Logica Universalis

ISSN: 1661-8297

22 found

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  1.  6
    A Modern Rigorous Approach to Stratification in NF/NFU.Tin Adlešić & Vedran Čačić - 2022 - Logica Universalis 16 (3):451-468.
    The main feature of NF/NFU is the notion of stratification, which sets it apart from other set theories. We define stratification and prove constructively that every stratified formula has the least assignment of types. The basic notion of stratification is concerned only with variables, but we extend it to abstraction terms in order to simplify further development. We reflect on nested abstraction terms, proving that they get the expected types. These extensions enable us to check whether some complex formula is (...)
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  2.  1
    Maximum Segments as Natural Deduction Images of Some Cuts.Mirjana Borisavljević - 2022 - Logica Universalis 16 (3):499-533.
    A special kind of maximum cuts in sequent derivations, actual maximum cuts, is defined. It is shown that each actual maximum cut of a sequent derivation makes maximum segments in its natural deduction image, and each maximum segment of a natural deduction derivation makes an actual maximum cut in its sequent image.
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  3.  6
    An Extended Paradefinite Logic Combining Conflation, Paraconsistent Negation, Classical Negation, and Classical Implication: How to Construct Nice Gentzen-Type Sequent Calculi.Norihiro Kamide - 2022 - Logica Universalis 16 (3):389-417.
    In this study, an extended paradefinite logic with classical negation (EPLC), which has the connectives of conflation, paraconsistent negation, classical negation, and classical implication, is introduced as a Gentzen-type sequent calculus. The logic EPLC is regarded as a modification of Arieli, Avron, and Zamansky’s ideal four-valued paradefinite logic (4CC) and as an extension of De and Omori’s extended Belnap–Dunn logic with classical negation (BD+) and Avron’s self-extensional four-valued paradefinite logic (SE4). The completeness, cut-elimination, and decidability theorems for EPLC are proved (...)
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  4.  27
    Frege’s Ontological Diagram Completed.David Makinson - 2022 - Logica Universalis 16 (3):381-387.
    In a letter of 1891, Frege drew a diagram to illustrate his logical ontology. We observe that it omits features that play an important role in his thought on the matter, propose an extension of the diagram to include them, and compare with a diagram of the ontology of current first-order logic.
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  5.  4
    First-Order Logics of Evidence and Truth with Constant and Variable Domains.Abilio Rodrigues & Henrique Antunes - 2022 - Logica Universalis 16 (3):419-449.
    The main aim of this paper is to introduce first-order versions of logics of evidence and truth, together with corresponding sound and complete Kripke semantics with variable and constant domains. According to the intuitive interpretation proposed here, these logics intend to represent possibly inconsistent and incomplete information bases over time. The paper also discusses the connections between Belnap-Dunn’s and da Costa’s approaches to paraconsistency, and argues that the logics of evidence and truth combine them in a very natural way.
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  6.  6
    Natural Deduction for Quantum Logic.K. Tokuo - 2022 - Logica Universalis 16 (3):469-497.
    This paper presents a natural deduction system for orthomodular quantum logic. The system is shown to be provably equivalent to Nishimura’s quantum sequent calculus. Through the Curry–Howard isomorphism, quantum \-calculus is also introduced for which strong normalization property is established.
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  7.  43
    Completeness: From Husserl to Carnap.Víctor Aranda - 2022 - Logica Universalis 16 (1):57-83.
    In his Doppelvortrag, Edmund Husserl introduced two concepts of “definiteness” which have been interpreted as a vindication of his role in the history of completeness. Some commentators defended that the meaning of these notions should be understood as categoricity, while other scholars believed that it is closer to syntactic completeness. A detailed study of the early twentieth-century axiomatics and Husserl’s Doppelvortrag shows, however, that many concepts of completeness were conflated as equivalent. Although “absolute definiteness” was principally an attempt to characterize (...)
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  8.  6
    On the Universality of Atomic and Molecular Logics via Protologics.Guillaume Aucher - 2022 - Logica Universalis 16 (1):285-322.
    After observing that the truth conditions of connectives of non–classical logics are generally defined in terms of formulas of first–order logic, we introduce ‘protologics’, a class of logics whose connectives are defined by arbitrary first–order formulas. Then, we introduce atomic and molecular logics, which are two subclasses of protologics that generalize our gaggle logics and which behave particularly well from a theoretical point of view. We also study and introduce a notion of equi-expressivity between two logics based on different classes (...)
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  9.  8
    A Probabilistic Logic Between $$LPP1$$ L P P 1 and $$LPP2$$ L P P 2.Šejla Dautović - 2022 - Logica Universalis 16 (1):323-333.
    An extension of the propositional probability logic \ given in Ognjanović et al. that allows mixing of propositional formulas and probabilistic formulas is introduced. We describe the corresponding class of models, and we show that the problem of deciding satisfiability is in NP. We provide infinitary axiomatization for the logic and we prove that the axiomatization is sound and strongly complete.
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  10.  6
    A Probabilistic Logic Between $$LPP1$$ L P P 1 and $$LPP2$$ L P P 2.Šejla Dautović - 2022 - Logica Universalis 16 (1-2):323-333.
    An extension of the propositional probability logic \ given in Ognjanović et al. that allows mixing of propositional formulas and probabilistic formulas is introduced. We describe the corresponding class of models, and we show that the problem of deciding satisfiability is in NP. We provide infinitary axiomatization for the logic and we prove that the axiomatization is sound and strongly complete.
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  11.  4
    Analytics vs. Elements.Costas Dimitracopoulos - 2022 - Logica Universalis 16 (1):237-252.
    On the basis of recent work concerning the meaning of the term stoicheion in Aristotle’s Analytics, we strengthen the view that this treatise can be viewed as a precursor of Euclid’s Elements.
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  12.  13
    A Universal Algebraic Set Theory Built on Mereology with Applications.Ioachim Drugus - 2022 - Logica Universalis 16 (1):253-283.
    Category theory is often treated as an algebraic foundation for mathematics, and the widely known algebraization of ZF set theory in terms of this discipline is referenced as “categorical set theory” or “set theory for category theory”. The method of algebraization used in this theory has not been formulated in terms of universal algebra so far. In current paper, a _universal algebraic_ method, i.e. one formulated in terms of universal algebra, is presented and used for algebraization of a ground mereological (...)
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  13.  3
    From Truth Degree Comparison Games to Sequents-of-Relations Calculi for Gödel Logic.Christian Fermüller, Timo Lang & Alexandra Pavlova - 2022 - Logica Universalis 16 (1):221-235.
    We introduce a game for Gödel logic where the players’ interaction stepwise reduces claims about the relative order of truth degrees of complex formulas to atomic truth comparison claims. Using the concept of disjunctive game states this semantic game is lifted to a provability game, where winning strategies correspond to proofs in a sequents-of-relations calculus.
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  14.  7
    On Induction Principles for Partial Orders.Ievgen Ivanov - 2022 - Logica Universalis 16 (1):105-147.
    Various forms of mathematical induction are applicable to domains with some kinds of order. This naturally leads to the questions about the possibility of unification of different inductions and their generalization to wider classes of ordered domains. In the paper we propose a common framework for formulating induction proof principles in various structures and apply it to partially ordered sets. In this framework we propose a fixed induction principle which is indirectly applicable to the class of all posets. In a (...)
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  15.  7
    Tableaux for Logics of Content Relationship and Set-Assignment Semantics.Tomasz Jarmużek & Mateusz Klonowski - 2022 - Logica Universalis 16 (1-3):195-219.
    In the paper, we examine tableau systems for R. Epstein’s logics of content relationship: D (Dependence Logic), DD (Dual Dependence Logic), Eq (Logic of Equality of Content), S (Symmetric Relatedness Logic) and R (Nonsymmetric Relatedness Logic) (cf. Epstein in Philos Stud 36:137–173, 1979, Epstein in Rep. Math. Logic 21:19–34, 1987, Klonowski in Logic Log Philos 30(4):579–629, 2021, Krajewski in J Non Class Logic 8:7–33, 1991). The first tableau systems for those logics were defined by Carnielli. However, his approach has some (...)
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  16.  12
    An Unexpected Boolean Connective.Sérgio Marcelino - 2022 - Logica Universalis 16 (1):85-103.
    We consider a 2-valued non-deterministic connective \({\wedge \!\!\!\!\!\vee }\) defined by the table resulting from the entry-wise union of the tables of conjunction and disjunction. Being half conjunction and half disjunction we named it _platypus_. The value of \({\wedge \!\!\!\!\!\vee }\) is not completely determined by the input, contrasting with usual notion of Boolean connective. We call non-deterministic Boolean connective any connective based on multi-functions over the Boolean set. In this way, non-determinism allows for an extended notion of truth-functional connective. (...)
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  17.  10
    A Methodological Shift in Favor of (Some) Paraconsistency in the Sciences.María del Rosario Martínez-Ordaz - 2022 - Logica Universalis 16 (1):335-354.
    Many have contended that non-classical logicians have failed at providing evidence of paraconsistent logics being applicable in cases of inconsistency toleration in the sciences. With this in mind, my main concern here is methodological. I aim at addressing the question of how should we study and explain cases of inconsistent science, using paraconsistent tools, without ruining into the most common methodological mistakes. My response is divided into two main parts: first, I provide some methodological guidance on how to approach cases (...)
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  18.  20
    A Pragmatic Dissolution of Curry’s Paradox.Rafael Félix Mora Ramirez - 2022 - Logica Universalis 16 (1):149-175.
    Although formal analysis provides us with interesting tools for treating Curry’s paradox, it certainly does not exhaust every possible reading of it. Thus, we suggest that this paradox should be analysed with non-formal tools coming from pragmatics. In this way, using Grice’s logic of conversation, we will see that Curry’s sentence can be reinterpreted as a peculiar conditional sentence implying its own consequent.
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  19.  7
    Modal Definability: Two Commuting Equivalence Relations.Yana Rumenova & Tinko Tinchev - 2022 - Logica Universalis 16 (1):177-194.
    We prove that modal definability with respect to the class of all structures with two commuting equivalence relations is an undecidable problem. The construction used in the proof shows that the same is true for the subclass of all finite structures. For that reason we prove that the first-order theories of these classes are undecidable and reduce the latter problem to the former.
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  20.  4
    Coproduct and Amalgamation of Deductive Systems by Means of Ordered Algebras.Ciro Russo - 2022 - Logica Universalis 16 (1):355-380.
    We propose various methods for combining or amalgamating propositional languages and deductive systems. We make heavy use of quantales and quantale modules in the wake of previous works by the present and other authors. We also describe quite extensively the relationships among the algebraic and order-theoretic constructions and the corresponding ones based on a purely logical approach.
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  21.  3
    Kneale’s Natural Deductions as a Notational Variant of Beth’s Tableaus.Zvonimir Šikić - 2022 - Logica Universalis 16 (1):11-26.
    Gentzen’s singular sequential system of first-order logic was an alternative notation for his system of natural deductions. His multiple sequential system was his symmetric generalization that was more appropriate to classical logic. Beth’s tableaus system was a system that was derived directly from the semantic analysis of connectives and quantifiers. It was soon realized that the Beth’s system and the Gentzen’s multiple system were only notational variants of each other. Kneale’s system of multiple natural deductions was a generalization of Gentzen’s (...)
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  22.  8
    A Formalism to Specify Unambiguous Instructions Inspired by Mīmāṁsā in Computational Settings.Bama Srinivasan & Ranjani Parthasarathi - 2022 - Logica Universalis 16 (1):27-55.
    Mīmāṁsā, an Indian hermeneutics provides an exhaustive methodology to interpret Vedic statements. A formalism namely, Mīmāṁsā Inspired Representation of Actions has already been proposed in a preliminary manner. This paper expands the formalism logically and includes Syntax and Semantics covering Soundness and Completeness. Here, several interpretation techniques from Mīmāṁsā have been considered for formalising the statements. Based on these, instructions that denote actions are categorized into positive and prohibitive unconditional imperatives and conditional imperatives that enjoin reason, temporal action and goal. (...)
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