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  1.  1
    Unification in Pretabular Extensions of S4.Stepan I. Bashmakov - 2021 - Logica Universalis 15 (3):381-397.
    L.L. Maksimova and L. Esakia, V. Meskhi showed that the modal logic \ has exactly 5 pretabular extensions PM1–PM5. In this paper, we study the problem of unification for all given logics. We showed that PM2 and PM3 have finitary, and PM1, PM4, PM5 have unitary types of unification. Complete sets of unifiers in logics are described.
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  2.  10
    Paraconsistent Orbits of Logics.Edelcio G. de Souza, Alexandre Costa-Leite & Diogo H. B. Dias - 2021 - Logica Universalis 15 (3):271-289.
    Some strategies to turn any logic into a paraconsistent system are examined. In the environment of universal logic, we show how to paraconsistentize logics at the abstract level using a transformation in the class of all abstract logics called paraconsistentization by consistent sets. Moreover, by means of the notions of paradeduction and paraconsequence we go on applying the process of changing a logic converting it into a paraconsistent system. We also examine how this transformation can be performed using multideductive abstract (...)
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  3.  11
    Why Make Things Simple When You Can Make Them Complicated? An Appreciation of Lewis Carroll’s Symbolic Logic.Amirouche Moktefi - 2021 - Logica Universalis 15 (3):359-379.
    Lewis Carroll published a system of logic in the symbolic tradition that developed in his time. Carroll’s readers may be puzzled by his system. On the one hand, it introduced innovations, such as his logic notation, his diagrams and his method of trees, that secure Carroll’s place on the path that shaped modern logic. On the other hand, Carroll maintained the existential import of universal affirmative Propositions, a feature that is rather characteristic of traditional logic. The object of this paper (...)
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  4.  14
    On the Origin of Logical Determinism in Babylonia.Andrew Schumann - 2021 - Logica Universalis 15 (3):331-357.
    In this paper, I show that the idea of logical determinism can be traced back from the Old Babylonian period at least. According to this idea, there are some signs which can explain the appearance of all events. These omens demonstrate the will of gods and their power realized through natural forces. As a result, each event either necessarily appears or necessarily disappears. This idea can be examined as the first version of eternalism – the philosophical belief that each temporal (...)
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  5.  20
    Mathematical Perspectives on Liar Paradoxes.José-Luis Usó-Doménech, Josué-Antonio Nescolarde-Selva, Lorena Segura-Abad, Kristian Alonso-Stenberg & Hugh Gash - 2021 - Logica Universalis 15 (3):251-269.
    The liar paradox is a famous and ancient paradox related to logic and philosophy. It shows it is perfectly possible to construct sentences that are correct grammatically and semantically but that cannot be true or false in the traditional sense. In this paper the authors show four approaches to interpreting paradoxes that illustrate the influence of: the levels of language, their belonging to indeterminate compatible propositions or indeterminate propositions, being based on universal antinomy and the theory of dialetheism.
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  6.  16
    Islamic Contradictory Theology . . . Is There Any Such Thing?Abbas Ahsan - 2021 - Logica Universalis 15 (2).
    The application of paraconsistent logics to theological contradictions is a fascinating move. Jc Beall’s (J Anal Theol, 7(1): 400–439, 2019) paper entitled ‘Christ—A Contradiction: A Defense of ‘Contradictory Christology’ is a notable example. Beall proposes a solution to the fundamental problem of Christology. His solution aims at making the case, and defending the viability of, what he has termed, ‘Contradictory Christology’. There are at least two essential components of Beall’s ‘Contradictory Christology’. These include the dogmatic statements of Chalcedon and FDE (...)
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  7.  7
    Bimodal Logic with Contingency and Accident: Bisimulation and Axiomatizations.Jie Fan - 2021 - Logica Universalis 15 (2):123-147.
    In this paper, a suitable notion of bisimulation is proposed for the bimodal logic with contingency and accident. We obtain several van Benthem Characterization Theorems, and axiomatize the bimodal logic over the class of Eulidean frames and over some more restricted classes, showing their strong completeness via a novel strategy, thereby answering two open questions raised in the literature. With the new bisimulation notion, we also correct an error in the expressivity results in the literature.
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  8.  14
    Calculi for Many-Valued Logics.Michael Kaminski & Nissim Francez - 2021 - Logica Universalis 15 (2):193-226.
    We present a number of equivalent calculi for many-valued logics and prove soundness and strong completeness theorems. The calculi are obtained from the truth tables of the logic under consideration in a straightforward manner and there is a natural duality among these calculi. We also prove the cut elimination theorems for the sequent-like systems.
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  9.  8
    On Nonmonotonic Consequence Relations.Alexei Muravitsky - 2021 - Logica Universalis 15 (2):227-249.
    We discuss nonmonotonic reasoning in terms of consequence relations and corresponding operators. Based on the matrix consequence that gives the monotonic case, we define a restricted matrix consequence that illustrates the nonmonotonic case. The latter is a generalization of the relation of logical friendliness introduced by D. Makinson. We prove that any restricted single matrix consequence, although it may be nonmonotonic, is always weakly monotonic and, in the case of a finite matrix, the restricted matrix consequence is very strongly finitary. (...)
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  10.  7
    A Note on Logicality of Generalized Quantifiers.Tin Perkov - 2021 - Logica Universalis 15 (2):149-152.
    This note follows up an earlier paper in which a possibility of defining logical constants within abstract logical frameworks was discussed, by using duals as a general method of applying the idea of invariance under replacement as a criterion for logicality. In the present note, this approach is applied to the discussion on logicality of generalized quantifiers. It is demonstrated that generalized quantifiers are logical constants by this criterion.
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  11.  16
    What is Identical?Marta Vlasáková - 2021 - Logica Universalis 15 (2):153-170.
    Numerical identity is standardly considered to be a relation between things. This means that two things are identical if they are only one thing. It is not only Wittgenstein who finds this claim rather odd. Another possibility is to understand identity as a relation between names which denote the same thing; or as a relation between the senses of those names which are modes of presentation of the same thing. Or identity statements can be considered as expressions of the fact (...)
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  12.  14
    A Reinterpretation of the Semilattice Semantics with Applications.Yale Weiss - 2021 - Logica Universalis 15 (2):171-191.
    In the early 1970s, Alasdair Urquhart proposed a semilattice semantics for relevance logic which he provided with an influential informational interpretation. In this article, I propose a BHK-inspired reinterpretation of the semantics which is related to Kit Fine’s truthmaker semantics. I discuss and compare Urquhart’s and Fine’s semantics and show how simple modifications of Urquhart’s semantics can be used to characterize both full propositional intuitionistic logic and Jankov’s logic. I then present (quasi-)relevant companions for both of these systems. Finally, I (...)
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  13.  12
    Axiomatisations of the Genuine Three-Valued Paraconsistent Logics $$Mathbf {L3AG}$$ L 3 A G and $$Mathbf {L3BG}$$ L 3 B G.Alejandro Hernández-Tello, Miguel Pérez-Gaspar & Verónica Borja Macías - 2021 - Logica Universalis 15 (1):87-121.
    Genuine Paraconsistent logics \ and \ were defined in 2016 by Béziau et al, including only three logical connectives, namely, negation disjunction and conjunction. Afterwards in 2017 Hernández-Tello et al, provide implications for both logics and define the logics \ and \. In this work we continue the study of these logics, providing sound and complete Hilbert-type axiomatic systems for each logic. We prove among other properties that \ and \ satisfy a restricted version of the Substitution Theorem, and that (...)
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  14.  6
    Correspondence Analysis for Some Fragments of Classical Propositional Logic.Yaroslav Petrukhin & Vasilyi Shangin - 2021 - Logica Universalis 15 (1):67-85.
    In the paper, we apply Kooi and Tamminga’s correspondence analysis to some conventional and functionally incomplete fragments of classical propositional logic. In particular, the paper deals with the implication, disjunction, and negation fragments. Additionally, we consider an application of correspondence analysis to some connectiveless fragment with certain basic properties of the logical consequence relation only. As a result of the application, one obtains a sound and complete natural deduction system for any binary extension of each fragment in question. With the (...)
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  15.  70
    Quantified Temporal Alethic Boulesic Doxastic Logic.Daniel Rönnedal - 2021 - Logica Universalis 15 (1):1-65.
    The paper develops a set of quantified temporal alethic boulesic doxastic systems. Every system in this set consists of five parts: a ‘quantified’ part, a temporal part, a modal part, a boulesic part and a doxastic part. There are no systems in the literature that combine all of these branches of logic. Hence, all systems in this paper are new. Every system is defined both semantically and proof-theoretically. The semantic apparatus consists of a kind of $$T \times W$$ T × (...)
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