18 found

Year:

  1.  5
    An Abductive Question-Answer System for the Minimal Logic of Formal Inconsistency $$\mathsf {mbC}$$ mbC.Szymon Chlebowski, Andrzej Gajda & Mariusz Urbański - 2022 - Studia Logica 110 (2):479-509.
    The aim in this paper is to define an Abductive Question-Answer System for the minimal logic of formal inconsistency \. As a proof-theoretical basis we employ the Socratic proofs method. The system produces abductive hypotheses; these are answers to abductive questions concerning derivability of formulas from sets of formulas. We integrated the generation of and the evaluation of hypotheses via constraints of consistency and significance being imposed on the system rules.
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  2.  7
    Sequent-Calculi for Metainferential Logics.Bruno Da Ré & Federico Pailos - 2022 - Studia Logica 110 (2):319-353.
    In recent years, some theorists have argued that the clogics are not only defined by their inferences, but also by their metainferences. In this sense, logics that coincide in their inferences, but not in their metainferences were considered to be different. In this vein, some metainferential logics have been developed, as logics with metainferences of any level, built as hierarchies over known logics, such as \, and \. What is distinctive of these metainferential logics is that they are mixed, i.e. (...)
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  3.  5
    Denotational Semantics for Languages of Epistemic Grounding Based on Prawitz’s Theory of Grounds.Antonio Piccolomini D’Aragona - 2022 - Studia Logica 110 (2):355-403.
    We outline a class of term-languages for epistemic grounding inspired by Prawitz’s theory of grounds. We show how denotation functions can be defined over these languages, relating terms to proof-objects built up of constructive functions. We discuss certain properties that the languages may enjoy both individually and with respect to their expansions. Finally, we provide a ground-theoretic version of Prawitz’s completeness conjecture, and adapt to our framework a refutation of this conjecture due to Piecha and Schroeder-Heister.
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  4.  2
    A Generalization of Monadic n-Valued Łukasiewicz Algebras.Carlos Gallardo & Alicia Ziliani - 2022 - Studia Logica 110 (2):457-478.
    \ of monadic m-generalized Łukasiewicz algebras of order n -algebras), namely a generalization of monadic n-valued Łukasiewicz algebras. In this article, we determine the congruences and we characterized the subdirectly irreducible \-algebras. From this last result we proved that \ is a discriminator variety and as a consequence we characterized the principal congruences. In the last part of this paper we find an immersion of these algebras in a functional algebra and we proved that in the finite case they are (...)
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  5.  6
    A Characterization of Probability-based Dichotomous Belief Revision.Sven Ove Hansson - 2022 - Studia Logica 110 (2):511-543.
    This article investigates the properties of multistate top revision, a dichotomous model of belief revision that is based on an underlying model of probability revision. A proposition is included in the belief set if and only if its probability is either 1 or infinitesimally close to 1. Infinitesimal probabilities are used to keep track of propositions that are currently considered to have negligible probability, so that they are available if future information makes them more plausible. Multistate top revision satisfies a (...)
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  6.  6
    Extending the Lambek Calculus with Classical Negation.Michael Kaminski - 2022 - Studia Logica 110 (2):295-317.
    We present an axiomatization of the non-associative Lambek calculus extended with classical negation for which the frame semantics with the classical interpretation of negation is sound and complete.
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  7.  4
    From Semantic Games to Provability: The Case of Gödel Logic.Alexandra Pavlova, Robert Freiman & Timo Lang - 2022 - Studia Logica 110 (2):429-456.
    We present a semantic game for Gödel logic and its extensions, where the players’ interaction stepwise reduces arbitrary claims about the relative order of truth degrees of complex formulas to atomic ones. The paper builds on a previously developed game for Gödel logic with projection operator in Fermüller et al., Information processing and management of uncertainty in knowledge-based systems, Springer, Cham, 2020, pp. 257–270). This game is extended to cover Gödel logic with involutive negations and constants, and then lifted to (...)
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  8.  8
    The Naturality of Natural Deduction (II): On Atomic Polymorphism and Generalized Propositional Connectives.Paolo Pistone, Luca Tranchini & Mattia Petrolo - 2022 - Studia Logica 110 (2):545-592.
    In a previous paper we investigated the extraction of proof-theoretic properties of natural deduction derivations from their impredicative translation into System F. Our key idea was to introduce an extended equational theory for System F codifying at a syntactic level some properties found in parametric models of polymorphic type theory. A different approach to extract proof-theoretic properties of natural deduction derivations was proposed in a recent series of papers on the basis of an embedding of intuitionistic propositional logic into a (...)
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  9.  2
    Frobenius Quantales, Serre Quantales and the Riemann–Roch Theorem.Wolfgang Rump - 2022 - Studia Logica 110 (2):405-427.
    The Riemann–Roch theorem for algebraic curves is derived from a theorem for Girard quantales. Serre duality is shown to be a quantalic phenomenon. An example provides a Girard quantale satisfying the Riemann–Roch theorem, where the associated curve is non-connected and irreducible.
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  10.  3
    Correction to: Undecidability of First-Order Modal and Intuitionistic Logics with Two Variables and One Monadic Predicate Letter.Mikhail Rybakov & Dmitry Shkatov - 2022 - Studia Logica 110 (2):597-598.
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  11.  15
    Unknown Truths and False Beliefs: Completeness and Expressivity Results for the Neighborhood Semantics.Jie Fan - 2022 - Studia Logica 110 (1):1-45.
    In this article, we study logics of unknown truths and false beliefs under neighborhood semantics. We compare the relative expressivity of the two logics. It turns out that they are incomparable over various classes of neighborhood models, and the combination of the two logics are equally expressive as standard modal logic over any class of neighborhood models. We propose morphisms for each logic, which can help us explore the frame definability problem, show a general soundness and completeness result, and generalize (...)
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  12.  1
    A Categorical Equivalence for Tense Nelson Algebras.Aldo V. Figallo, Jonathan Sermento & Gustavo Pelaitay - 2022 - Studia Logica 110 (1):241-263.
    In this paper we present a category equivalent to that of tense Nelson algebras. The objects in this new category are pairs consisting of an IKt-algebra and a Boolean IKt-congruence and the morphisms are a special kind of IKt-homomorphisms. This categorical equivalence permits understanding tense Nelson algebras in terms of the better–known IKt-algebras.
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  13.  2
    Poset Products as Relational Models.Wesley Fussner - 2022 - Studia Logica 110 (1):95-120.
    We introduce a relational semantics based on poset products, and provide sufficient conditions guaranteeing its soundness and completeness for various substructural logics. We also demonstrate that our relational semantics unifies and generalizes two semantics already appearing in the literature: Aguzzoli, Bianchi, and Marra’s temporal flow semantics for Hájek’s basic logic, and Lewis-Smith, Oliva, and Robinson’s semantics for intuitionistic Łukasiewicz logic. As a consequence of our general theory, we recover the soundness and completeness results of these prior studies in a uniform (...)
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  14.  14
    Idempotent Variations on the Theme of Exclusive Disjunction.L. Humberstone - 2022 - Studia Logica 110 (1):121-163.
    An exclusive disjunction is true when exactly one of the disjuncts is true. In the case of the familiar binary exclusive disjunction, we have a formula occurring as the first disjunct and a formula occurring as the second disjunct, so, if what we have is two formula-tokens of the same formula-type—one formula occurring twice over, that is—the question arises as to whether, when that formula is true, to count the case as one in which exactly one of the disjuncts is (...)
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  15.  5
    On Blass Translation for Leśniewski’s Propositional Ontology and Modal Logics.Takao Inoué - 2022 - Studia Logica 110 (1):265-289.
    In this paper, we shall give another proof of the faithfulness of Blass translation of the propositional fragment \ of Leśniewski’s ontology in the modal logic \ by means of Hintikka formula. And we extend the result to von Wright-type deontic logics, i.e., ten Smiley-Hanson systems of monadic deontic logic. As a result of observing the proofs we shall give general theorems on the faithfulness of B-translation with respect to normal modal logics complete to certain sets of well-known accessibility relations (...)
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  16.  2
    On Inclusions Between Quantified Provability Logics.Taishi Kurahashi - 2022 - Studia Logica 110 (1):165-188.
    We investigate several consequences of inclusion relations between quantified provability logics. Moreover, we give a necessary and sufficient condition for the inclusion relation between quantified provability logics with respect to \ arithmetical interpretations.
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  17.  90
    A Binary Quantifier for Definite Descriptions for Cut Free Free Logics.Nils Kürbis - 2022 - Studia Logica 110 (1):219-239.
    This paper presents rules in sequent calculus for a binary quantifier I to formalise definite descriptions: Ix[F, G] means ‘The F is G’. The rules are suitable to be added to a system of positive free logic. The paper extends the proof of a cut elimination theorem for this system by Indrzejczak by proving the cases for the rules of I. There are also brief comparisons of the present approach to the more common one that formalises definite descriptions with a (...)
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  18.  7
    $$\mathrm {ZF}$$ ZF Between Classicality and Non-classicality.Sourav Tarafder & Giorgio Venturi - 2022 - Studia Logica 110 (1):189-218.
    We present a generalization of the algebra-valued models of \ where the axioms of set theory are not necessarily mapped to the top element of an algebra, but may get intermediate values, in a set of designated values. Under this generalization there are many algebras which are neither Boolean, nor Heyting, but that still validate \.
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