Results for 'Non-normal modalities'

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  1. Non-normal modalities in variants of linear logic.D. Porello & N. Troquard - 2015 - Journal of Applied Non-Classical Logics 25 (3):229-255.
    This article presents modal versions of resource-conscious logics. We concentrate on extensions of variants of linear logic with one minimal non-normal modality. In earlier work, where we investigated agency in multi-agent systems, we have shown that the results scale up to logics with multiple non-minimal modalities. Here, we start with the language of propositional intuitionistic linear logic without the additive disjunction, to which we add a modality. We provide an interpretation of this language on a class of Kripke (...)
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  2.  19
    Explicit Non-normal Modal Logic.Atefeh Rohani & Thomas Studer - 2021 - In Alexandra Silva, Renata Wassermann & Ruy de Queiroz, Logic, Language, Information, and Computation: 27th International Workshop, Wollic 2021, Virtual Event, October 5–8, 2021, Proceedings. Springer Verlag. pp. 64-81.
    Faroldi argues that deontic modals are hyperintensional and thus traditional modal logic cannot provide an appropriate formalization of deontic situations. To overcome this issue, we introduce novel justification logics as hyperintensional analogues to non-normal modal logics. We establish soundness and completness with respect to various models and we study the problem of realization.
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  3.  51
    Intuitionistic Non-normal Modal Logics: A General Framework.Tiziano Dalmonte, Charles Grellois & Nicola Olivetti - 2020 - Journal of Philosophical Logic 49 (5):833-882.
    We define a family of intuitionistic non-normal modal logics; they can be seen as intuitionistic counterparts of classical ones. We first consider monomodal logics, which contain only Necessity or Possibility. We then consider the more important case of bimodal logics, which contain both modal operators. In this case we define several interactions between Necessity and Possibility of increasing strength, although weaker than duality. We thereby obtain a lattice of 24 distinct bimodal logics. For all logics we provide both a (...)
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  4.  35
    Quantification in Some Non-normal Modal Logics.Erica Calardo & Antonino Rotolo - 2017 - Journal of Philosophical Logic 46 (5):541-576.
    This paper offers a semantic study in multi-relational semantics of quantified N-Monotonic modal logics with varying domains with and without the identity symbol. We identify conditions on frames to characterise Barcan and Ghilardi schemata and present some related completeness results. The characterisation of Barcan schemata in multi-relational frames with varying domains shows the independence of BF and CBF from well-known propositional modal schemata, an independence that does not hold with constant domains. This fact was firstly suggested for classical modal systems (...)
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  5.  29
    Uniform Lyndon Interpolation for Basic Non-normal Modal Logics.Amirhossein Akbar Tabatabai, Rosalie Iemhoff & Raheleh Jalali - 2021 - In Alexandra Silva, Renata Wassermann & Ruy de Queiroz, Logic, Language, Information, and Computation: 27th International Workshop, Wollic 2021, Virtual Event, October 5–8, 2021, Proceedings. Springer Verlag. pp. 287-301.
    In this paper, a proof-theoretic method to prove uniform Lyndon interpolation for non-normal modal logics is introduced and applied to show that the logics E\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {E}$$\end{document}, M\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {M}$$\end{document}, MC\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {MC}$$\end{document}, EN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {EN}$$\end{document}, MN\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathsf {MN}$$\end{document} have (...)
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  6.  64
    Variants of multi-relational semantics for propositional non-normal modal logics.Erica Calardo & Antonino Rotolo - 2014 - Journal of Applied Non-Classical Logics 24 (4):293-320.
    A number of significant contributions in the last four decades show that non-normal modal logics can be fruitfully employed in several applied fields. Well-known domains are epistemic logic, deontic logic, and systems capturing different aspects of action and agency such as the modal logic of agency, concurrent propositional dynamic logic, game logic, and coalition logic. Semantics for such logics are traditionally based on neighbourhood models. However, other model-theoretic semantics can be used for this purpose. Here, we systematically study multi-relational (...)
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  7.  24
    An extension of Jónsson‐Tarski representation and model existence in predicate non‐normal modal logics.Yoshihito Tanaka - 2022 - Mathematical Logic Quarterly 68 (2):189-201.
    We give an extension of the Jónsson‐Tarski representation theorem for both normal and non‐normal modal algebras so that it preserves countably many infinite meets and joins. In order to extend the Jónsson‐Tarski representation to non‐normal modal algebras we consider neighborhood frames instead of Kripke frames just as Došen's duality theorem for modal algebras, and to deal with infinite meets and joins, we make use of Q‐filters, which were introduced by Rasiowa and Sikorski, instead of prime filters. By (...)
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  8.  55
    Sequent Calculi and Interpolation for Non-Normal Modal and Deontic Logics.Eugenio Orlandelli - 2021 - Logic and Logical Philosophy 30 (1):139-183.
    G3-style sequent calculi for the logics in the cube of non-normal modal logics and for their deontic extensions are studied. For each calculus we prove that weakening and contraction are height-preserving admissible, and we give a syntactic proof of the admissibility of cut. This implies that the subformula property holds and that derivability can be decided by a terminating proof search whose complexity is in Pspace. These calculi are shown to be equivalent to the axiomatic ones and, therefore, they (...)
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  9.  18
    Epistemic Logic, Skepticism, and Non-Normal Modal Logic.R. E. Jennings - 1981 - Philosophical Studies 40 (1):47-67.
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  10.  83
    Epistemic logic, skepticism, and non-normal modal logic.P. K. Schotch & R. E. Jennings - 1981 - Philosophical Studies 40 (1):47 - 67.
    An epistemic logic is built up on the basis of an analysis of two skeptical arguments. the method used is to first construct an inference relation appropriate to epistemic contexts and introduce "a knows that..." as an operator giving rise to sentences closed with respect to this new concept of inference. soundness and completeness proofs are provided using auxiliary three-valued valuations.
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  11. Quantified modal logic: Non-normal worlds and propositional attitudes.Veikko Rantala - 1982 - Studia Logica 41 (1):41 - 65.
    One way to obtain a comprehensive semantics for various systems of modal logic is to use a general notion of non-normal world. In the present article, a general notion of modal system is considered together with a semantic framework provided by such a general notion of non-normal world. Methodologically, the main purpose of this paper is to provide a logical framework for the study of various modalities, notably prepositional attitudes. Some specific systems are studied together with semantics (...)
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  12.  91
    Interpretations of intuitionist logic in non-normal modal logics.Colin Oakes - 1999 - Journal of Philosophical Logic 28 (1):47-60.
    Historically, it was the interpretations of intuitionist logic in the modal logic S4 that inspired the standard Kripke semantics for intuitionist logic. The inspiration of this paper is the interpretation of intuitionist logic in the non-normal modal logic S3: an S3 model structure can be 'looked at' as an intuitionist model structure and the semantics for S3 can be 'cashed in' to obtain a non-normal semantics for intuitionist propositional logic. This non-normal semantics is then extended to intuitionist (...)
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  13.  96
    Remarks on the semantics of non-normal modal logics.Peter K. Schotch - 1984 - Topoi 3 (1):85-90.
    The standard semantics for sentential modal logics uses a truth condition for necessity which first appeared in the early 1950s. in this paper the status of that condition is investigated and a more general condition is proposed. in addition to meeting certain natural adequacy criteria, the more general condition allows one to capture logics like s1 and s0.9 in a way which brings together the work of segerberg and cresswell.
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  14. (1 other version)Semantical Analysis of Modal Logic II. Non-Normal Modal Propositional Calculi.Saul A. Kripke - 1965 - In J. W. Addison, The theory of models. Amsterdam,: North-Holland Pub. Co.. pp. 206-20.
  15. A sequence of normal modal systems with non-contingency bases.Chris Mortensen - 1976 - Logique Et Analyse 19 (74):341-344.
  16. Colin oakes/interpretations of intuitionist logic in non-normal modal logics 47–60 Aviad heifetz/iterative and fixed point common belief 61–79 dw mertz/the logic of instance ontology 81–111. [REVIEW]Richard Bradley, Roya Sorensen, Mirror Notation & Philip Kremer - 1999 - Journal of Philosophical Logic 28:661-662.
     
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  17.  44
    Thomas van Aquino, niet-normale modale logica's en het probleem van toekomstige contingenties.Luca Gili & Lorenz Demey - 2017 - Tijdschrift Voor Filosofie 79 (2):259-276.
    Thomas Aquinas maintained that God foreknows future contingent events and that his foreknowledge does not entail that they are necessarily the case. More specifically, he stated that if God knows a future contingent event, this future contingent event will be necessarily the case de sensu composito, but not de sensu diviso. After emphasizing the unified nature of Aquinas’ notion of necessity, we propose an interpretation of his theses by restating them within the framework of non-normal modal logics. In this (...)
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  18.  53
    Labelled Sequent Calculi for Lewis’ Non-normal Propositional Modal Logics.Matteo Tesi - 2020 - Studia Logica 109 (4):725-757.
    C. I. Lewis’ systems were the first axiomatisations of modal logics. However some of those systems are non-normal modal logics, since they do not admit a full rule of necessitation, but only a restricted version thereof. We provide G3-style labelled sequent calculi for Lewis’ non-normal propositional systems. The calculi enjoy good structural properties, namely admissibility of structural rules and admissibility of cut. Furthermore they allow for straightforward proofs of admissibility of the restricted versions of the necessitation rule. We (...)
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  19.  27
    Interpolation in Algebraizable Logics Semantics for Non-Normal Multi-Modal Logic.Judit X. Madarász - 1998 - Journal of Applied Non-Classical Logics 8 (1):67-105.
    ABSTRACT The two main directions pursued in the present paper are the following. The first direction was started by Pigozzi in 1969. In [Mak 91] and [Mak 79] Maksimova proved that a normal modal logic has the Craig interpolation property iff the corresponding class of algebras has the superamalgamation property. In this paper we extend Maksimova's theorem to normal multi-modal logics with arbitrarily many, not necessarily unary modalities, and to not necessarily normal multi-modal logics with (...) of ranks smaller than 2. To extend the characterization beyond multi-modal logics, we look at arbitrary algebraizable logics. We will introduce an algebraic property equivalent with the Craig interpolation property in algebraizable logics, and prove that the superamalgamation property implies the Craig interpolation property. The problem of extending the characterization result to non-normal non-unary modal logics also will be discussed. In the second direction pursued herein: for non-normal modal logic with one unary modality Lemmon [Lem 66] gave a possible worlds semantics. Here we give a more general possible worlds semantics for not necessarily normal multi-modal logics with arbitrarily many not necessarily unary modalities. Strongly related to the above is the theorem, proved, e.g., in Jóns son-Tarski [JT 52] and Henkin-Monk-Tarski [HMT 71], that every normal Boolean algebra with operators can be represented as a subalgebra of the complex algebra of some relational structure. We extend this result to not necessarily normal BAO's as follows. We define partial relational structures and show that every not necessarily normal BAO is embeddable into the complex algebra of a partial relational structure. This gives a possible worlds semantics for not necessarily normal multi-modal logics. (shrink)
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  20.  59
    Saul A. Kripke. Semantical analysis of modal logic II. Non-normal modal propositional calculi. The theory of models, Proceedings of the 1963 International Symposium at Berkeley, edited by J. W. Addison, Leon Henkin, and Alfred Tarski, Studies in logic and the foundations of mathematics, North-Holland Publishing Company, Amsterdam1965, pp. 206–220. - R. Routley and H. Montgomery. The inadequacy of Kripke's semantical analysis of D2 and D3. The journal of symbolic logic, vol. 33 , p. 568. [REVIEW]David Makinson - 1970 - Journal of Symbolic Logic 35 (1):135.
    Reviews of the papers mentioned in the title.
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  21.  62
    Nearly every normal modal logic is paranormal.Joao Marcos - 2005 - Logique Et Analyse 48 (189-192):279-300.
    An overcomplete logic is a logic that ‘ceases to make the difference’: According to such a logic, all inferences hold independently of the nature of the statements involved. A negation-inconsistent logic is a logic having at least one model that satisfies both some statement and its negation. A negation-incomplete logic has at least one model according to which neither some statement nor its negation are satisfied. Paraconsistent logics are negation-inconsistent yet non-overcomplete; paracomplete logics are negation-incomplete yet non-overcomplete. A paranormal logic (...)
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  22.  73
    Heuristique formelle et logiques modales non-normales.Laurent Keiff - 2004 - Philosophia Scientiae 8 (2):39-57.
    Nous présentons ici une version modale des dialogues de recherche de conditions (SSD) que nous avons introduits dans [Rahman & Keiff 2004]. La sémantique utilisée correspond à celle des systèmes modaux non normaux.
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  23. Proving unprovability in some normal modal logics.Valentin Goranko - 1991 - Bulletin of the Section of Logic 20 (1):23-29.
    This note considers deductive systems for the operator a of unprovability in some particular propositional normal modal logics. We give thus complete syntactic characterization of these logics in the sense of Lukasiewicz: for every formula  either `  or a  (but not both) is derivable. In particular, purely syntactic decision procedure is provided for the logics under considerations.
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  24. Contingency and non-contingency bases for normal modal logics.Hugh Montgomery & Richard Routley - 1966 - Logique Et Analyse 9 (35):318.
     
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  25.  15
    Non-normal Modalisation.Rogerio A. S. Fajardo & Marcelo Finer - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev, Advances in Modal Logic. CSLI Publications. pp. 83-95.
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  26.  24
    Remarks about the unification type of several non-symmetric non-transitive modal logics.Philippe Balbiani - 2019 - Logic Journal of the IGPL 27 (5):639-658.
    The problem of unification in a normal modal logic $L$ can be defined as follows: given a formula $\varphi$, determine whether there exists a substitution $\sigma$ such that $\sigma $ is in $L$. In this paper, we prove that for several non-symmetric non-transitive modal logics, there exists unifiable formulas that possess no minimal complete set of unifiers.
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  27.  86
    Modal Extensions of Sub-classical Logics for Recovering Classical Logic.Marcelo E. Coniglio & Newton M. Peron - 2013 - Logica Universalis 7 (1):71-86.
    In this paper we introduce non-normal modal extensions of the sub-classical logics CLoN, CluN and CLaN, in the same way that S0.5 0 extends classical logic. The first modal system is both paraconsistent and paracomplete, while the second one is paraconsistent and the third is paracomplete. Despite being non-normal, these systems are sound and complete for a suitable Kripke semantics. We also show that these systems are appropriate for interpreting □ as “is provable in classical logic”. This allows (...)
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  28.  32
    Modal Logic With Non-Deterministic Semantics: Part II—Quantified Case.Marcelo E. Coniglio, Luis Fariñasdelcerro & Newton Marques Peron - 2022 - Logic Journal of the IGPL 30 (5):695-727.
    In the first part of this paper we analyzed finite non-deterministic matrix semantics for propositional non-normal modal logics as an alternative to the standard Kripke possible world semantics. This kind of modal system characterized by finite non-deterministic matrices was originally proposed by Ju. Ivlev in the 70s. The aim of this second paper is to introduce a formal non-deterministic semantical framework for the quantified versions of some Ivlev-like non-normal modal logics. It will be shown that several well-known controversial (...)
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  29.  72
    Normal monomodal logics can simulate all others.Marcus Kracht & Frank Wolter - 1999 - Journal of Symbolic Logic 64 (1):99-138.
    This paper shows that non-normal modal logics can be simulated by certain polymodal normal logics and that polymodal normal logics can be simulated by monomodal (normal) logics. Many properties of logics are shown to be reflected and preserved by such simulations. As a consequence many old and new results in modal logic can be derived in a straightforward way, sheding new light on the power of normal monomodal logic.
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  30. Logics of Formal Inconsistency Enriched with Replacement: An Algebraic and Modal Account.Walter Carnielli, Marcelo E. Coniglio & David Fuenmayor - 2022 - Review of Symbolic Logic 15 (3):771-806.
    One of the most expected properties of a logical system is that it can be algebraizable, in the sense that an algebraic counterpart of the deductive machinery could be found. Since the inception of da Costa's paraconsistent calculi, an algebraic equivalent for such systems have been searched. It is known that these systems are non self-extensional (i.e., they do not satisfy the replacement property). More than this, they are not algebraizable in the sense of Blok-Pigozzi. The same negative results hold (...)
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  31.  58
    Errata and Addenda to ‘Finite non-deterministic semantics for some modal systems’.Marcelo E. Coniglio, Luis Fariñas del Cerro & Newton M. Peron - 2016 - Journal of Applied Non-Classical Logics 26 (4):336-345.
    In this note, an error in the axiomatization of Ivlev’s modal system Sa+ which we inadvertedly reproduced in our paper “Finite non-deterministic semantics for some modal systems”, is fixed. Additionally, some axioms proposed in were slightly modified. All the technical results in which depend on the previous axiomatization were also fixed. Finally, the discussion about decidability of the level valuation semantics initiated in is taken up. The error in Ivlev’s axiomatization was originally pointed out by H. Omori and D. Skurt (...)
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  32.  44
    What groups do, can do, and know they can do: an analysis in normal modal logics.Jan Broersen, Andreas Herzig & Nicolas Troquard - 2009 - Journal of Applied Non-Classical Logics 19 (3):261-289.
    We investigate a series of logics that allow to reason about agents' actions, abilities, and their knowledge about actions and abilities. These logics include Pauly's Coalition Logic CL, Alternating-time Temporal Logic ATL, the logic of ‘seeing-to-it-that' (STIT), and epistemic extensions thereof. While complete axiomatizations of CL and ATL exist, only the fragment of the STIT language without temporal operators and without groups has been axiomatized by Xu (called Ldm). We start by recalling a simplification of the Ldm that has been (...)
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  33.  39
    Neighborhood Semantics for Modal Logic.Eric Pacuit - 2017 - Cham, Switzerland: Springer.
    This book offers a state-of-the-art introduction to the basic techniques and results of neighborhood semantics for modal logic. In addition to presenting the relevant technical background, it highlights both the pitfalls and potential uses of neighborhood models – an interesting class of mathematical structures that were originally introduced to provide a semantics for weak systems of modal logic. In addition, the book discusses a broad range of topics, including standard modal logic results ; bisimulations for neighborhood models and other model-theoretic (...)
  34.  48
    Normal predicative logics with graded modalities.Francesco Caro - 1988 - Studia Logica 47 (1):11 - 22.
    In this work we extend results from [4], [3] and [2] about propositional calculi with graded modalities to the predicative level. Our semantic is based on Kripke models with a single domain of interpretation for all the worlds. Therefore the axiomatic system will need a suitable generalization of the Barcan formula. We haven't considered semantics with world-relative domains because they don't present any new difficulties with respect to classical case. Our language will have, as in [1], constant and function (...)
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  35. Probabilistic semantics for epistemic modals: Normality assumptions, conditional epistemic spaces and the strength of must and might.Guillermo Del Pinal - 2021 - Linguistics and Philosophy 45 (4):985-1026.
    The epistemic modal auxiliaries must and might are vehicles for expressing the force with which a proposition follows from some body of evidence or information. Standard approaches model these operators using quantificational modal logic, but probabilistic approaches are becoming increasingly influential. According to a traditional view, must is a maximally strong epistemic operator and might is a bare possibility one. A competing account—popular amongst proponents of a probabilisitic turn—says that, given a body of evidence, must \ entails that \\) is (...)
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  36.  35
    A Non-Standard Kripke Semantics for the Minimal Deontic Logic.Edson Bezerra & Giorgio Venturi - 2021 - Logic and Logical Philosophy 30 (1):97-107.
    In this paper we study a new operator of strong modality ⊞, related to the non-contingency operator ∆. We then provide soundness and completeness theorems for the minimal logic of the ⊞-operator.
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  37. Logics of essence and accident.Joao Marcos - 2005 - Bulletin of the Section of Logic 34 (1):43-56.
    We say that things happen accidentally when they do indeed happen, but only by chance. In the opposite situation, an essential happening is inescapable, its inevitability being the sine qua non for its very occurrence. This paper will investigate modal logics on a language tailored to talk about essential and accidental statements. Completeness of some among the weakest and the strongest such systems is attained. The weak expressibility of the classical propositional language enriched with the non-normal modal operators of (...)
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  38.  18
    8 Valued Non-Deterministic Semantics for Modal Logics.Pawel Pawlowski & Daniel Skurt - 2024 - Journal of Philosophical Logic 53 (2):351-371.
    The aim of this paper is to study a particular family of non-deterministic semantics for modal logics that has eight truth-values. These eight-valued semantics can be traced back to Omori and Skurt (2016), where a particular member of this family was used to characterize the normal modal logic K. The truth-values in these semantics convey information about a proposition’s truth/falsity, whether the proposition is necessary/not necessary, and whether it is possible/not possible. Each of these triples is represented by a (...)
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  39.  43
    On the non-availability of Dawson-modeling into certain relevance alethic modal logics.John Chidgey - 1979 - Studia Logica 38 (2):89 - 94.
    This paper shows that the Dawson technique of modelling deontic logics into alethic modal logics to gain insight into deontic formulas is not available for modelling a normal (in the spirit of Anderson) relevance deontic modal logic into either of the normal relevance alethic modal logics R S4or R M. The technique is to construct an extension of the well known entailment matrix set M 0and show that the model of the deontic formula P (A v B). PA (...)
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  40. A resource-sensitive logic of agency.Daniele Porello & Nicolas Troquard - 2014 - In Ios Press, Proceedings of the 21st European Conference on Artificial Intelligence (ECAI'14), Prague, Czech Republic. 2014. pp. 723-728.
    We study a fragment of Intuitionistic Linear Logic combined with non-normal modal operators. Focusing on the minimal modal logic, we provide a Gentzen-style sequent calculus as well as a semantics in terms of Kripke resource models. We show that the proof theory is sound and complete with respect to the class of minimal Kripke resource models. We also show that the sequent calculus allows cut elimination. We put the logical framework to use by instantiating it as a logic of (...)
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  41. Epistemic Closure and Epistemic Logic I: Relevant Alternatives and Subjunctivism.Wesley H. Holliday - 2015 - Journal of Philosophical Logic 44 (1):1-62.
    Epistemic closure has been a central issue in epistemology over the last forty years. According to versions of the relevant alternatives and subjunctivist theories of knowledge, epistemic closure can fail: an agent who knows some propositions can fail to know a logical consequence of those propositions, even if the agent explicitly believes the consequence (having “competently deduced” it from the known propositions). In this sense, the claim that epistemic closure can fail must be distinguished from the fact that agents do (...)
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  42. On Displaying Negative Modalities.Sergey Drobyshevich - 2018 - Logic and Logical Philosophy 27 (2):161-192.
    We extend Takuro Onishi’s result on displaying substructural negations by formulating display calculi for non-normal versions of impossibility and unnecessity operators, called regular and co-regular negations, respectively, by Dimiter Vakarelov. We make a number of connections between Onishi’s work and Vakarelov’s study of negation. We also prove a decidability result for our display calculus, which can be naturally extended to obtain decidability results for a large number of display calculi for logics with negative modal operators.
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  43. Swap structures semantics for Ivlev-like modal logics.Marcelo E. Coniglio & Ana Claudia Golzio - 2019 - Soft Computing 23 (7):2243-2254.
    In 1988, J. Ivlev proposed some (non-normal) modal systems which are semantically characterized by four-valued non-deterministic matrices in the sense of A. Avron and I. Lev. Swap structures are multialgebras (a.k.a. hyperalgebras) of a special kind, which were introduced in 2016 by W. Carnielli and M. Coniglio in order to give a non-deterministic semantical account for several paraconsistent logics known as logics of formal inconsistency, which are not algebraizable by means of the standard techniques. Each swap structure induces naturally (...)
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  44.  59
    Proof theory for quantified monotone modal logics.Sara Negri & Eugenio Orlandelli - 2019 - Logic Journal of the IGPL 27 (4):478-506.
    This paper provides a proof-theoretic study of quantified non-normal modal logics. It introduces labelled sequent calculi based on neighbourhood semantics for the first-order extension, with both varying and constant domains, of monotone NNML, and studies the role of the Barcan formulas in these calculi. It will be shown that the calculi introduced have good structural properties: invertibility of the rules, height-preserving admissibility of weakening and contraction and syntactic cut elimination. It will also be shown that each of the calculi (...)
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  45.  28
    Neighbourhood Semantics for FDE-Based Modal Logics.S. Drobyshevich & D. Skurt - 2021 - Studia Logica 109 (6):1273-1309.
    We investigate some non-normal variants of well-studied paraconsistent and paracomplete modal logics that are based on N. Belnap’s and M. Dunn’s four-valued logic. Our basic non-normal modal logics are characterized by a weak extensionality rule, which reflects the four-valued nature of underlying logics. Aside from introducing our basic framework of bi-neighbourhood semantics, we develop a correspondence theory in order to prove completeness results with respect to our neighbourhood semantics for non-normal variants of \, \ and \.
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  46.  17
    Hypergraphs, Local Reasoning, and Weakly Aggregative Modal Logic.Yifeng Ding, Jixin Liu & Yanjing Wang - 2021 - In Sujata Ghosh & Thomas Icard, Logic, Rationality, and Interaction: 8th International Workshop, Lori 2021, Xi’an, China, October 16–18, 2021, Proceedings. Springer Verlag. pp. 58-72.
    This paper connects the following three apparently unrelated topics: an epistemic framework fighting logical omniscience, a class of generalized graphs without the arities of relations, and a family of non-normal modal logics rejecting the aggregative axiom. Through neighborhood frames as their meeting point, we show that, among many completeness results obtained in this paper, the limit of a family of weakly aggregative logics is both exactly the modal logic of hypergraphs and also the epistemic logic of local reasoning with (...)
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  47. Modal Logic and the “Possible".Francois Schmitz - 1997 - Logica Trianguli 1:105-114.
    If we accept the idea that the value of a “logic” depends on its ability to fit the usual meaning of the “logical constants” which it formalises and the inferences we draw on their basis, we may ask if the meaning of “possible” is well captured by normal modal logic. We are faced with the following puzzle: if is meaningful and non contradictory is it not a logical truth that ? First, it is shown why there is no logical (...)
     
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  48. Information closure and the sceptical objection.Luciano Floridi - 2014 - Synthese 191 (6):1037-1050.
    In this article, I define and then defend the principle of information closure (pic) against a sceptical objection similar to the one discussed by Dretske in relation to the principle of epistemic closure. If I am successful, given that pic is equivalent to the axiom of distribution and that the latter is one of the conditions that discriminate between normal and non-normal modal logics, a main result of such a defence is that one potentially good reason to look (...)
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    Olivier Gasquet and Andreas Herzig.From Classical to Normal Modal Logics - 1996 - In Heinrich Wansing, Proof theory of modal logic. Boston: Kluwer Academic Publishers.
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  50.  18
    The logic of modal changes LMC.Marcin Łyczak - 2020 - Journal of Applied Non-Classical Logics 30 (1):50-67.
    The logic of change formulated by K. Świętorzecka, has its motivation coming from the Aristotelian theory of substantial change which is undrstood as a transformation consisting in the disappearing and becoming of individual substances. The transition: becoming/disapearing (and conversely) is expressed in by the primitive operator C, to be read: it changes that …, and it is mapped by the progressively expanding language. We are interested in attributive changes of individual substances. We consider a formalism with two non-normal and (...)
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