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  • Lambek Calculus with Conjugates
    Stud. Log. (IF 0.674) Pub Date : 2020-07-28
    Igor Sedlár, Andrew Tedder

    We study an expansion of the Distributive Non-associative Lambek Calculus with conjugates of the Lambek product operator and residuals of those conjugates. The resulting logic is well-motivated, under-investigated and difficult to tackle. We prove completeness for some of its fragments and establish that it is decidable. Completeness of the logic is an open problem; some difficulties with applying

    更新日期:2020-07-28
  • Proof-Theoretic Analysis of the Logics of Agency: The Deliberative STIT
    Stud. Log. (IF 0.674) Pub Date : 2020-07-15
    S. Negri, E. Pavlović

    A sequent calculus methodology for systems of agency based on branching-time frames with agents and choices is proposed, starting with a complete and cut-free system for multi-agent deliberative STIT; the methodology allows a transparent justification of the rules, good structural properties, analyticity, direct completeness and decidability proofs.

    更新日期:2020-07-15
  • Non-classical Models of ZF
    Stud. Log. (IF 0.674) Pub Date : 2020-07-09
    S. Jockwich Martinez, G. Venturi

    This paper contributes to the generalization of lattice-valued models of set theory to non-classical contexts. First, we show that there are infinitely many complete bounded distributive lattices, which are neither Boolean nor Heyting algebra, but are able to validate the negation-free fragment of \(\mathsf {ZF}\). Then, we build lattice-valued models of full \(\mathsf {ZF}\), whose internal logic

    更新日期:2020-07-09
  • The Entropy-Limit (Conjecture) for $$\Sigma _2$$ Σ 2 -Premisses
    Stud. Log. (IF 0.674) Pub Date : 2020-06-30
    Jürgen Landes

    The application of the maximum entropy principle to determine probabilities on finite domains is well-understood. Its application to infinite domains still lacks a well-studied comprehensive approach. There are two different strategies for applying the maximum entropy principle on first-order predicate languages: (i) applying it to finite sublanguages and taking a limit; (ii) comparing finite entropies

    更新日期:2020-06-30
  • Correspondence, Canonicity, and Model Theory for Monotonic Modal Logics
    Stud. Log. (IF 0.674) Pub Date : 2020-06-24
    Kentarô Yamamoto

    We investigate the role of coalgebraic predicate logic, a logic for neighborhood frames first proposed by Chang, in the study of monotonic modal logics. We prove analogues of the Goldblatt–Thomason theorem and Fine’s canonicity theorem for classes of monotonic neighborhood frames closed under elementary equivalence in coalgebraic predicate logic. The elementary equivalence here can be relativized to

    更新日期:2020-06-24
  • Axiomatization of Crisp Gödel Modal Logic
    Stud. Log. (IF 0.674) Pub Date : 2020-06-08
    Ricardo Oscar Rodriguez, Amanda Vidal

    In this paper we consider the modal logic with both \(\Box \) and \(\Diamond \) arising from Kripke models with a crisp accessibility and whose propositions are valued over the standard Gödel algebra \([0,1]_G\). We provide an axiomatic system extending the one from Caicedo and Rodriguez (J Logic Comput 25(1):37–55, 2015) for models with a valued accessibility with Dunn axiom from positive modal logics

    更新日期:2020-06-08
  • Double Negation Semantics for Generalisations of Heyting Algebras
    Stud. Log. (IF 0.674) 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 0.674) 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 0.674) 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 0.674) 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
  • A Proof Theory for the Logic of Provability in True Arithmetic
    Stud. Log. (IF 0.674) Pub Date : 2019-12-19
    Hirohiko Kushida

    In a classical 1976 paper, Solovay proved the arithmetical completeness of the modal logic GL; provability of a formula in GL coincides with provability of its arithmetical interpretations of it in Peano Arithmetic. In that paper, he also provided an axiomatic system GLS and proved arithmetical completeness for GLS; provability of a formula in GLS coincides with truth of its arithmetical interpretations

    更新日期:2019-12-19
  • Basic Conditional Reasoning: How Children Mimic Counterfactual Reasoning.
    Stud. Log. (IF 0.674) 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
  • Herzberger’s Limit Rule with Labelled Sequent Calculus
    Stud. Log. (IF 0.674) Pub Date : 2019-10-24
    Andreas Fjellstad

    Inspired by recent work on proof theory for modal logic, this paper develops a cut-free labelled sequent calculus obtained by imitating Herzberger’s limit rule for revision sequences as a clause in a possible world semantics. With the help of two completeness theorems, one between the labelled sequent calculus and the corresponding possible world semantics, and one between the axiomatic theory of truth

    更新日期:2019-10-24
  • Proof Theory of Paraconsistent Weak Kleene Logic
    Stud. Log. (IF 0.674) Pub Date : 2019-10-24
    Francesco Paoli, Michele Pra Baldi

    Paraconsistent Weak Kleene Logic (PWK) is the 3-valued propositional logic defined on the weak Kleene tables and with two designated values. Most of the existing proof systems for PWK are characterised by the presence of linguistic restrictions on some of their rules. This feature can be seen as a shortcoming. We provide a cut-free calculus (a hybrid between a natural deduction calculus and a sequent

    更新日期:2019-10-24
  • Satisfiability is False Intuitionistically: A Question from Dana Scott
    Stud. Log. (IF 0.674) Pub Date : 2019-10-14
    Charles McCarty

    Satisfiability or Sat\(^{1}\) is the metatheoretic statement Every formally intuitionistically consistent set of first-order sentences has a model. The models in question are the Tarskian relational structures familiar from standard first-order model theory (Chang and Keisler in Model theory, 3rd edn, Dover Publications Inc., Mineola, 2012), but here treated within intuitionistic metamathematics. We

    更新日期:2019-10-14
  • L -effect Algebras
    Stud. Log. (IF 0.674) Pub Date : 2019-08-24
    Wolfgang Rump, Xia Zhang

    L-effect algebras are introduced as a class of L-algebras which specialize to all known generalizations of effect algebras with a \(\wedge \)-semilattice structure. Moreover, L-effect algebras X arise in connection with quantum sets and Frobenius algebras. The translates of X in the self-similar closure S(X) form a covering, and the structure of X is shown to be equivalent to the compatibility of overlapping

    更新日期:2019-08-24
  • Justification Logic with Confidence
    Stud. Log. (IF 0.674) Pub Date : 2019-08-21
    Ted Shear, John Quiggin

    Justification logics are a family of modal logics whose non-normal modalities are parametrised by a type-theoretic calculus of terms. The first justification logic was developed by Sergei Artemov to provide an explicit modal logic for arithmetical provability in which these terms were taken to pick out proofs. But, justification logics have been given various other interpretations as well. In this

    更新日期:2019-08-21
  • A Note on Strong Axiomatization of Gödel Justification Logic
    Stud. Log. (IF 0.674) Pub Date : 2019-08-01
    Nicholas Pischke

    Justification logics are special kinds of modal logics which provide a framework for reasoning about epistemic justifications. For this, they extend classical boolean propositional logic by a family of necessity-style modal operators “t : ”, indexed over t by a corresponding set of justification terms, which thus explicitly encode the justification for the necessity assertion in the syntax. With these

    更新日期:2019-08-01
  • Proof Theory for Positive Logic with Weak Negation
    Stud. Log. (IF 0.674) Pub Date : 2019-07-24
    Marta Bílková, Almudena Colacito

    Proof-theoretic methods are developed for subsystems of Johansson’s logic obtained by extending the positive fragment of intuitionistic logic with weak negations. These methods are exploited to establish properties of the logical systems. In particular, cut-free complete sequent calculi are introduced and used to provide a proof of the fact that the systems satisfy the Craig interpolation property

    更新日期:2019-07-24
  • Interpolation in Extensions of First-Order Logic
    Stud. Log. (IF 0.674) 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 0.674) 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 0.674) 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 0.674) 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 0.674) 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 0.674) 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 0.674) 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 0.674) 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 0.674) 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 0.674) 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 0.674) 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 0.674) 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 0.674) 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 0.674) 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 0.674) 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 0.674) 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 0.674) 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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