46 found

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Forthcoming articles
  1. Joongol Kim (forthcoming). A Logical Foundation of Arithmetic. Studia Logica:1-32.
    The aim of this paper is to shed new light on the logical roots of arithmetic by presenting a logical framework (ALA) that takes seriously ordinary locutions like ‘at least n Fs’, ‘n more Fs than Gs’ and ‘n times as many Fs as Gs’, instead of paraphrasing them away in terms of expressions of the form ‘the number of Fs’. It will be shown that the basic concepts of arithmetic can be intuitively defined in the language of ALA, and (...)
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  2. M. Baaz & A. Leitsch (forthcoming). Cut-Elimination: Syntax and Semantics. Studia Logica:1-28.
    In this paper we first give a survey of reductive cut-elimination methods in classical logic. In particular we describe the methods of Gentzen and Schütte-Tait from the abstract point of view of proof reduction. We also present the method CERES (cut-elimination by resolution) which we classify as a semi-semantic method. In a further section we describe the so-called semantic methods. In the second part of the paper we carry the proof analysis further by generalizing the CERES method to CERESD (this (...)
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  3. Ermanno Bencivenga (forthcoming). Jaśkowski's Universally Free Logic. Studia Logica:1-8.
    A universally free logic is a system of quantification theory, with or without identity, whose theses remain logically true if (a) the domain of quantification is empty and (b) some of the singular terms present in the language do not denote existing objects. In the West, (inclusive) logics satisfying (a) and (free) ones satisfying (b) were developed starting in the 1950s. But Stanisław Jaśkowski preceded all this work by some twenty years: his paper “On the Rules of Supposition in Formal (...)
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  4. Agata Ciabattoni, Revantha Ramanayake & Heinrich Wansing (forthcoming). Hypersequent and Display Calculi – a Unified Perspective. Studia Logica:1-50.
    This paper presents an overview of the methods of hypersequents and display sequents in the proof theory of non-classical logics. In contrast with existing surveys dedicated to hypersequent calculi or to display calculi, our aim is to provide a unified perspective on these two formalisms highlighting their differences and similarities and discussing applications and recent results connecting and comparing them.
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  5. Allen P. Hazen & Francis Jeffry Pelletier (forthcoming). Gentzen and Jaśkowski Natural Deduction: Fundamentally Similar but Importantly Different. Studia Logica:1-40.
    Gentzen’s and Jaśkowski’s formulations of natural deduction are logically equivalent in the normal sense of those words. However, Gentzen’s formulation more straightforwardly lends itself both to a normalization theorem and to a theory of “meaning” for connectives (which leads to a view of semantics called ‘inferentialism’). The present paper investigates cases where Jaskowski’s formulation seems better suited. These cases range from the phenomenology and epistemology of proof construction to the ways to incorporate novel logical connectives into the language. We close (...)
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  6. Andrzej Indrzejczak (forthcoming). Introduction. Studia Logica:1-4.
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  7. Peter Schroeder-Heister (forthcoming). The Calculus of Higher-Level Rules, Propositional Quantification, and the Foundational Approach to Proof-Theoretic Harmony. Studia Logica:1-32.
    We present our calculus of higher-level rules, extended with propositional quantification within rules. This makes it possible to present general schemas for introduction and elimination rules for arbitrary propositional operators and to define what it means that introductions and eliminations are in harmony with each other. This definition does not presuppose any logical system, but is formulated in terms of rules themselves. We therefore speak of a foundational (rather than reductive) account of proof-theoretic harmony. With every set of introduction rules (...)
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  8. Jan von Plato (forthcoming). From Axiomatic Logic to Natural Deduction. Studia Logica:1-18.
    Recently discovered documents have shown how Gentzen had arrived at the final form of natural deduction, namely by trying out a great number of alternative formulations. What led him to natural deduction in the first place, other than the general idea of studying “mathematical inference as it appears in practice,” is not indicated anywhere in his publications or preserved manuscripts. It is suggested that formal work in axiomatic logic lies behind the birth of Gentzen’s natural deduction, rather than any single (...)
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  9. William Young (forthcoming). From Interior Algebras to Unital ℓ-Groups: A Unifying Treatment of Modal Residuated Lattices. Studia Logica:1-22.
    Much work has been done on specific instances of residuated lattices with modal operators (either nuclei or conuclei). In this paper, we develop a general framework that subsumes three important classes of modal residuated lattices: interior algebras, Abelian ℓ-groups with conuclei, and negative cones of ℓ-groups with nuclei. We then use this framework to obtain results about these three cases simultaneously. In particular, we show that a categorical equivalence exists in each of these cases. The approach used here emphasizes the (...)
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  10. A. M. Suardiaz A. Quantifier (forthcoming). M. Abad Varieties of Three-Valued. Studia Logica.
     
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  11. Peter Aczel, Benno van den Berg, Johan Granström & Peter Schuster (forthcoming). Are There Enough Injective Sets? Studia Logica.
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  12. H. Arlo-Costa (forthcoming). First-Order Modal Logic', to Appear in V. Hendricks & SA Pedersen, Eds.,'40 Years of Possible Worlds', Special Issue Of. Studia Logica.
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  13. T. S. Blyth, Jie Fang & Lei-bo Wang (forthcoming). De Morgan Algebras with a Quasi-Stone Operator. Studia Logica:1-16.
    We investigate the class of those algebras (L; º, *) in which (L; º) is a de Morgan algebra, (L; *) is a quasi-Stone algebra, and the operations ${x \mapsto x^{\circ}}$ and ${x \mapsto x^{*}}$ are linked by the identity x**º = x*º*. We show that such an algebra is subdirectly irreducible if and only if its congruence lattice is either a 2-element chain or a 3-element chain. In particular, there are precisely eight non-isomorphic subdirectly irreducible Stone de Morgan algebras.
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  14. Branislav Boričić & Mirjana Ilić (forthcoming). An Alternative Normalization of the Implicative Fragment of Classical Logic. Studia Logica:1-34.
    A normalizable natural deduction formulation, with subformula property, of the implicative fragment of classical logic is presented. A traditional notion of normal deduction is adapted and the corresponding weak normalization theorem is proved. An embedding of the classical logic into the intuitionistic logic, restricted on propositional implicational language, is described as well. We believe that this multiple-conclusion approach places the classical logic in the same plane with the intuitionistic logic, from the proof-theoretical viewpoint.
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  15. D. Busneag & M. Ghita (forthcoming). Some Properties of Epimorphisms of Implicative Algebras. Studia Logica.
     
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  16. A. V. Chagrov & M. V. Zakharyaschev (forthcoming). Modal Companions of Intermediate Logics: A Survey. Studia Logica.
     
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  17. Jānis Cīrulis (forthcoming). On Some Classes of Commutative Weak BCK-Algebras. Studia Logica:1-12.
    Formally, a description of weak BCK-algebras can be obtained by replacing (in the standard axiom set by K. Iseki and S. Tanaka) the first BCK axiom \({(x - y) - (x - z) \le z - y}\) by its weakening \({z \le y \Rightarrow x - y \le x - z}\) . It is known that every weak BCK-algebra is completely determined by the structure of its initial segments (sections). We consider weak BCK-algebras with De Morgan complemented, orthocomplemented and orthomodular (...)
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  18. Frank Wolter First Order Common (forthcoming). Knowledge Logics. Studia Logica.
     
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  19. Shan Du (forthcoming). On Pretabular Logics in NExtK4 (Part II). Studia Logica:1-24.
    In this paper we prove the pretabularity criteria for the logics of infinite depth in NExtK4. Then we use the criteria to resolve the problems of pretabular logics in NExtQ4 and prove that there is a continuum of pretabular logics in NExtQ4 just like NExtK4.
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  20. Josep Maria Font & Tommaso Moraschini (forthcoming). M-Sets and the Representation Problem. Studia Logica:1-31.
    The “representation problem” in abstract algebraic logic is that of finding necessary and sufficient conditions for a structure, on a well defined abstract framework, to have the following property: that for every structural closure operator on it, every structural embedding of the expanded lattice of its closed sets into that of the closed sets of another structural closure operator on another similar structure is induced by a structural transformer between the base structures. This question arose from Blok and Jónsson abstract (...)
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  21. Rohan French (forthcoming). In the Mood for S4: The Expressive Power of the Subjunctive Modal Language in Weak Background Logics. Studia Logica:1-25.
    Our concern here is with the extent to which the expressive equivalence of Wehmeier’s Subjunctive Modal Language (SML) and the Actuality Modal Language (AML) is sensitive to the choice of background modal logic. In particular we will show that, when we are enriching quantified modal logics weaker than S5, AML is strictly expressively stronger than SML, this result following from general considerations regarding the relationship between operators and predicate markers. This would seem to complicate arguments given in favour of SML (...)
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  22. D. Gabbay & F. Pirri (forthcoming). Special Issue on Combining Logics, Volume 59 (1, 2) Of. Studia Logica.
     
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  23. David R. Gilbert & Paolo Maffezioli (forthcoming). Modular Sequent Calculi for Classical Modal Logics. Studia Logica:1-43.
    This paper develops sequent calculi for several classical modal logics. Utilizing a polymodal translation of the standard modal language, we are able to establish a base system for the minimal classical modal logic E from which we generate extensions (to include M, C, and N) in a modular manner. Our systems admit contraction and cut admissibility, and allow a systematic proof-search procedure of formal derivations.
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  24. Dov Guido Boella, Leendert der Torre M. Gabbavany & Serena Villata (forthcoming). Meta-Argumentation Modelling I: Methodology and Techniques. Studia Logica.
    In this paper, we introduce the methodology and techniques of meta-argumentation to model argumentation. The methodology of meta-argumentation instantiates Dung’s abstract argumentation theory with an extended argumentation theory, and is thus based on a combination of the methodology of instantiating abstract arguments, and the methodology of extending Dung’s basic argumentation frameworks with other relations among abstract arguments. The technique of meta-argumentation applies Dung’s theory of abstract argumentation to itself, by instantiating Dung’s abstract arguments with meta-arguments using a technique called flattening. (...)
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  25. Sven Ove Hansson (forthcoming). Descriptor Revision. Studia Logica:1-26.
    A descriptor is a set of sentences that are truth-functional combinations of expressions of the form ${\mathfrak{B}p}$ B p , where ${\mathfrak{B}}$ B is a metalinguistic belief predicate and p a sentence in the object language in which beliefs are expressed. Descriptor revision (denoted ${\circ}$ ∘ ) is an operation of belief change that takes us from a belief set K to a new belief set ${K \circ \Psi}$ K ∘ Ψ where ${\Psi}$ Ψ is a descriptor representing the success (...)
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  26. Simon M. Huttegger & Brian Skyrms (forthcoming). Learning to Transfer Information. Studia Logica.
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  27. Thomas Icard (forthcoming). Exclusion and Containment in Natural Language. Studia Logica.
     
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  28. Andrzej Indrzejczak (forthcoming). A Survey of Nonstandard Sequent Calculi. Studia Logica:1-28.
    The paper is a brief survey of some sequent calculi (SC) which do not follow strictly the shape of sequent calculus introduced by Gentzen. We propose the following rough classification of all SC: Systems which are based on some deviations from the ordinary notion of a sequent are called generalised; remaining ones are called ordinary. Among the latter we distinguish three types according to the proportion between the number of primitive sequents and rules. In particular, in one of these types, (...)
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  29. Jarmo Kontinen (forthcoming). Coherence and Complexity of Quantifier-Free Dependence Logic Formulas. Studia Logica.
     
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  30. AgneS Kurucz & Arrow Logic (forthcoming). Infinite Counting. Studia Logica.
     
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  31. Franco Montagna & Sara Ugolini (forthcoming). A Categorical Equivalence for Product Algebras. Studia Logica:1-29.
    In this paper we provide a categorical equivalence for the category \({\mathcal{P}}\) of product algebras, with morphisms the homomorphisms. The equivalence is shown with respect to a category whose objects are triplets consisting of a Boolean algebra B, a cancellative hoop C and a map \({\vee_e}\) from B × C into C satisfying suitable properties. To every product algebra P, the equivalence associates the triplet consisting of the maximum boolean subalgebra B(P), the maximum cancellative subhoop C(P), of P, and the (...)
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  32. Koji Nakazawa & Hiroto Naya (forthcoming). Strong Reduction of Combinatory Calculus with Streams. Studia Logica:1-13.
    This paper gives the strong reduction of the combinatory calculus SCL, which was introduced as a combinatory calculus corresponding to the untyped Lambda-mu calculus. It proves the confluence of the strong reduction. By the confluence, it also proves the conservativity of the extensional equality of SCL over the combinatory calculus CL, and the consistency of SCL.
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  33. Marek Nowak (forthcoming). A Proof of Tarski's Fixed Point Theorem by Application of Galois Connections. Studia Logica:1-15.
    Two examples of Galois connections and their dual forms are considered. One of them is applied to formulate a criterion when a given subset of a complete lattice forms a complete lattice. The second, closely related to the first, is used to prove in a short way the Knaster-Tarski’s fixed point theorem.
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  34. Sergei P. Odintsov & Heinrich Wansing (forthcoming). The Logic of Generalized Truth Values and the Logic of Bilattices. Studia Logica:1-22.
    This paper sheds light on the relationship between the logic of generalized truth values and the logic of bilattices. It suggests a definite solution to the problem of axiomatizing the truth and falsity consequence relations, \({\models_t}\) and \({\models_f}\) , considered in a language without implication and determined via the truth and falsity orderings on the trilattice SIXTEEN 3 (Shramko and Wansing, J Philos Logic, 34:121–153, 2005). The solution is based on the fact that a certain algebra isomorphic to SIXTEEN 3 (...)
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  35. Gillman Payette & Peter K. Schotch (forthcoming). Remarks on the Scott–Lindenbaum Theorem. Studia Logica:1-18.
    In the late 1960s and early 1970s, Dana Scott introduced a kind of generalization (or perhaps simplification would be a better description) of the notion of inference, familiar from Gentzen, in which one may consider multiple conclusions rather than single formulas. Scott used this idea to good effect in a number of projects including the axiomatization of many-valued logics (of various kinds) and a reconsideration of the motivation of C.I. Lewis. Since he left the subject it has been vigorously prosecuted (...)
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  36. Arthur Paul Pedersen (forthcoming). An Extension Theorem and a Numerical Representation Theorem for Qualitative Comparative Expectations. Studia Logica.
     
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  37. Dana Piciu & A. Jeflea (forthcoming). Localization of MTL-Algebras. Studia Logica.
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  38. J. Rasga, A. Sernadas & C. Sernadas (forthcoming). Fibring as Biporting Subsumes Asymmetric Combinations. Studia Logica:1-34.
    The transference of preservation results between importing (a logic combination mechanism that subsumes several asymmetrical mechanisms for combining logics like temporalization, modalization and globalization) and unconstrained fibring is investigated. For that purpose, a new (more convenient) formulation of fibring, called biporting, is introduced, and importing is shown to be subsumed by biporting. In consequence, particular cases of importing, like temporalization, modalization and globalization are subsumed by fibring. Capitalizing on these results, the preservation of the finite model property by fibring is (...)
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  39. F. Sebastiani (forthcoming). A Fully Model-Theoretic Semantics for Model-Preference Default Systems', Istituto di Elaborazione dell'Informazione, Pisa. Studia Logica.
     
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  40. Angelina Ilić Stepić & Zoran Ognjanović (forthcoming). Logics for Reasoning About Processes of Thinking with Information Coded by P-Adic Numbers. Studia Logica:1-30.
    In this paper we present two types of logics (denoted \({L^{D}_{Q_{p}}}\) and \({L^{\rm thinking}_{Z_{p}}}\) ) where certain p-adic functions are associated to propositional formulas. Logics of the former type are p-adic valued probability logics. In each of these logics we use probability formulas K r,ρ α and D ρ α,β which enable us to make sentences of the form “the probability of α belongs to the p-adic ball with the center r and the radius ρ”, and “the p-adic distance between (...)
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  41. L. Tatjana & I. Boris (forthcoming). In Databases* T. Studia Logica.
     
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  42. Robert Trypuz & Piotr Kulicki (forthcoming). Jerzy Kalinowski's Logic of Normative Sentences Revisited. Studia Logica:1-24.
    The paper tackles two problems. The first one is to grasp the real meaning of Jerzy Kalinowski’s theory of normative sentences. His formal system K 1 is a simple logic formulated in a very limited language (negation is the only operator defined on actions). While presenting it Kalinowski formulated a few interesting philosophical remarks on norms and actions. He did not, however, possess the tools to formalise them fully. We propose a formulation of Kalinowski’s ideas with the use of a (...)
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  43. Hans van Ditmarsch (forthcoming). Johan van Benthem, Modal Logic for Open Minds, CSLI Lecture Notes, Stanford University, 2010, Pp. 350. ISBN: 9781575865997 (Hardcover) US 70.00,ISBN:9781575865980(Paperback)US 30.00. [REVIEW] Studia Logica.
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  44. Y. Venema (forthcoming). Meeting Strength in Substructural Logics'. UU Logic Preprint. Studia Logica.
     
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  45. Dag Westerståhl & Jfak van Benthem (forthcoming). Directions in Generalized Quantifier Theory. Studia Logica.
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  46. Evgeny Zolin (forthcoming). Undecidability of the Problem of Recognizing Axiomatizations of Superintuitionistic Propositional Calculi. Studia Logica:1-19.
    We give a new proof of the following result (originally due to Linial and Post): it is undecidable whether a given calculus, that is a finite set of propositional formulas together with the rules of modus ponens and substitution, axiomatizes the classical logic. Moreover, we prove the same for every superintuitionistic calculus. As a corollary, it is undecidable whether a given calculus is consistent, whether it is superintuitionistic, whether two given calculi have the same theorems, whether a given formula is (...)
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