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  1.  2
    Self-Extensional Three-Valued Paraconsistent Logics.Arnon Avron - 2017 - Logica Universalis 11 (3):297-315.
    A logic \ is called self-extensional if it allows to replace occurrences of a formula by occurrences of an \-equivalent one in the context of claims about logical consequence and logical validity. It is known that no three-valued paraconsistent logic which has an implication can be self-extensional. In this paper we show that in contrast, there is exactly one self-extensional three-valued paraconsistent logic in the language of \ for which \ is a disjunction, and \ is a conjunction. We also (...)
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  2.  2
    Compositional Meaning in Logic.Carlos Caleiro & Luca Viganò - 2017 - Logica Universalis 11 (3):283-295.
    The Fregean-inspired Principle of Compositionality of Meaning for formal languages asserts that the meaning of a compound expression is analysable in terms of the meaning of its constituents, taking into account the mode in which these constituents are combined so as to form the compound expression. From a logical point of view, this amounts to prescribing a constraint—that may or may not be respected—on the internal mechanisms that build and give meaning to a given formal system. Within the domain of (...)
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  3.  1
    Modal Multilattice Logic.Norihiro Kamide & Yaroslav Shramko - 2017 - Logica Universalis 11 (3):317-343.
    A modal extension of multilattice logic, called modal multilattice logic, is introduced as a Gentzen-type sequent calculus \. Theorems for embedding \ into a Gentzen-type sequent calculus S4C and vice versa are proved. The cut-elimination theorem for \ is shown. A Kripke semantics for \ is introduced, and the completeness theorem with respect to this semantics is proved. Moreover, the duality principle is proved as a characteristic property of \.
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  4. Sequent Systems for Negative Modalities.Ori Lahav, João Marcos & Yoni Zohar - 2017 - Logica Universalis 11 (3):345-382.
    Non-classical negations may fail to be contradictory-forming operators in more than one way, and they often fail also to respect fundamental meta-logical properties such as the replacement property. Such drawbacks are witnessed by intricate semantics and proof systems, whose philosophical interpretations and computational properties are found wanting. In this paper we investigate congruential non-classical negations that live inside very natural systems of normal modal logics over complete distributive lattices; these logics are further enriched by adjustment connectives that may be used (...)
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  5. Locally Tabular Ne Locally Finite.Sérgio Marcelino & Umberto Rivieccio - 2017 - Logica Universalis 11 (3):383-400.
    We show that for an arbitrary logic being locally tabular is a strictly weaker property than being locally finite. We describe our hunt for a logic that allows us to separate the two properties, revealing weaker and weaker conditions under which they must coincide, and showing how they are intertwined. We single out several classes of logics where the two notions coincide, including logics that are determined by a finite set of finite matrices, selfextensional logics, algebraizable and equivalential logics. Furthermore, (...)
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  6.  1
    A Note on Two’s Company: “The Humbug of Many Logical Values”.Daniel Skurt - 2017 - Logica Universalis 11 (3):401-407.
    The present note offers a proof for separating the truth-values of an arbitrary finitely many valued Łukasiewicz logic by making use of Gray codes.
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  7.  2
    Translating Non-Classical Logics Into Classical Logic by Using Hidden Variables.Juan C. Agudelo-Agudelo - 2017 - Logica Universalis 11 (2):205-224.
    Dyadic semantics is a sort of non-truth-functional bivalued semantics introduced in Caleiro et al. Logica Universalis, Birkhäuser, Basel, pp 169–189, 2005). Here we introduce an algorithmic procedure for constructing conservative translations of logics characterised by dyadic semantics into classical propositional logic. The procedure uses fresh propositional variables, which we call hidden variables, to represent the indeterminism of dyadic semantics. An alternative algorithmic procedure for constructing conservative translations of any finite-valued logic into classical logic is also introduced. In this alternative procedure (...)
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  8.  1
    Topological Representation of Intuitionistic and Distributive Abstract Logics.Andreas Bernhard Michael Brunner & Steffen Lewitzka - 2017 - Logica Universalis 11 (2):153-175.
    We continue work of our earlier paper :219–241, 2009) where abstract logics and particularly intuitionistic abstract logics are studied.logics can be topologized in a direct and natural way. This facilitates a topological study of classes of concrete logics whenever they are given in abstract form. Moreover, such a direct topological approach avoids the often complex algebraic and lattice-theoretic machinery usually applied to represent logics. Motivated by that point of view, we define in this paper the category of intuitionistic abstract logics (...)
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  9.  3
    The Semiotics of Spider Diagrams.Jim Burton & John Howse - 2017 - Logica Universalis 11 (2):177-204.
    Spider diagrams are based on Euler and Venn/Peirce diagrams, forming a system which is as expressive as monadic first order logic with equality. Rather than being primarily intended for logicians, spider diagrams were developed at the end of the 1990s in the context of visual modelling and software specification. We examine the original goals of the designers, the ways in which the notation has evolved and its connection with the philosophical origins of the logical diagrams of Euler, Venn and Peirce (...)
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  10.  4
    Is ‘No’ a Force-Indicator? Yes, Sooner or Later!Fabien Schang & James Trafford - 2017 - Logica Universalis 11 (2):225-251.
    This paper discusses the philosophical and logical motivations for rejectivism, primarily by considering a dialogical approach to logic, which is formalized in a Question–Answer Semantics. We develop a generalised account of rejectivism through close consideration of Mark Textor’s arguments against rejectivism that the negative expression ‘No’ is never used as an act of rejection and is equivalent with a negative sentence. In doing so, we also shed light upon well-known issues regarding the supposed non-embeddability and non-iterability of force indicators.
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  11.  3
    Interconnection of the Lattices of Extensions of Four Logics.Alexei Y. Muravitsky - 2017 - Logica Universalis 11 (2):253-281.
    We show that the lattices of the normal extensions of four well-known logics—propositional intuitionistic logic \, Grzegorczyk logic \, modalized Heyting calculus \ and \—can be joined in a commutative diagram. One connection of this diagram is an isomorphism between the lattices of the normal extensions of \ and \; we show some preservation properties of this isomorphism. Two other connections are join semilattice epimorphims of the lattice of the normal extensions of \ onto that of \ and of the (...)
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  12.  5
    From Logic in Islam to Islamic Logic.Musa Akrami - 2017 - Logica Universalis 11 (1):61-83.
    Speaking of relations between logic and religion in Islamic world may refer to logic in two respects: logic in religious texts, from doctrinal sacred texts such as Qur’ān and sayings of the Prophet to the Qur’ānic commentaries and the texts related to the principles and fundamentals of jurisprudence, all of which make use of some reasoning to persuade the audiences or to infer the rules and prescripts for religious behavior of the members of religious community; and logic as a discipline (...)
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  13.  5
    Monotonic and Non-Monotonic Embeddings of Anselm’s Proof.Archambault Jacob - 2017 - Logica Universalis 11 (1):121-138.
    A consequence relation \ is monotonic iff for premise sets \ and conclusion \, if \, \, then \; and non-monotonic if this fails in some instance. More plainly, a consequence relation is monotonic when whatever is entailed by a premise set remains entailed by any of its supersets. From the High Middle Ages through the Early Modern period, consequence in theology is assumed to be monotonic. Concomitantly, to the degree the argument formulated by Anselm at Proslogion 2–4 is taken (...)
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  14.  3
    Computer-Assisted Analysis of the Anderson–Hájek Ontological Controversy.C. Benzmüller, L. Weber & Paleo B. Woltzenlogel - 2017 - Logica Universalis 11 (1):139-151.
    A universal reasoning approach based on shallow semantical embeddings of higher-order modal logics into classical higher-order logic is exemplarily employed to analyze several modern variants of the ontological argument on the computer. Several novel findings are reported which contribute to the clarification of a long-standing dispute between Anderson and Hájek. The technology employed in this work, which to some degree realizes Leibniz’s dream of a characteristica universalis and a calculus ratiocinator for solving philosophical controversies, is ready to be fruitfully adopted (...)
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  15.  12
    Logic and Religion.Jean-Yves Beziau & Ricardo Silvestre - 2017 - Logica Universalis 11 (1):1-12.
    We first start by describing the happening of the 1st World Congress on Logic and Religion. We then explain the motivation for developing the interaction between logic and religion. In a third part we discuss some papers presented at this event published in the present special issue.
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  16.  2
    Thinking Negation in Early Hinduism and Classical Indian Philosophy.Purushottama Bilimoria - 2017 - Logica Universalis 11 (1):13-33.
    A number of different kinds of negation and negation of negation are developed in Indian thought, from ancient religious texts to classical philosophy. The paper explores the Mīmāṃsā, Nyāya, Jaina and Buddhist theorizing on the various forms and permutations of negation, denial, nullity, nothing and nothingness, or emptiness. The main thesis argued for is that in the broad Indic tradition, negation cannot be viewed as a mere classical operator turning the true into the false, nor reduced to the mainstream Boolean (...)
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  17.  3
    A Logical Analysis of the Anselm’s Unum Argumentum.Jean-Pierre Desclés - 2017 - Logica Universalis 11 (1):105-119.
    Anselm of Cantorbery wrote Proslogion, where is formulated the famous ‘Unum argumentum’ about the existence of God. This argument was been disputed and criticized by numerous logicians from an extensional view point. The classical predicate logic is not able to give a formal frame to develop an adequate analysis of this argument. According to us, this argument is not an ontological proof; it analyses the meaning of the “quo nihil maius cogitari posit”, a characterization of God, and establish, by absurd, (...)
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  18.  12
    Leibniz’s Ontological Proof of the Existence of God and the Problem of »Impossible Objects«.Wolfgang Lenzen - 2017 - Logica Universalis 11 (1):85-104.
    The core idea of the ontological proof is to show that the concept of existence is somehow contained in the concept of God, and that therefore God’s existence can be logically derived—without any further assumptions about the external world—from the very idea, or definition, of God. Now, G.W. Leibniz has argued repeatedly that the traditional versions of the ontological proof are not fully conclusive, because they rest on the tacit assumption that the concept of God is possible, i.e. free from (...)
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  19.  6
    Karma Theory, Determinism, Fatalism and Freedom of Will.Ricardo Sousa Silvestre - 2017 - Logica Universalis 11 (1):35-60.
    The so-called theory of karma is one of the distinguishing aspects of Hinduism and other non-Hindu south-Asian traditions. At the same time that the theory can be seen as closely connected with the freedom of will and action that we humans supposedly have, it has many times been said to be determinist and fatalist. The purpose of this paper is to analyze in some deepness the relations that are between the theory of karma on one side and determinism, fatalism and (...)
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