuitionistic epistemic logic is and more technical and conceptual work is needed to obtain a better understanding. This article tries to make a small technical contribution to this enterprise. Roughly speaking, a proposition is distributed knowledge among a group of agents if it follows from their combined knowledge. We are interested in formalizing intuitionistic distributed knowledge. Our focus is on two theories IDK and IDT, presented as Hilbert-style systems, and the proof of the completeness of these theories; their correctness is obvious. Intuitionistic distributed knowledge is semantically treated following the standard \u0000lines of intuitionistic modal logic. Motivated by an approach due to Fagin, Halpern, and Vardi, though significantly simplified for the treatment of IDK and IDT, we show completeness of these systems via a canonical model construction.","PeriodicalId":129696,"journal":{"name":"Advances in Modal Logic","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131332290","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Algorithmic Correspondence Theory for Substructural Categorial Logic","authors":"M. Finger","doi":"10.1142/9789812776471_0009","DOIUrl":"https://doi.org/10.1142/9789812776471_0009","url":null,"abstract":"","PeriodicalId":129696,"journal":{"name":"Advances in Modal Logic","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117191425","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"S5 × S5 × S5 Lacks the Finite Model Property","authors":"Á. Kurucz","doi":"10.1142/9789812776471_0017","DOIUrl":"https://doi.org/10.1142/9789812776471_0017","url":null,"abstract":"It follows from algebraic results of Maddux that every multi-modal logic L such that [S5, S5,. .. , S5] ⊆ L ⊆ S5 n is undecidable, whenever n ≥ 3. This implies that the product logic S5 × S5 × S5 does not have the product finite model property. Here we answer a question of Gabbay and Shehtman by showing that S5 × S5 × S5 also lacks the 'real' finite model property (fmp). We prove that every logic L from the above interval lacks the fmp. (In algebraic setting: If V is a variety of n-dimensional diagonal-free cylindric algebras which contains all the representables then V does not have the finite algebra property.)","PeriodicalId":129696,"journal":{"name":"Advances in Modal Logic","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127068089","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Bimodal Logics for Reasoning About Continuous Dynamics","authors":"J. Davoren, R. Goré","doi":"10.1142/9789812776471_0006","DOIUrl":"https://doi.org/10.1142/9789812776471_0006","url":null,"abstract":"We study a propositional bimodal logic consisting of two S4 modalities and [a], together with the interaction axiom scheme h ai ' → h ai '. In the intended semantics, the plain is given the McKinsey-Tarski interpretation as the interior operator of a topology, while the labelled [a] is given the standard Kripke semantics using a reflexive and transitive binary relation Ra. The interaction axiom expresses the property that the Ra relation is lower semi-continuous with respect to the topology. The class of topological Kripke frames axiomatised by the logic includes all frames over Euclidean space where Ra is the positive flow relation of a differential equation. We establish the completeness of the axiomatisation with respect to the intended class of topological Kripke frames, and investigate tableau calculi for the logic, although decidability is still an open question.","PeriodicalId":129696,"journal":{"name":"Advances in Modal Logic","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130664091","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Belief, Names, and Modes of Presentation","authors":"Ruili Ye, M. Fitting","doi":"10.1142/9789812776471_0021","DOIUrl":"https://doi.org/10.1142/9789812776471_0021","url":null,"abstract":"","PeriodicalId":129696,"journal":{"name":"Advances in Modal Logic","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116624982","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Towards a Many-Dimensional Modal Logic for Semantic Processing","authors":"T. Fernando","doi":"10.1142/9789812776471_0008","DOIUrl":"https://doi.org/10.1142/9789812776471_0008","url":null,"abstract":"Notions of context for natural language interpretation are factored in terms of three processes: translation, entailment and attunement. The processes are linked by accessibility relations of the kind studied in many-dimensional modal logic, modulo complications from constraints between translation and entailment (violations in which may trigger re-attunement) and from refinement and underspecification.","PeriodicalId":129696,"journal":{"name":"Advances in Modal Logic","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128248666","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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