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  1.  4
    New Logics for Quantum Non-Individuals?Jonas R. Becker Arenhart - 2018 - Logica Universalis 12 (3-4):375-395.
    According to a very widespread interpretation of the metaphysical nature of quantum entities—the so-called Received View on quantum non-individuality—, quantum entities are non-individuals. Still according to this understanding, non-individuals are entities for which identity is restricted or else does not apply at all. As a consequence, it is said, such approach to quantum mechanics would require that classical logic be revised, given that it is somehow committed with the unrestricted validity of identity. In this paper we examine the arguments to (...)
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  2.  3
    Logic Prizes Et Cætera.Jean-Yves Beziau - 2018 - Logica Universalis 12 (3-4):271-296.
    I discuss the origin and development of logic prizes around the world. In a first section I describe how I started this project by creating the Newton da Costa Logic Prize in Brazil in 2014. In a second section I explain how this idea was extended into the world through the manifesto A Logic Prize in Every Country! and how was organized the Logic Prizes Contest at the 6th UNILOG in Vichy in June 2018 with the participation of 9 logic (...)
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  3.  3
    Dualities for Płonka Sums.Stefano Bonzio - 2018 - Logica Universalis 12 (3-4):327-339.
    Płonka sums consist of an algebraic construction similar, in some sense, to direct limits, which allows to represent classes of algebras defined by means of regular identities. Recently, Płonka sums have been connected to logic, as they provide algebraic semantics to logics obtained by imposing a syntactic filter to given logics. In this paper, I present a very general topological duality for classes of algebras admitting a Płonka sum representation in terms of dualisable algebras.
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  4.  18
    On the Modal Logic of Jeffrey Conditionalization.Zalán Gyenis - 2018 - Logica Universalis 12 (3-4):351-374.
    We continue the investigations initiated in the recent papers where Bayes logics have been introduced to study the general laws of Bayesian belief revision. In Bayesian belief revision a Bayesian agent revises his prior belief by conditionalizing the prior on some evidence using the Bayes rule. In this paper we take the more general Jeffrey formula as a conditioning device and study the corresponding modal logics that we call Jeffrey logics, focusing mainly on the countable case. The containment relations among (...)
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  5.  2
    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.  4
    Pecularities of Some Three- and Four-Valued Second Order Logics.Allen P. Hazen & Francis Jeffry Pelletier - 2018 - Logica Universalis 12 (3-4):493-509.
    Logics that have many truth values—more than just True and False—have been argued to be useful in the analysis of very many philosophical and linguistic puzzles. In this paper, which is a followup to, we will start with a particularly well-motivated four-valued logic that has been studied mainly in its propositional and first-order versions. And we will then investigate its second-order version. This four-valued logic has two natural three-valued extensions: what is called a “gap logic”, and what is called a (...)
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  7.  6
    Abstract Logical Constants.Tin Perkov - 2018 - Logica Universalis 12 (3-4):341-350.
    A possibility of defining logical constants within abstract logical frameworks is discussed, in relation to abstract definition of logical consequence. We propose using duals as a general method of applying the idea of invariance under replacement as a criterion for logicality.
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  8.  3
    Generalized Correspondence Analysis for Three-Valued Logics.Yaroslav Petrukhin - 2018 - Logica Universalis 12 (3-4):423-460.
    Correspondence analysis is Kooi and Tamminga’s universal approach which generates in one go sound and complete natural deduction systems with independent inference rules for tabular extensions of many-valued functionally incomplete logics. Originally, this method was applied to Asenjo–Priest’s paraconsistent logic of paradox LP. As a result, one has natural deduction systems for all the logics obtainable from the basic three-valued connectives of LP -language) by the addition of unary and binary connectives. Tamminga has also applied this technique to the paracomplete (...)
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  9.  46
    Developing Metalogic to Formalize Ontological Disputes of the Systems in Metaphysics by Introducing the Notion of Functionally Isomorphic Quantifiers.Jolly Thomas - 2018 - Logica Universalis 12 (3-4):461-492.
    A general meta-logical theory is developed by considering ontological disputes in the systems of metaphysics. The usefulness of this general meta-logical theory is demonstrated by considering the case of the ontological dispute between the metaphysical systems of Lewis’ Modal Realism and Terence Parsons’ Meinongianism. Using Quine’s criterion of ontological commitments and his views on ontological disagreement, three principles of metalogic is formulated. Based on the three principles of metalogic, the notions of independent variable and dependent variable are introduced. Then, the (...)
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  10.  3
    A Note on a Description Logic of Concept and Role Typicality for Defeasible Reasoning Over Ontologies.Ivan Varzinczak - 2018 - Logica Universalis 12 (3-4):297-325.
    In this work, we propose a meaningful extension of description logics for non-monotonic reasoning. We introduce \, a logic allowing for the representation of and reasoning about both typical class-membership and typical instances of a relation. We propose a preferential semantics for \ in terms of partially-ordered DL interpretations which intuitively captures the notions of typicality we are interested in. We define a tableau-based algorithm for checking \ knowledge-base consistency that always terminates and we show that it is sound and (...)
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  11.  12
    Universal Logic: Evolution of a Project.Jean-Yves Beziau - 2018 - Logica Universalis 12 (1-2):1-8.
    We discuss the origin and development of the universal logic project. We describe in particular the structure of UNILOG, a series of events created for promoting the universal logic project, with a school, a congress, a secret speaker and a contest. We explain how the contest has evolved into a session of logic prizes.
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  12.  7
    Is the Principle of Contradiction a Consequence of $$X^{2}=X$$X2=X?Jean-Yves Beziau - 2018 - Logica Universalis 12 (1-2):55-81.
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  13.  9
    Is the Principle of Contradiction a Consequence of $$X^{2}=X$$?Jean-Yves Beziau - 2018 - Logica Universalis 12 (1-2):55-81.
    According to Boole it is possible to deduce the principle of contradiction from what he calls the fundamental law of thought and expresses as \. We examine in which framework this makes sense and up to which point it depends on notation. This leads us to make various comments on the history and philosophy of modern logic.
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  14.  4
    Venn Diagram with Names of Individuals and Their Absence: A Non-Classical Diagram Logic.Reetu Bhattacharjee, Mihir Kr Chakraborty & Lopamudra Choudhury - 2018 - Logica Universalis 12 (1-2):141-206.
    Venn diagram system has been extended by introducing names of individuals and their absence. Absence gives a kind of negation of singular propositions. We have offered here a non-classical interpretation of this negation. Soundness and completeness of the present diagram system have been established with respect to this interpretation.
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  15.  3
    Composition-Nominative Logics as Institutions.Alexey Chentsov & Mykola Nikitchenko - 2018 - Logica Universalis 12 (1-2):221-238.
    Composition-nominative logics are program-oriented logics. They are based on algebras of partial predicates which do not have fixed arity. The aim of this work is to present CNL as institutions. Homomorphisms of first-order CNL are introduced, satisfaction condition is proved. Relations with institutions for classical first-order logic are considered. Directions for further investigation are outlined.
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  16.  11
    Aristotle’s Prototype Rule-Based Underlying Logic.John Corcoran - 2018 - Logica Universalis 12 (1-2):9-35.
    This expository paper on Aristotle’s prototype underlying logic is intended for a broad audience that includes non-specialists. It requires as background a discussion of Aristotle’s demonstrative logic. Demonstrative logic or apodictics is the study of demonstration as opposed to persuasion. It is the subject of Aristotle’s two-volume Analytics, as its first sentence says. Many of Aristotle’s examples are geometrical. A typical geometrical demonstration requires a theorem that is to be demonstrated, known premises from which the theorem is to be deduced, (...)
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  17.  7
    Two Early Arabic Applications of Model-Theoretic Consequence.Wilfrid Hodges - 2018 - Logica Universalis 12 (1-2):37-54.
    We trace two logical ideas further back than they have previously been traced. One is the idea of using diagrams to prove that certain logical premises do—or don’t—have certain logical consequences. This idea is usually credited to Venn, and before him Euler, and before him Leibniz. We find the idea correctly and vigorously used by Abū al-Barakāt in 12th century Baghdad. The second is the idea that in formal logic, P logically entails Q if and only if every model of (...)
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  18.  5
    A Molecular Logic of Chords and Their Internal Harmony.Ingolf Max - 2018 - Logica Universalis 12 (1-2):239-269.
    Chords are not pure sets of tones or notes. They are mainly characterized by their matrices. A chord matrix is the pattern of all the lengths of intervals given without further context. Chords are well-structured invariants. They show their inner logical form. This opens up the possibility to develop a molecular logic of chords. Chords are our primitive, but, nevertheless, already interrelated expressions. The logical space of internal harmony is our well-known chromatic scale represented by an infinite line of integers. (...)
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  19.  2
    A Characterisation of Some $$Mathbf {}$$-Like Logics.Krystyna Mruczek-Nasieniewska & Marek Nasieniewski - 2018 - Logica Universalis 12 (1-2):207-219.
    In Béziau a logic \ was defined with the help of the modal logic \. In it, the negation operator is understood as meaning ‘it is not necessary that’. The strong soundness–completeness result for \ with respect to a version of Kripke semantics was also given there. Following the formulation of \ we can talk about \-like logics or Beziau-style logics if we consider other modal logics instead of \—such a possibility has been mentioned in [1]. The correspondence result between (...)
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  20.  4
    A Characterisation of Some $$\Mathbf {Z}$$ Z -Like Logics.Krystyna Mruczek-Nasieniewska & Marek Nasieniewski - 2018 - Logica Universalis 12 (1-2):207-219.
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  21.  6
    On a Generalization of Equilogical Spaces.Fabio Pasquali - 2018 - Logica Universalis 12 (1-2):129-140.
    We use the theory of triposes to prove that every locale H is the set of truth values of a complete and co-complete quasi-topos into which the category of topological spaces embeds and the topos of sheaves over H reflectively embeds.
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  22.  5
    Natural Deduction for Post’s Logics and Their Duals.Yaroslav Petrukhin - 2018 - Logica Universalis 12 (1-2):83-100.
    In this paper, we introduce the notion of dual Post’s negation and an infinite class of Dual Post’s finitely-valued logics which differ from Post’s ones with respect to the definitions of negation and the sets of designated truth values. We present adequate natural deduction systems for all Post’s k-valued ) logics as well as for all Dual Post’s k-valued logics.
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  23.  6
    Positive Jonsson Theories.Bruno Poizat & Aibat Yeshkeyev - 2018 - Logica Universalis 12 (1-2):101-127.
    This paper is a general introduction to Positive Logic, where only what we call h-inductive sentences are under consideration, allowing the extension to homomorphisms of model-theoric notions which are classically associated to embeddings; in particular, the existentially closed models, that were primitively defined by Abraham Robinson, become here positively closed models. It accounts for recent results in this domain, and is oriented towards the positivisation of Jonsson theories.
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