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  1. Leonard Nelson: A Theory of Philosophical Fallacies: Translated by Fernando Leal and David Carus Springer, Cham, Switzerland, 2016, vi + 211 pp. [REVIEW]Andrew Aberdein - 2017 - Argumentation 31 (2):455-461.
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  • Logically-consistent hypothesis testing and the hexagon of oppositions.Julio Michael Stern, Rafael Izbicki, Luis Gustavo Esteves & Rafael Bassi Stern - 2017 - Logic Journal of the IGPL 25 (5):741-757.
    Although logical consistency is desirable in scientific research, standard statistical hypothesis tests are typically logically inconsistent. To address this issue, previous work introduced agnostic hypothesis tests and proved that they can be logically consistent while retaining statistical optimality properties. This article characterizes the credal modalities in agnostic hypothesis tests and uses the hexagon of oppositions to explain the logical relations between these modalities. Geometric solids that are composed of hexagons of oppositions illustrate the conditions for these modalities to be logically (...)
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  • A Triangle of Opposites for Types of Propositions in Aristotelian Logic.Paul Jacoby - 1950 - New Scholasticism 24 (1):32-56.
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  • (1 other version)Logic: Part I.W. E. Johnson - 1921 - Mind 30 (120):448-455.
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  • (1 other version)The syllogism revised.Hans Reichenbach - 1952 - Philosophy of Science 19 (1):1-16.
    The syllogism has often been criticized. Yet the theory of the syllogism cannot be omitted from logic. Even if it were not for its historical significance, its nature as a chapter of class logic assigns to it a place in any presentation of logic.The usual exposition of the theory of the syllogism, however, whether given by the use of the familiar rules of the syllogism, or by the help of diagrams, appears clumsy and lacks the lucidity of modern chapters of (...)
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  • (1 other version)The theory of quaternality.W. H. Gottschalk - 1953 - Journal of Symbolic Logic 18 (3):193-196.
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  • 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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  • Combinatorial Bitstring Semantics for Arbitrary Logical Fragments.Lorenz6 Demey & Hans5 Smessaert - 2018 - Journal of Philosophical Logic 47 (2):325-363.
    Logical geometry systematically studies Aristotelian diagrams, such as the classical square of oppositions and its extensions. These investigations rely heavily on the use of bitstrings, which are compact combinatorial representations of formulas that allow us to quickly determine their Aristotelian relations. However, because of their general nature, bitstrings can be applied to a wide variety of topics in philosophical logic beyond those of logical geometry. Hence, the main aim of this paper is to present a systematic technique for assigning bitstrings (...)
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  • From Blanché’s Hexagonal Organization of Concepts to Formal Concept Analysis and Possibility Theory.Didier Dubois & Henri Prade - 2012 - Logica Universalis 6 (1-2):149-169.
    The paper first introduces a cube of opposition that associates the traditional square of opposition with the dual square obtained by Piaget’s reciprocation. It is then pointed out that Blanché’s extension of the square-of-opposition structure into an conceptual hexagonal structure always relies on an abstract tripartition. Considering quadripartitions leads to organize the 16 binary connectives into a regular tetrahedron. Lastly, the cube of opposition, once interpreted in modal terms, is shown to account for a recent generalization of formal concept analysis, (...)
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  • Structures intellectuelles.Robert Blanché & Georges Davy - 1966 - Les Etudes Philosophiques 21 (4):541-542.
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  • Sur l'opposition des concepts.Robert Blanche - 1953 - Theoria 19 (3):89-130.
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  • Traité de logique.Jean Piaget - 1951 - Les Etudes Philosophiques 6 (1):120-122.
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