Logica Universalis

ISSN: 1661-8297

22 found

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  1.  6
    Unified Deductive Systems: An Outline.Alex Citkin - 2023 - Logica Universalis 17 (4):483-509.
    Our goal is to develop a syntactical apparatus for propositional logics in which the accepted and rejected propositions have the same status and obeying treated in the same way. The suggested approach is based on the ideas of Łukasiewicz used for the classical logic and in addition, it includes the use of multiple conclusion rules. More precisely, a consequence relation is defined on a set of statements of forms “proposition _A_ is accepted” and “proposition _A_ is rejected”, where _A_ is (...)
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  2.  5
    Preface to the Rejection Special Issue.Alex Citkin & Alexei Muravitsky - 2023 - Logica Universalis 17 (4):405-410.
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  3.  4
    Rejection: A Historico-Epistemological View.Alexei Muravitsky - 2023 - Logica Universalis 17 (4):461-482.
    We seek to trace how the assertion–rejection dichotomy arose, as well as in what forms it was realized in logical discourse. From this viewpoint, we observe the approaches to the concept of rejection by Łukasiewicz, Carnap, and Słupecki. We also explore the controversy between rejection and negation. Our main observation is that for a correct understanding of this dichotomy, it is necessary to distinguish between the object language and metalanguages of different levels.
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  4.  3
    On Consequence and Rejection as Operators.Alexei Muravitsky - 2023 - Logica Universalis 17 (4):443-460.
    This paper is devoted to the concepts of consequence and rejection, formulated as operators on a nonempty set of sentences, which may initially be unstructured. One of the issues that we pay attention to is the “cyclicity” of these concepts when they are defined one through the other. In addition, we explore this cyclicity, when the set of all sentences acquires some structure, or we can assume some structure of sentences in the sense that the operation of substitution can be (...)
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  5.  12
    Complementary Proof Nets for Classical Logic.Gabriele Pulcini & Achille C. Varzi - 2023 - Logica Universalis 17 (4):411-432.
    A complementary system for a given logic is a proof system whose theorems are exactly the formulas that are not valid according to the logic in question. This article is a contribution to the complementary proof theory of classical propositional logic. In particular, we present a complementary proof-net system, $$\textsf{CPN}$$ CPN, that is sound and complete with respect to the set of all classically invalid (one-side) sequents. We also show that cut elimination in $$\textsf{CPN}$$ CPN enjoys strong normalization along with (...)
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  6.  1
    Finite Tree-Countermodels via Refutation Systems in Extensions of Positive Logic with Strong Negation.Tomasz Skura - 2023 - Logica Universalis 17 (4):433-441.
    A sufficient condition for an extension of positive logic with strong negation to be characterized by a class of finite trees is given.
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  7.  51
    Operator Counterparts of Types of Reasoning.Urszula Wybraniec-Skardowska - 2023 - Logica Universalis 17 (4):511-528.
    Logical and philosophical literature provides different classifications of reasoning. In the Polish literature on the subject, for instance, there are three popular ones accepted by representatives of the Lvov-Warsaw School: Jan Łukasiewicz, Tadeusz Czeżowski and Kazimierz Ajdukiewicz (Ajdukiewicz in Logika pragmatyczna [Pragmatic Logic]. PWN, Warsaw (1965, 2nd ed. 1974). Translated as: Pragmatic Logic. Reidel & PWN, Dordrecht, 1975). The author of this paper, having modified those classifications, distinguished the following types of reasoning: (1) deductive and (2) non-deductive, and additionally two (...)
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  8.  3
    Measuring Inconsistency in Generalized Propositional Logic Extended with Nonunary Operators.John Grant - 2023 - Logica Universalis 17 (3):373-404.
    As consistency is such an important topic in logic, researchers have for a long time investigated how to attain and maintain it. But consistency can also be studied from the point of view of its opposite, inconsistency. The problem with inconsistency in classical logic is that by the principle of explosion a single inconsistency leads to triviality. Paraconsistent logics were introduced to get around this problem by defining logics in such a way that the explosion principle does not apply to (...)
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  9.  12
    Ultravaluations and their Applications in $$\textsf{CPL}$$.Krzysztof A. Krawczyk & Bożena Piȩta - 2023 - Logica Universalis 17 (3):259-267.
    This paper introduces the construct of an ultravaluation inspired by the well-known ultraproduct. Basic properties and exemplary applications of this notion are shown: for compactness and definability theorems. We also use ultravaluations to check failure of compactness and undefinability.
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  10.  8
    Rooted Hypersequent Calculus for Modal Logic S5.Hamzeh Mohammadi & Mojtaba Aghaei - 2023 - Logica Universalis 17 (3):269-295.
    We present a rooted hypersequent calculus for modal propositional logic S5. We show that all rules of this calculus are invertible and that the rules of weakening, contraction, and cut are admissible. Soundness and completeness are established as well.
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  11.  12
    A Study of the Metatheory of Assertoric Syllogistic.Maristela Rocha - 2023 - Logica Universalis 17 (3):347-371.
    We show how a semantics based on Aristotle’s texts and ecthetic proofs can be reconstructed. All truth conditions are given by means of set inclusion. Perfect syllogisms reveal to be valid arguments that deserve a validity proof. It turns out of these proofs that transitivity of set inclusion is the necessary and sufficient condition for the validity and perfection of a syllogism. The proofs of validity for imperfect syllogisms are direct proofs without conversion in a calculus of natural deduction. Transitivity (...)
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  12.  10
    Epistemic Logics with Quantification Over Epistemic Operators: Decidability and Expressiveness.Gennady Shtakser - 2023 - Logica Universalis 17 (3):297-330.
    The optimal balance between decidability and expressiveness is a big problem of logical systems, in particular, of quantified epistemic logics (QELs). On the one hand, decidability is a very significant characteristic of logics that allows us to use such logics in the framework of artificial intelligence. On the other hand, QELs have important expressive capabilities that should not be lost when we construct decidable fragments of these logics. QELs are known to be much more expressive than first-order logics. One important (...)
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  13.  5
    On Rearrangement Inequalities for Triangular Norms and Co-norms in Multi-valued Logic.Chai Wah Wu - 2023 - Logica Universalis 17 (3):331-346.
    The rearrangement inequality states that the sum of products of permutations of 2 sequences of real numbers are maximized when the terms are similarly ordered and minimized when the terms are ordered in opposite order. We show that similar inequalities exist in algebras of multi-valued logic when the multiplication and addition operations are replaced with various T-norms and T-conorms respectively. For instance, we show that the rearrangement inequality holds when the T-norms and T-conorms are derived from Archimedean copulas.
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  14.  5
    An Intensional Formalization of Generic Statements.Hugolin Bergier - 2023 - Logica Universalis 17 (2):139-160.
    A statement is generic if it expresses a generalization about the members of a kind, as in, ’Pear trees blossom in May,’ or, ’Birds lay egg’. In classical logic, generic statements are formalized as universally quantified conditionals: ‘For all x, if..., then....’ We want to argue that such a logical interpretation fails to capture the intensional character of generic statements because it cannot express the generic statement as a simple proposition in Aristotle’s sense, i.e., a proposition containing only one single (...)
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  15.  12
    A Dialectic Contra-Classical Logic.Nissim Francez - 2023 - Logica Universalis 17 (2):221-229.
    The paper presents a contra-classical dialectic logic, inspired and motivated by Hegel s dialectics. Its axiom schemes are 0.1 Thus, in a sense, this dialectic logic is a kind of “mirror image“ of connexive logic. The informal interpretation of ‘ $$\rightarrow $$ ’ emerging from the above four axiom schemes is not of a conditional (or implication); rather, it is the relation of determination in the presence of truth-value gaps: $$\varphi \rightarrow \psi $$ is read as $$\varphi $$ determines $$\psi (...)
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  16.  8
    Probability Logics for Reasoning About Quantum Observations.Angelina Ilić Stepić, Zoran Ognjanović & Aleksandar Perović - 2023 - Logica Universalis 17 (2):175-219.
    In this paper we present two families of probability logics (denoted _QLP_ and \(QLP^{ORT}\) ) suitable for reasoning about quantum observations. Assume that \(\alpha \) means “O = a”. The notion of measuring of an observable _O_ can be expressed using formulas of the form \(\square \lozenge \alpha \) which intuitively means “if we measure _O_ we obtain \(\alpha \) ”. In that way, instead of non-distributive structures (i.e., non-distributive lattices), it is possible to relay on classical logic extended with (...)
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  17.  6
    Revising the Elenchus via Belief Revision.Ekaterina Kubyshkina & Mattia Petrolo - 2023 - Logica Universalis 17 (2):231-258.
    Vlastos’ famous characterization of the Socratic elenchus focuses on two main aspects of this method: its epistemic roots and its dialogical nature. Our aim is to lay the groundwork to formally capture this characterization. To do so, first, we outline an epistemic framework in which the elenchus can be inscribed. More precisely, we focus our analysis on the passage from unconscious ignorance to conscious (or Socratic) ignorance and provide new insights about the epistemic outcome of an elenctic argument. Secondly, from (...)
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  18.  51
    The Decision Problem for Effective Procedures.Nathan Salmón - 2023 - Logica Universalis 17 (2):161-174.
    The “somewhat vague, intuitive” notion from computability theory of an effective procedure (method) or algorithm can be fairly precisely defined even if it is not sufficiently formal and precise to belong to mathematics proper (in a narrow sense)—and even if (as many have asserted) for that reason the Church–Turing thesis is unprovable. It is proved logically that the class of effective procedures is not decidable, i.e., that there is no effective procedure for ascertaining whether a given procedure is effective. This (...)
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  19.  29
    Abstract Categorical Logic.Marc Aiguier & Isabelle Bloch - 2023 - Logica Universalis 17 (1):23-67.
    We present in this paper an abstract categorical logic based on an abstraction of quantifier. More precisely, the proposed logic is abstract because no structural constraints are imposed on models (semantics free). By contrast, formulas are inductively defined from an abstraction both of atomic formulas and of quantifiers. In this sense, the proposed approach differs from other works interested in formalizing the notion of abstract logic and of which the closest to our approach are the institutions, which in addition to (...)
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  20.  19
    Games and Lindström Theorems.Cheng Liao - 2023 - Logica Universalis 17 (1):1-21.
    The Ehrenfeucht–Fraïsse game for a logic usually provides an intuitive characterizarion of its expressive power while in abstract model theory, logics are compared by their expressive powers. In this paper, I explore this connection in details by proving a general Lindström theorem for logics which have certain types of Ehrenfeucht–Fraïsse games. The results generalize and uniform some known results and may be applied to get new Lindström theorems for logics.
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  21.  8
    Lindenbaum-Type Logical Structures.Sayantan Roy, Sankha S. Basu & Mihir K. Chakraborty - 2023 - Logica Universalis 17 (1):69-102.
    In this paper, we study some classes of logical structures from the universal logic standpoint, viz., those of the Tarski- and the Lindenbaum-types. The characterization theorems for the Tarski- and two of the four different Lindenbaum-type logical structures have been proved as well. The separations between the five classes of logical structures, viz., the four Lindenbaum-types and the Tarski-type have been established via examples. Finally, we study the logical structures that are of both Tarski- and a Lindenbaum-type, show their separations, (...)
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  22.  5
    Negative Predication and Distinctness.Bartosz Więckowski - 2023 - Logica Universalis 17 (1):103-138.
    It is argued that the intuitionistic conception of negation as implication of absurdity is inadequate for the proof-theoretic semantic analysis of negative predication and distinctness. Instead, it is suggested to construe negative predication proof-theoretically as subatomic derivation failure, and to define distinctness—understood as a qualified notion—by appeal to negative predication. This proposal is elaborated in terms of intuitionistic bipredicational subatomic natural deduction systems. It is shown that derivations in these systems normalize and that normal derivations have the subexpression (incl. subformula) (...)
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