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  1.  9
    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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  2.  5
    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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  3.  5
    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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  4.  2
    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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  5.  2
    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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  6.  9
    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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  7.  3
    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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  8.  2
    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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  9.  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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  10.  2
    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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  11.  3
    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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  12.  4
    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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  13.  3
    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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