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  1.  21
    Truth Without Standard Models: Some Conceptual Problems Reloaded.Eduardo Barrio & Bruno Da Ré - 2018 - Journal of Applied Non-Classical Logics 28 (1):122-139.
    A theory of truth is usually demanded to be consistent, but -consistency is less frequently requested. Recently, Yatabe has argued in favour of -inconsistent first-order theories of truth, minimising their odd consequences. In view of this fact, in this paper, we present five arguments against -inconsistent theories of truth. In order to bring out this point, we will focus on two very well-known -inconsistent theories of truth: the classical theory of symmetric truth FS and the non-classical theory of naïve truth (...)
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  2.  3
    Assertive Graphs.F. Bellucci, D. Chiffi & A.-V. Pietarinen - 2018 - Journal of Applied Non-Classical Logics 28 (1):72-91.
    Peirce and Frege both distinguished between the propositional content of an assertion and the assertion of a propositional content, but with different notational means. We present a modification of Peirce’s graphical method of logic that can be used to reason about assertions in a manner similar to Peirce’s original method. We propose a new system of Assertive Graphs, which unlike the tradition that follows Frege involves no ad hoc sign of assertion. We show that axioms of intuitionistic logic can be (...)
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  3.  1
    From KLM-Style Conditionals to Defeasible Modalities, and Back.Katarina Britz & Ivan Varzinczak - 2018 - Journal of Applied Non-Classical Logics 28 (1):92-121.
    We investigate an aspect of defeasibility that has somewhat been overlooked by the non-monotonic reasoning community, namely that of defeasible modes of reasoning. These aim to formalise defeasibility of the traditional notion of necessity in modal logic, in particular of its different readings as action, knowledge and others in specific contexts, rather than defeasibility of conditional forms. Building on an extension of the preferential approach to modal logics, we introduce new modal osperators with which to formalise the notion of defeasible (...)
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  4. Logics for Extended Distributive Contact Lattices.T. Ivanova - 2018 - Journal of Applied Non-Classical Logics 28 (1):140-162.
    The notion of contact algebra is one of the main tools in the region-based theory of space. It is an extension of Boolean algebra with an additional relation C called contact. There are some problems related to the motivation of the operation of Boolean complementation. Because of this operation is dropped and the language of distributive lattices is extended by considering as non-definable primitives the relations of contact, nontangential inclusion and dual contact. It is obtained an axiomatization of the theory (...)
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  5.  8
    Frames for Fusions of Modal Logics.Sławomir Kost - 2018 - Journal of Applied Non-Classical Logics 28 (1):1-19.
    Let us consider multimodal logics and. We assume that is characterised by a class of connected frames, and there exists an -frame with a so-called -starting point. Similarly, the logic is characterised by a class of connected frames, and there exists an -frame with a -starting point. Using isomorphic copies of the frames and, we construct a connected frame which characterises the fusion. The frame thus obtained has some useful properties. Among others, is countable if both and are countable, and (...)
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  6.  4
    An Independent Axiomatisation for Free Short-Circuit Logic.Alban Ponse & Daan J. C. Staudt - 2018 - Journal of Applied Non-Classical Logics 28 (1):35-71.
    Short-circuit evaluation denotes the semantics of propositional connectives in which the second argument is evaluated only if the first argument does not suffice to determine the value of the expression. Free short-circuit logic is the equational logic in which compound statements are evaluated from left to right, while atomic evaluations are not memorised throughout the evaluation, i.e. evaluations of distinct occurrences of an atom in a compound statement may yield different truth values. We provide a simple semantics for free short-circuit (...)
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  7.  7
    Bi-Intuitionistic Implication Structures.Daniel Skurt - 2018 - Journal of Applied Non-Classical Logics 28 (1):20-34.
    In this contribution, we will present some results concerning the connectives of bi-intuitionistic logic in the setting of Arnold Koslow’s implication structures. Furthermore, we will present soundness and completeness results of Koslow’s implication structures with respect to bi-intuitionistic logic.
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