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  1.  6
    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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  2.  1
    Modelling Reasoning Processes in Natural Agents: A Partial-Worlds-Based Logical Framework for Elemental Non-Monotonic Inferences and Learning.Christel Grimaud - 2016 - Journal of Applied Non-Classical Logics 26 (4):251-285.
    In this paper we address the modelling of reasoning processes in natural agents. We focus on a very basic kind of non-monotonic inference for which we identify a simple and plausible underlying process, and we develop a family of logical models that allow to match this process. Partial worlds models, as we call them, are a variant of Kraus, Lehmann and Magidor’s cumulative models. We show that the inference relations they induce form a strict subclass of cumulative relations and tackle (...)
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  3. The Discovery/Justification Context Dichotomy Within Formal and Computational Models of Scientific Theories: A Weakening of the Distinction Based on the Perspective of Non-Monotonic Logics.Jorge A. Morales & Mauricio Molina Delgado - 2016 - Journal of Applied Non-Classical Logics 26 (4):315-335.
    The present paper analyses the topic of scientific discovery and the problem of the existence of a logical framework involved in such endeavour. We inquire how several non-monotonic logic frameworks and other formalisms can account for such a task. In the same vein, we analyse some key aspects of the historical and theoretical debate surrounding scientific discovery, in particular, the context of discovery and context of justification context distinction. We present an argument concerning the weakening of the discovery/justification context dichotomy (...)
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  4.  1
    Defining LFIs and LFUs in Extensions of Infectious Logics.Szmuc Damian Enrique - 2016 - Journal of Applied Non-Classical Logics 26 (4):286-314.
    The aim of this paper is to explore the peculiar case of infectious logics, a group of systems obtained generalizing the semantic behavior characteristic of the -fragment of the logics of nonsense, such as the ones due to Bochvar and Halldén, among others. Here, we extend these logics with classical negations, and we furthermore show that some of these extended systems can be properly regarded as logics of formal inconsistency and logics of formal undeterminedness.
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  5.  4
    Knowledge Means ‘All’, Belief Means ‘Most’.Dimitris Askounis, Costas D. Koutras & Yorgos Zikos - 2016 - Journal of Applied Non-Classical Logics 26 (3):173-192.
    We introduce a bimodal epistemic logic intended to capture knowledge as truth in all epistemically alternative states and belief as a generalised ‘majority’ quantifier, interpreted as truth in most of the epistemically alternative states. This doxastic interpretation is of interest in knowledge-representation applications and it also holds an independent philosophical and technical appeal. The logic comprises an epistemic modal operator, a doxastic modal operator of consistent and complete belief and ‘bridge’ axioms which relate knowledge to belief. To capture the notion (...)
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  6.  7
    Game Theoretical Semantics for Some Non-Classical Logics.Can Başkent - 2016 - Journal of Applied Non-Classical Logics 26 (3):208-239.
    Paraconsistent logics are the formal systems in which absurdities do not trivialise the logic. In this paper, we give Hintikka-style game theoretical semantics for a variety of paraconsistent and non-classical logics. For this purpose, we consider Priest’s Logic of Paradox, Dunn’s First-Degree Entailment, Routleys’ Relevant Logics, McCall’s Connexive Logic and Belnap’s four-valued logic. We also present a game theoretical characterisation of a translation between Logic of Paradox/Kleene’s K3 and S5. We underline how non-classical logics require different verification games and prove (...)
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  7.  2
    On a Paraconsistentization Functor in the Category of Consequence Structures.Edelcio G. De Souza, Alexandre Costa-Leite & Diogo H. B. Dias - 2016 - Journal of Applied Non-Classical Logics 26 (3):240-250.
    This paper is an attempt to solve the following problem: given a logic, how to turn it into a paraconsistent one? In other words, given a logic in which ex falso quodlibet holds, how to convert it into a logic not satisfying this principle? We use a framework provided by category theory in order to define a category of consequence structures. Then, we propose a functor to transform a logic not able to deal with contradictions into a paraconsistent one. Moreover, (...)
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  8.  1
    Four Ways From Universal to Particular: How Chomsky’s Principles-and-Parameters Model is Not Selectionist.David P. Ellerman - 2016 - Journal of Applied Non-Classical Logics 26 (3):193-207.
    Following the development of the selectionist theory of the immune system, there was an attempt to characterise many biological mechanisms as being ‘selectionist’ as juxtaposed with ‘instructionist’. However, this broad definition would group Darwinian evolution, the immune system, embryonic development, and Chomsky’s principles-and-parameters language-acquisition mechanism together under the ‘selectionist’ umbrella, even though Chomsky’s mechanism and embryonic development are significantly different from the selectionist mechanisms of biological evolution and the immune system. Surprisingly, there is an abstract way using two dual mathematical (...)
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  9.  4
    On Polynomial Semantics for Propositional Logics.Juan C. Agudelo-Agudelo, Carlos A. Agudelo-González & Oscar E. García-Quintero - 2016 - Journal of Applied Non-Classical Logics 26 (2):103-125.
    Some properties and an algorithm for solving systems of multivariate polynomial equations over finite fields are presented. It is then shown how formulas of propositional logics can be translated into polynomials over finite fields in such a way that several logic problems are expressed in terms of algebraic problems. Consequently, algebraic properties and algorithms can be used to solve the algebraically-represented logic problems. The methods described herein combine and generalise those of various previous works.
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  10.  2
    A Comparison Between Monoidal and Substructural Logics.Clayton Peterson - 2016 - Journal of Applied Non-Classical Logics 26 (2):126-159.
    Monoidal logics were introduced as a foundational framework to analyse the proof theory of deontic logic. Building on Lambek’s work in categorical logic, logical systems are defined as deductive systems, that is, as collections of equivalence classes of proofs satisfying specific rules and axiom schemata. This approach enables the classification of deductive systems with respect to their categorical structure. When looking at their proof theory, however, one can see that there are similarities between monoidal and substructural logics. The purpose of (...)
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  11.  32
    In Defence of a Logic for ‘Because’.B. Schnieder - 2016 - Journal of Applied Non-Classical Logics 26 (2):160-171.
    The present author developed a calculus for the logic of ‘because’. In a recent paper in this journal, it has been claimed that the central inference rules for the logic are invalid and that the intuition upon which the rules are based is not accounted for. This note criticises these arguments and presents an independent argument in favour of the rules used in the logic.
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  12.  1
    Axiomatisation of General Concept Inclusions From Finite Interpretations.D. Borchmann, F. Distel & F. Kriegel - 2016 - Journal of Applied Non-Classical Logics 26 (1):1-46.
    Description logic knowledge bases can be used to represent knowledge about a particular domain in a formal and unambiguous manner. Their practical relevance has been shown in many research areas, especially in biology and the Semantic Web. However, the tasks of constructing knowledge bases itself, often performed by human experts, is difficult, time-consuming and expensive. In particular the synthesis of terminological knowledge is a challenge that every expert has to face. Because human experts cannot be omitted completely from the construction (...)
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  13.  1
    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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  14.  4
    The Logic Determined by Smiley’s Matrix for Anderson and Belnap’s First-Degree Entailment Logic.José M. Méndez & Gemma Robles - 2016 - Journal of Applied Non-Classical Logics 26 (1):47-68.
    The aim of this paper is to define the logical system Sm4 characterised by the degree of truth-preserving consequence relation defined on the ordered set of values of Smiley’s four-element matrix MSm4. The matrix MSm4 has been of considerable importance in the development of relevant logics and it is at the origin of bilattice logics. It will be shown that Sm4 is a most interesting paraconsistent logic which encloses a sound theory of logical necessity similar to that of Anderson and (...)
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  15.  3
    Propositional Quantification in Logics of Contingency.Hans van Ditmarsch & Jie Fan - 2016 - Journal of Applied Non-Classical Logics 26 (1):81-102.
    In this work we define contingency logic with arbitrary announcement. In contingency logic, the primitive modality contingency formalises that a proposition may be true but also may be false, so that if it is non-contingent then it is necessarily true or necessarily false. To this logic one can add dynamic operators to describe change of contingency. Our logic has operators for public announcement and operators for arbitrary public announcement, as in the dynamic epistemic logic called arbitrary public announcement logic. However, (...)
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