Equivalent overdetermined and underdetermined bivalent Belnap–Dunn type semantics for the logics determined by all natural implicative expansions of Kleene’s strong 3-valued matrix with only one designated value are provided.
{"title":"Partiality and its dual in natural implicative expansions of Kleene's strong 3-valued matrix with only one designated value","authors":"G. Robles, J. Méndez","doi":"10.1093/jigpal/jzz021","DOIUrl":"https://doi.org/10.1093/jigpal/jzz021","url":null,"abstract":"\u0000 Equivalent overdetermined and underdetermined bivalent Belnap–Dunn type semantics for the logics determined by all natural implicative expansions of Kleene’s strong 3-valued matrix with only one designated value are provided.","PeriodicalId":304915,"journal":{"name":"Log. J. IGPL","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125263022","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}
Knowledge representation is a central issue for Artificial Intelligence and the Semantic Web. In particular, the problem of representing n-ary relations in RDF-based languages such as RDFS or OWL by no means is an obvious one. With respect to previous attempts, we show why the solutions proposed by the well known W3C Working Group Note on n-ary relations are not satisfactory on several scores. We then present our abstract model for representing n-ary relations as directed labeled graphs, and we show how this model gives rise to a new ontological pattern (parametric pattern) for the representation of such relations in the Semantic Web. To this end, we define PROL (Parametric Relational Ontology Language). PROL is an ontological language designed to express any n-ary fact as a parametric pattern, which turns out to be a special RDF graph. The vocabulary of PROL is defined by a simple RDFS ontology. We argue that the parametric pattern may be particularly beneficial in the context of the Semantic Web, in virtue of its high expressive power, technical simplicity, and faithful meaning rendition. Examples are also provided.
{"title":"Representing n-ary relations in the Semantic Web","authors":"M. Giunti, G. Sergioli, G. Vivanet, Simone Pinna","doi":"10.1093/jigpal/jzz047","DOIUrl":"https://doi.org/10.1093/jigpal/jzz047","url":null,"abstract":"\u0000 Knowledge representation is a central issue for Artificial Intelligence and the Semantic Web. In particular, the problem of representing n-ary relations in RDF-based languages such as RDFS or OWL by no means is an obvious one. With respect to previous attempts, we show why the solutions proposed by the well known W3C Working Group Note on n-ary relations are not satisfactory on several scores. We then present our abstract model for representing n-ary relations as directed labeled graphs, and we show how this model gives rise to a new ontological pattern (parametric pattern) for the representation of such relations in the Semantic Web. To this end, we define PROL (Parametric Relational Ontology Language). PROL is an ontological language designed to express any n-ary fact as a parametric pattern, which turns out to be a special RDF graph. The vocabulary of PROL is defined by a simple RDFS ontology. We argue that the parametric pattern may be particularly beneficial in the context of the Semantic Web, in virtue of its high expressive power, technical simplicity, and faithful meaning rendition. Examples are also provided.","PeriodicalId":304915,"journal":{"name":"Log. J. IGPL","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128928384","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}
Pub Date : 2019-11-14DOI: 10.1007/978-3-030-33607-3_6
N. Ishii, Toshinori Deguchi, M. Kawaguchi, Hiroshi Sasaki, T. Matsuo
{"title":"Adaptive Orthogonal Characteristics of Bio-inspired Neural Networks","authors":"N. Ishii, Toshinori Deguchi, M. Kawaguchi, Hiroshi Sasaki, T. Matsuo","doi":"10.1007/978-3-030-33607-3_6","DOIUrl":"https://doi.org/10.1007/978-3-030-33607-3_6","url":null,"abstract":"","PeriodicalId":304915,"journal":{"name":"Log. J. IGPL","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115853212","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}
We introduce game-theoretic semantics for systems without the conveniences of either a De Morgan negation, or of distribution of conjunction over disjunction and conversely. Much of game playing rests on challenges issued by one player to the other to satisfy, or refute, a sentence, while forcing him/her to move to some other place in the game’s chessboard-like configuration. Correctness of the game-theoretic semantics is proven for both a training game, corresponding to Positive Lattice Logic and for more advanced games for the logics of lattices with weak negation and modal operators (Modal Lattice Logic).
{"title":"Game-theoretic semantics for non-distributive logics","authors":"C. Hartonas","doi":"10.1093/JIGPAL/JZY079","DOIUrl":"https://doi.org/10.1093/JIGPAL/JZY079","url":null,"abstract":"We introduce game-theoretic semantics for systems without the conveniences of either a De Morgan negation, or of distribution of conjunction over disjunction and conversely. Much of game playing rests on challenges issued by one player to the other to satisfy, or refute, a sentence, while forcing him/her to move to some other place in the game’s chessboard-like configuration. Correctness of the game-theoretic semantics is proven for both a training game, corresponding to Positive Lattice Logic and for more advanced games for the logics of lattices with weak negation and modal operators (Modal Lattice Logic).","PeriodicalId":304915,"journal":{"name":"Log. J. IGPL","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114971183","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":"Unification in first-order transitive modal logic","authors":"W. Dzik, P. Wojtylak","doi":"10.1093/JIGPAL/JZY077","DOIUrl":"https://doi.org/10.1093/JIGPAL/JZY077","url":null,"abstract":"","PeriodicalId":304915,"journal":{"name":"Log. J. IGPL","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121791022","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}
The cut-free Gentzen-type sequent calculus LLK for the logic of likelihood (LL) is introduced in the paper. It is proved that the calculus is sound and complete for LL. Using the introduced calculus LLK, a decision procedure for LL is presented.
{"title":"A proof-search system for the logic of likelihood","authors":"R. Alonderis, H. Giedra","doi":"10.1093/JIGPAL/JZZ022","DOIUrl":"https://doi.org/10.1093/JIGPAL/JZZ022","url":null,"abstract":"\u0000 The cut-free Gentzen-type sequent calculus LLK for the logic of likelihood (LL) is introduced in the paper. It is proved that the calculus is sound and complete for LL. Using the introduced calculus LLK, a decision procedure for LL is presented.","PeriodicalId":304915,"journal":{"name":"Log. J. IGPL","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121965366","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}
We present a sequent calculus of a paraconsistent logic QMPT0, which has the paraconsistent-type excluded middle law (PEML) as an initial sequent. Our system shows that the presence of PEML is essentially important for QMPT0. It also has special rules when the set of constant symbols is finite. We also discuss the cut-elimination property of our system.
{"title":"Sequent calculus for 3-valued paraconsistent logic QMPT0","authors":"Naoyuki Nide, Yukiya Goto, Megumi Fujita","doi":"10.1093/JIGPAL/JZZ016","DOIUrl":"https://doi.org/10.1093/JIGPAL/JZZ016","url":null,"abstract":"We present a sequent calculus of a paraconsistent logic QMPT0, which has the paraconsistent-type excluded middle law (PEML) as an initial sequent. Our system shows that the presence of PEML is essentially important for QMPT0. It also has special rules when the set of constant symbols is finite. We also discuss the cut-elimination property of our system.","PeriodicalId":304915,"journal":{"name":"Log. J. IGPL","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129727079","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}
In relevant logics, necessary truths need not imply each other. In justification logic, necessary truths need not all be justified by the same reason. There is an affinity to these two approaches that suggests their pairing will provide good logics for tracking reasons in a fine-grained way. In this paper, I will show how to extend relevant logics with some of the basic operators of justification logic in order to track justifications or reasons. I will define and study three kinds of frames for these logics. For the first kind of frame, I show soundness and highlight a difficulty in proving completeness. This motivates two alternative kinds of frames, with respect to which completeness results are obtained. Axioms to strengthen the justification logic portions of these logics are considered. I close by developing an analogy between the dot operator of justification logic and theory fusion in relevant logics.
{"title":"Tracking reasons with extensions of relevant logics","authors":"Shawn Standefer","doi":"10.1093/JIGPAL/JZZ018","DOIUrl":"https://doi.org/10.1093/JIGPAL/JZZ018","url":null,"abstract":"\u0000 In relevant logics, necessary truths need not imply each other. In justification logic, necessary truths need not all be justified by the same reason. There is an affinity to these two approaches that suggests their pairing will provide good logics for tracking reasons in a fine-grained way. In this paper, I will show how to extend relevant logics with some of the basic operators of justification logic in order to track justifications or reasons. I will define and study three kinds of frames for these logics. For the first kind of frame, I show soundness and highlight a difficulty in proving completeness. This motivates two alternative kinds of frames, with respect to which completeness results are obtained. Axioms to strengthen the justification logic portions of these logics are considered. I close by developing an analogy between the dot operator of justification logic and theory fusion in relevant logics.","PeriodicalId":304915,"journal":{"name":"Log. J. IGPL","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128945714","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}
Intuitionistic modal logics are extensions of intuitionistic propositional logic with modal axioms. We treat with two modal languages ${mathscr{L}}_Diamond $ and $mathscr{L}_{Diamond ,Box }$ which extend the intuitionistic propositional language with $Diamond $ and $Diamond ,Box $, respectively. Gentzen sequent calculi are established for several intuitionistic modal logics. In particular, we introduce a Gentzen sequent calculus for the well-known intuitionistic modal logic $textsf{MIPC}$. These sequent calculi admit cut elimination and subformula property. They are decidable.
{"title":"Gentzen sequent calculi for some intuitionistic modal logics","authors":"Zhe Lin, Minghui Ma","doi":"10.1093/JIGPAL/JZZ020","DOIUrl":"https://doi.org/10.1093/JIGPAL/JZZ020","url":null,"abstract":"\u0000 Intuitionistic modal logics are extensions of intuitionistic propositional logic with modal axioms. We treat with two modal languages ${mathscr{L}}_Diamond $ and $mathscr{L}_{Diamond ,Box }$ which extend the intuitionistic propositional language with $Diamond $ and $Diamond ,Box $, respectively. Gentzen sequent calculi are established for several intuitionistic modal logics. In particular, we introduce a Gentzen sequent calculus for the well-known intuitionistic modal logic $textsf{MIPC}$. These sequent calculi admit cut elimination and subformula property. They are decidable.","PeriodicalId":304915,"journal":{"name":"Log. J. IGPL","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121870966","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}
In this paper we argue that normative reasons are hyperintensional and put forward a formal account of this thesis. That reasons are hyperintensional means that a reason for a proposition does not imply that it is also a reason for a logically equivalent proposition. In the first part we consider three arguments for the hyperintensionality of reasons: (i) an argument from the nature of reasons, (ii) an argument from substitutivity and (iii) an argument from explanatory power. In the second part we describe a hyperintensional logic of reasons based on justification logics. Eventually we discuss the philosophical import of this proposal and highlight some limitations and possible developments.
{"title":"A hyperintensional logical framework for deontic reasons","authors":"Federico L. G. Faroldi, Tudor Protopopescu","doi":"10.1093/JIGPAL/JZZ012","DOIUrl":"https://doi.org/10.1093/JIGPAL/JZZ012","url":null,"abstract":"\u0000 In this paper we argue that normative reasons are hyperintensional and put forward a formal account of this thesis. That reasons are hyperintensional means that a reason for a proposition does not imply that it is also a reason for a logically equivalent proposition. In the first part we consider three arguments for the hyperintensionality of reasons: (i) an argument from the nature of reasons, (ii) an argument from substitutivity and (iii) an argument from explanatory power. In the second part we describe a hyperintensional logic of reasons based on justification logics. Eventually we discuss the philosophical import of this proposal and highlight some limitations and possible developments.","PeriodicalId":304915,"journal":{"name":"Log. J. IGPL","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130610052","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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