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  • Double Negation Semantics for Generalisations of Heyting Algebras
    Stud. Log. (IF 0.467) Pub Date : 2020-05-25
    Rob Arthan, Paulo Oliva

    This paper presents an algebraic framework for investigating proposed translations of classical logic into intuitionistic logic, such as the four negative translations introduced by Kolmogorov, Gödel, Gentzen and Glivenko. We view these as variant semantics and present a semantic formulation of Troelstra’s syntactic criteria for a satisfactory negative translation. We consider how each of the above-mentioned

    更新日期:2020-05-25
  • Kripke Semantics for Intuitionistic Łukasiewicz Logic
    Stud. Log. (IF 0.467) Pub Date : 2020-04-21
    A. Lewis-Smith, P. Oliva, E. Robinson

    This paper proposes a generalization of the Kripke semantics of intuitionistic logic IL appropriate for intuitionistic Łukasiewicz logicIŁL —a logic in the intersection between IL and (classical) Łukasiewicz logic. This generalised Kripke semantics is based on the poset sum construction, used in Bova and Montagna (Theoret Comput Sci 410(12):1143–1158, 2009). to show the decidability (and PSPACE completeness)

    更新日期:2020-04-21
  • A Generalized Proof-Theoretic Approach to Logical Argumentation Based on Hypersequents
    Stud. Log. (IF 0.467) Pub Date : 2020-04-02
    AnneMarie Borg, Christian Straßer, Ofer Arieli

    In this paper we introduce hypersequent-based frameworks for the modelling of defeasible reasoning by means of logic-based argumentation and the induced entailment relations. These structures are an extension of sequent-based argumentation frameworks, in which arguments and the attack relations among them are expressed not only by Gentzen-style sequents, but by more general expressions, called hypersequents

    更新日期:2020-04-02
  • An Algebraic Study of Tense Operators on Nelson Algebras
    Stud. Log. (IF 0.467) Pub Date : 2020-04-02
    A. V. Figallo, G. Pelaitay, J. Sarmiento

    Ewald considered tense operators G, H, F and P on intuitionistic propositional calculus and constructed an intuitionistic tense logic system called IKt. In 2014, Figallo and Pelaitay introduced the variety IKt of IKt-algebras and proved that the IKt system has IKt-algebras as algebraic counterpart. In this paper, we introduce and study the variety of tense Nelson algebras. First, we give some examples

    更新日期:2020-04-02
  • Basic Conditional Reasoning: How Children Mimic Counterfactual Reasoning.
    Stud. Log. Pub Date : 2015-03-03
    Brian Leahy,Eva Rafetseder,Josef Perner

    Children approach counterfactual questions about stories with a reasoning strategy that falls short of adults' Counterfactual Reasoning (CFR). It was dubbed "Basic Conditional Reasoning" (BCR) in Rafetseder et al. (Child Dev 81(1):376-389, 2010). In this paper we provide a characterisation of the differences between BCR and CFR using a distinction between permanent and nonpermanent features of stories

    更新日期:2019-11-01
  • Interpolation in Extensions of First-Order Logic
    Stud. Log. (IF 0.467) Pub Date : 2019-07-06
    Guido Gherardi, Paolo Maffezioli, Eugenio Orlandelli

    We prove a generalization of Maehara’s lemma to show that the extensions of classical and intuitionistic first-order logic with a special type of geometric axioms, called singular geometric axioms, have Craig’s interpolation property. As a corollary, we obtain a direct proof of interpolation for (classical and intuitionistic) first-order logic with identity, as well as interpolation for several mathematical

    更新日期:2019-07-06
  • Rosser Provability and Normal Modal Logics
    Stud. Log. (IF 0.467) Pub Date : 2019-05-16
    Taishi Kurahashi

    In this paper, we investigate Rosser provability predicates whose provability logics are normal modal logics. First, we prove that there exists a Rosser provability predicate whose provability logic is exactly the normal modal logic \(\mathsf{KD}\). Secondly, we introduce a new normal modal logic \(\mathsf{KDR}\) which is a proper extension of \(\mathsf{KD}\), and prove that there exists a Rosser provability

    更新日期:2019-05-16
  • Completeness and Cut-Elimination for First-Order Ideal Paraconsistent Four-Valued Logic
    Stud. Log. (IF 0.467) Pub Date : 2019-05-10
    Norihiro Kamide, Yoni Zohar

    In this study, we prove the completeness and cut-elimination theorems for a first-order extension F4CC of Arieli, Avron, and Zamansky’s ideal paraconsistent four-valued logic known as 4CC. These theorems are proved using Schütte’s method, which can simultaneously prove completeness and cut-elimination.

    更新日期:2019-05-10
  • Inner-Model Reflection Principles
    Stud. Log. (IF 0.467) Pub Date : 2019-04-20
    Neil Barton, Andrés Eduardo Caicedo, Gunter Fuchs, Joel David Hamkins, Jonas Reitz, Ralf Schindler

    We introduce and consider the inner-model reflection principle, which asserts that whenever a statement \(\varphi (a)\) in the first-order language of set theory is true in the set-theoretic universe V, then it is also true in a proper inner model \(W\subsetneq V\). A stronger principle, the ground-model reflection principle, asserts that any such \(\varphi (a)\) true in V is also true in some non-trivial

    更新日期:2019-04-20
  • The Explosion Calculus
    Stud. Log. (IF 0.467) Pub Date : 2019-04-12
    Michael Arndt

    A calculus for classical propositional sequents is introduced that consists of a restricted version of the cut rule and local variants of the logical rules. Employed in the style of proof search, this calculus explodes a given sequent into its elementary structural sequents—the topmost sequents in a derivation thus constructed—which do not contain any logical constants. Some of the properties exhibited

    更新日期:2019-04-12
  • A Refined Interpretation of Intuitionistic Logic by Means of Atomic Polymorphism
    Stud. Log. (IF 0.467) Pub Date : 2019-03-27
    José Espírito Santo, Gilda Ferreira

    We study an alternative embedding of IPC into atomic system F whose translation of proofs is based, not on instantiation overflow, but instead on the admissibility of the elimination rules for disjunction and absurdity (where these connectives are defined according to the Russell–Prawitz translation). As compared to the embedding based on instantiation overflow, the alternative embedding works equally

    更新日期:2019-03-27
  • Simplified Kripke-Style Semantics for Some Normal Modal Logics
    Stud. Log. (IF 0.467) Pub Date : 2019-03-19
    Andrzej Pietruszczak, Mateusz Klonowski, Yaroslav Petrukhin

    Pietruszczak (Bull Sect Log 38(3/4):163–171, 2009. https://doi.org/10.12775/LLP.2009.013) proved that the normal logics \(\mathrm {K45}\), \(\mathrm {KB4}\) (\(=\mathrm {KB5}\)), \(\mathrm {KD45}\) are determined by suitable classes of simplified Kripke frames of the form \(\langle W,A\rangle \), where \(A\subseteq W\). In this paper, we extend this result. Firstly, we show that a modal logic is determined

    更新日期:2019-03-19
  • Bayesian Confirmation or Ordinary Confirmation?
    Stud. Log. (IF 0.467) Pub Date : 2019-03-18
    Yongfeng Yuan

    This article reveals one general scheme for creating counter examples to Bayesian confirmation theory. The reason of the problems is that: in daily life the degree of confirmation is affected not only by probability but also by some non-probabilistic factors, e.g., structural similarity, quantity of evidence, and marginal utility, while Bayesian confirmation theory considers only probabilities to measure

    更新日期:2019-03-18
  • A General Framework for Probabilistic Measures of Coherence
    Stud. Log. (IF 0.467) Pub Date : 2019-02-20
    Michael Schippers, Jakob Koscholke

    Coherence is a property of propositions hanging together or dovetailing with each other. About two decades ago, formal epistemologists started to engage in the project of explicating the seemingly elusive concept of coherence by means of probability theory. Since then, a plethora of coherence measures have been discussed in the literature. In this paper, we propose a general framework for coherence

    更新日期:2019-02-20
  • Simple Axiomatizations for Pretabular Classical Relevance Logics
    Stud. Log. (IF 0.467) Pub Date : 2019-02-19
    Asadollah Fallahi

    KR is Anderson and Belnap’s relevance logic R with the addition of the axiom of EFQ: \( (p \,\, \& \sim p) \rightarrow q\). Since KR is relevantistic as to implication but classical as to negation, it has been dubbed, among many others, a ‘classical relevance logic.’ For KR, there have been known so far just two pretabular normal extensions. For these pretabular logics, no simple axiomatizations have

    更新日期:2019-02-19
  • Normality, Non-contamination and Logical Depth in Classical Natural Deduction
    Stud. Log. (IF 0.467) Pub Date : 2019-02-18
    Marcello D’Agostino, Dov Gabbay, Sanjay Modgil

    In this paper we provide a detailed proof-theoretical analysis of a natural deduction system for classical propositional logic that (i) represents classical proofs in a more natural way than standard Gentzen-style natural deduction, (ii) admits of a simple normalization procedure such that normal proofs enjoy the Weak Subformula Property, (iii) provides the means to prove a Non-contamination Property

    更新日期:2019-02-18
  • Infinite Forcing and the Generic Multiverse
    Stud. Log. (IF 0.467) Pub Date : 2019-02-12
    Giorgio Venturi

    In this article we present a technique for selecting models of set theory that are complete in a model-theoretic sense. Specifically, we will apply Robinson infinite forcing to the collections of models of ZFC obtained by Cohen forcing. This technique will be used to suggest a unified perspective on generic absoluteness principles.

    更新日期:2019-02-12
  • Epimorphisms, Definability and Cardinalities
    Stud. Log. (IF 0.467) Pub Date : 2019-02-07
    T. Moraschini, J. G. Raftery, J. J. Wannenburg

    We characterize, in syntactic terms, the ranges of epimorphisms in an arbitrary class of similar first-order structures (as opposed to an elementary class). This allows us to strengthen a result of Bacsich, as follows: in any prevariety having at most \(\mathfrak {s}\) non-logical symbols and an axiomatization requiring at most \(\mathfrak {m}\) variables, if the epimorphisms into structures with at

    更新日期:2019-02-07
  • Extended Contact Algebras and Internal Connectedness
    Stud. Log. (IF 0.467) Pub Date : 2019-01-24
    Tatyana Ivanova

    The notion of contact algebra is one of the main tools in the region-based theory of space. It is an extension of Boolean algebra with an additional relation C, called contact. Standard models of contact algebras are topological and are the contact algebras of regular closed sets in a given topological space. In such a contact algebra we add the predicate of internal connectedness with the following

    更新日期:2019-01-24
  • Complexity of the Universal Theory of Modal Algebras
    Stud. Log. (IF 0.467) Pub Date : 2019-01-17
    Dmitry Shkatov, Clint J. Van Alten

    We apply the theory of partial algebras, following the approach developed by Van Alten (Theor Comput Sci 501:82–92, 2013), to the study of the computational complexity of universal theories of monotonic and normal modal algebras. We show how the theory of partial algebras can be deployed to obtain co-NP and EXPTIME upper bounds for the universal theories of, respectively, monotonic and normal modal

    更新日期:2019-01-17
  • When is a Schema Not a Schema? On a Remark by Suszko
    Stud. Log. (IF 0.467) Pub Date : 2019-01-02
    Lloyd Humberstone, Allen Hazen

    A 1971 paper by Roman Suszko, ‘Identity Connective and Modality’, claimed that a certain identity-free schema expressed the condition that there are at most two objects in the domain. Section 1 here gives that schema and enough of the background to this claim to explain Suszko’s own interest in it and related conditions—via non-Fregean logic, in which the objects in question are situations and the

    更新日期:2019-01-02
  • Countably Many Weakenings of Belnap–Dunn Logic
    Stud. Log. (IF 0.467) Pub Date : 2018-12-12
    Minghui Ma, Yuanlei Lin

    Every Berman’s variety \(\mathbb {K}_p^q\) which is the subvariety of Ockham algebras defined by the equation \({\sim ^{2p+q}}a = {\sim ^q}a\) (\(p\ge 1\) and \(q\ge 0\)) determines a finitary substitution invariant consequence relation \(\vdash _p^q\). A sequent system \(\mathsf {S}_p^q\) is introduced as an axiomatization of the consequence relation \(\vdash _p^q\). The system \(\mathsf {S}_p^q\)

    更新日期:2018-12-12
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