16 found
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  1.  27
    Order-Dual Relational Semantics for Non-Distributive Propositional Logics: A General Framework.Chrysafis Hartonas - 2018 - Journal of Philosophical Logic 47 (1):67-94.
    The contribution of this paper lies with providing a systematically specified and intuitive interpretation pattern and delineating a class of relational structures and models providing a natural interpretation of logical operators on an underlying propositional calculus of Positive Lattice Logic and subsequently proving a generic completeness theorem for the related class of logics, sometimes collectively referred to as Generalized Galois Logics.
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  2.  22
    Stone Duality for Lattice Expansions.Chrysafis Hartonas - 2018 - Logic Journal of the IGPL 26 (5):475-504.
  3.  12
    Modal and Temporal Extensions of Non-Distributive Propositional Logics.Chrysafis Hartonas - 2016 - Logic Journal of the IGPL 24 (2):156-185.
  4.  4
    Order- Dual Realational Semantics for Non-Distributive Propositional Logics.Chrysafis Hartonas - 2017 - Logic Journal of the IGPL 25 (2):145-182.
    This article addresses and resolves some issues of relational, Kripke-style, semantics for the logics of bounded lattice expansions with operators of well-defined distribution types, focusing on the case where the underlying lattice is not assumed to be distributive. It therefore falls within the scope of the theory of Generalized Galois Logics, introduced by Dunn, and it contributes to its extension. We introduce order-dual relational semantics and present a semantic analysis and completeness theorems for non-distributive lattice logic with n -ary additive (...)
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  5.  7
    Canonical Extensions and Kripke–Galois Semantics for Non-Distributive Logics.Chrysafis Hartonas - 2018 - Logica Universalis 12 (3-4):397-422.
    This article presents an approach to the semantics of non-distributive propositional logics that is based on a lattice representation theorem that delivers a canonical extension of the lattice. Our approach supports both a plain Kripke-style semantics and, by restriction, a general frame semantics. Unlike the framework of generalized Kripke frames, the semantic approach presented in this article is suitable for modeling applied logics, as it respects the intended interpretation of the logical operators. This is made possible by restricting admissible interpretations.
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  6.  16
    Lattice Logic as a Fragment of (2-Sorted) Residuated Modal Logic.Chrysafis Hartonas - 2019 - Journal of Applied Non-Classical Logics 29 (2):152-170.
    ABSTRACTCorrespondence and Shalqvist theories for Modal Logics rely on the simple observation that a relational structure is at the same time the basis for a model of modal logic and for a model of first-order logic with a binary predicate for the accessibility relation. If the underlying set of the frame is split into two components,, and, then frames are at the same time the basis for models of non-distributive lattice logic and of two-sorted, residuated modal logic. This suggests that (...)
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  7.  54
    Duality for Lattice-Ordered Algebras and for Normal Algebraizable Logics.Chrysafis Hartonas - 1997 - Studia Logica 58 (3):403-450.
    Part I of this paper is developed in the tradition of Stone-type dualities, where we present a new topological representation for general lattices (influenced by and abstracting over both Goldblatt's [17] and Urquhart's [46]), identifying them as the lattices of stable compact-opens of their dual Stone spaces (stability refering to a closure operator on subsets). The representation is functorial and is extended to a full duality.In part II, we consider lattice-ordered algebras (lattices with additional operators), extending the Jónsson and Tarski (...)
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  8.  8
    First-Order Frames for Orthomodular Quantum Logic.Chrysafis Hartonas - 2016 - Journal of Applied Non-Classical Logics 26 (1):69-80.
    One of the main problems of the orthoframe approach to quantum logic was that orthomodularity could not be captured by any first-order condition. This paper studies an elementary and natural class of orthomodular frames that can work around this limitation. Set-theoretically, the frames we propose form a natural subclass of the orthoframes, where is an irreflexive and symmetric relation on X. More specifically, they are partially-ordered orthoframes with a designated subset. Our frame class contains the canonical orthomodular frame of the (...)
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  9.  10
    Duality Results for (Co)Residuated Lattices.Chrysafis Hartonas - 2019 - Logica Universalis 13 (1):77-99.
    We present dualities for implicative and residuated lattices. In combination with our recent article on a discrete duality for lattices with unary modal operators, the present article contributes in filling in a gap in the development of Orłowska and Rewitzky’s research program of discrete dualities, which seemed to have stumbled on the case of non-distributive lattices with operators. We discuss dualities via truth, which are essential in relating the non-distributive logic of two-sorted frames with their sorted, residuated modal logic, as (...)
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  10.  8
    Modal Translation of Substructural Logics.Chrysafis Hartonas - 2020 - Journal of Applied Non-Classical Logics 30 (1):16-49.
    ABSTRACTIn an article dating back in 1992, Kosta Došen initiated a project of modal translations in substructural logics, aiming at generalising the well-known Gödel–McKinsey–Tarski translation of intuitionistic logic into S4. Došen's translation worked well for BCI and stronger systems, but not for systems below BCI. Dropping structural rules results in logic systems without distribution. In this article, we show, via translation, that every substructural logic is a fragment of a corresponding sorted, residuated modal logic. At the conceptual and philosophical level, (...)
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  11.  13
    On the Logic of Information Flow.Jon Barwise, Dov Gabby & Chrysafis Hartonas - 1995 - Logic Journal of the IGPL 3 (1):7-50.
    This paper is an investigation into the logic of information flow. The basic perspective is that logic flows in virtue of constraints and that constraints classify channels connecting particulars In this paper we explore some logics intended to model reasoning in the case of idealized information flow, that is, where the constraints involved are exceptionless. We look at this as a step toward the far more challenging task of understanding the logic of imperfect information flow, that is where the constraints (...)
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  12.  17
    An Algebraic Theory of Structured Objects.Chrysafis Hartonas - 1997 - Notre Dame Journal of Formal Logic 38 (1):65-80.
    We present an algebraic theory of structured objects based on and generalizing Aczel's theory of form systems. Notions of identity of structured objects and of transformations of systems of such objects are discussed. A generalization of Aczel's representation theorem is proven.
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  13. Algebraic and Kripke Semantics for Substructural Logics.Chrysafis Hartonas - 1994 - Dissertation, Indiana University
    A systematic approach to the algebraic and Kripke semantics for logics with restricted structural rules, notably for logics on an underlying non-distributive lattice, is developed. We provide a new topological representation theorem for general lattices, using the filter space X. Our representation involves a galois connection on subsets of X, hence a closure operator $\Gamma$, and the image of the representation map is characterized as the collection of $\Gamma$-stable, compact-open subsets of the filter space . The original lattice ${\cal L}$ (...)
     
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  14.  3
    Game-Theoretic Semantics for Non-Distributive Logics.Chrysafis Hartonas - 2019 - Logic Journal of the IGPL 27 (5):718-742.
    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 (...)
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  15.  78
    On the Dynamic Logic of Agency and Action.Chrysafis Hartonas - 2014 - Studia Logica 102 (3):441-478.
    We present a Hilbert style axiomatization and an equational theory for reasoning about actions and capabilities. We introduce two novel features in the language of propositional dynamic logic, converse as backwards modality and abstract processes specified by preconditions and effects, written as \({\varphi \Rightarrow \psi}\) and first explored in our recent paper (Hartonas, Log J IGPL Oxf Univ Press, 2012), where a Gentzen-style sequent calculus was introduced. The system has two very natural interpretations, one based on the familiar relational semantics (...)
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  16. Reasoning with Incomplete Information in Generalized Galois Logics Without Distribution: The Case of Negation and Modal Operators.Chrysafis Hartonas - 2016 - In Katalin Bimbó (ed.), J. Michael Dunn on Information Based Logics. Springer.
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