Year:

  1.  8
    Beyond Logical Pluralism and Logical Monism.Pavel Arazim - 2020 - Logica Universalis 14 (2):151-174.
    Logical pluralism as a thesis that more than one logic is correct seems very plausible for two basic reasons. First, there are so many logical systems on the market today. And it is unclear how we should decide which of them gets the logical rules right. On the other hand, logical monism as the opposite thesis still seems plausible, as well, because of normativity of logic. An approach which would manage to bring a synthesis of both logical pluralism and logical (...)
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  2.  13
    Positive Amalgamation.Mohammed Belkasmi - 2020 - Logica Universalis 14 (2):243-258.
    We study the amalgamation property in positive logic, where we shed light on some connections between the amalgamation property, Robinson theories, model-complete theories and the Hausdorff property.
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  3.  5
    Introducing H, an Institution-Based Formal Specification and Verification Language.Răzvan Diaconescu - 2020 - Logica Universalis 14 (2):259-277.
    This is a short survey on the development of the formal specification and verification language H with emphasis on the scientific part. H is a modern highly expressive language solidly based upon advanced mathematical theories such as the internalisation of Kripke semantics within institution theory.
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  4.  4
    Correction to: Some Restricted Lindenbaum Theorems Equivalent to the Axiom of Choice.David W. Miller - 2020 - Logica Universalis 14 (2):279-279.
    The publisher would like to confirm that the author owns the copyright of the article.
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  5.  6
    Essential Structure of Proofs as a Measure of Complexity.Jaime Ramos, João Rasga & Cristina Sernadas - 2020 - Logica Universalis 14 (2):209-242.
    The essential structure of proofs is proposed as the basis for a measure of complexity of formulas in FOL. The motivating idea was the recognition that distinct theorems can have the same derivation modulo some non essential details. Hence the difficulty in proving them is identical and so their complexity should be the same. We propose a notion of complexity of formulas capturing this property. With this purpose, we introduce the notions of schema calculus, schema derivation and description complexity of (...)
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  6.  2
    Eigenlogic in the Spirit of George Boole.Zeno Toffano - 2020 - Logica Universalis 14 (2):175-207.
    This work presents an operational and geometric approach to logic. It starts from the multilinear elective decomposition of binary logical functions in the original form introduced by George Boole. A justification on historical grounds is presented bridging Boole’s theory and the use of his arithmetical logical functions with the axioms of Boolean algebra using sets and quantum logic. It is shown that this algebraic polynomial formulation can be naturally extended to operators in finite vector spaces. Logical operators will appear as (...)
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  7.  13
    The Cretan Square.Jean-Yves Beziau & Jens Lemanski - 2020 - Logica Universalis 14 (1):1-5.
    This special issue is related to the 6th World Congress on the Square of Opposition which took place at the Orthodox Academy of Crete in November 2018. In this introductory paper we explain the context of the event and the topics discussed.
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  8.  6
    Structures of Opposition and Comparisons: Boolean and Gradual Cases.Didier Dubois, Henri Prade & Agnès Rico - 2020 - Logica Universalis 14 (1):115-149.
    This paper first investigates logical characterizations of different structures of opposition that extend the square of opposition in a way or in another. Blanché’s hexagon of opposition is based on three disjoint sets. There are at least two meaningful cubes of opposition, proposed respectively by two of the authors and by Moretti, and pioneered by philosophers such as J. N. Keynes, W. E. Johnson, for the former, and H. Reichenbach for the latter. These cubes exhibit four and six squares of (...)
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  9.  15
    Kant’s Antinomies of Pure Reason and the ‘Hexagon of Predicate Negation’.Peter McLaughlin & Oliver Schlaudt - 2020 - Logica Universalis 14 (1):51-67.
    Based on an analysis of the category of “infinite judgments” in Kant, we will introduce the logical hexagon of predicate negation. This hexagon allows us to visualize in a single diagram the general structure of both Kant’s solution of the antinomies of pure reason and his argument in favor of Transcendental Idealism.
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  10.  12
    A Cube of Opposition for Predicate Logic.Jørgen Fischer Nilsson - 2020 - Logica Universalis 14 (1):103-114.
    The traditional square of opposition is generalized and extended to a cube of opposition covering and conveniently visualizing inter-sentential oppositions in relational syllogistic logic with the usual syllogistic logic sentences obtained as special cases. The cube comes about by considering Frege–Russell’s quantifier predicate logic with one relation comprising categorical syllogistic sentence forms. The relationships to Buridan’s octagon, to Aristotelian modal logic, and to Klein’s 4-group are discussed.GraphicThe photo shows a prototype sculpture for the cube.
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  11.  2
    Swyneshed, Aristotle and the Rule of Contradictory Pairs.Stephen Read - 2020 - Logica Universalis 14 (1):27-50.
    Roger Swyneshed, in his treatise on insolubles, dating from the early 1330s, drew three notorious corollaries from his solution. The third states that there is a contradictory pair of propositions both of which are false. This appears to contradict what Whitaker, in his iconoclastic reading of Aristotle’s De Interpretatione, dubbed “The Rule of Contradictory Pairs”, which requires that in every such pair, one must be true and the other false. Whitaker argued that, immediately after defining the notion of a contradictory (...)
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  12.  5
    Existential Import, Aristotelian Logic, and its Generalizations.Corina Strößner - 2020 - Logica Universalis 14 (1):69-102.
    The paper uses the theory of generalized quantifiers to discuss existential import and its implications for Aristotelian logic, namely the square of opposition, conversions and the assertoric syllogistic, as well as for more recent generalizations to intermediate quantifiers like “most”. While this is a systematic discussion of the semantic background one should assume in order to obtain the inferences and oppositions Aristotle proposed, it also sheds some light on the interpretation of his writings. Moreover by applying tools from modern formal (...)
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  13.  14
    On the Historical Transformations of the Square of Opposition as Semiotic Object.Ioannis M. Vandoulakis & Tatiana Yu Denisova - 2020 - Logica Universalis 14 (1):7-26.
    In this paper, we would show how the logical object “square of opposition”, viewed as semiotic object, has been historically transformed since its appearance in Aristotle’s texts until the works of Vasiliev. These transformations were accompanied each time with a new understanding and interpretation of Aristotle’s original text and, in the last case, with a transformation of its geometric configuration. The initial textual codification of the theory of opposition in Aristotle’s works is transformed into a diagrammatic one, based on a (...)
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