50 found

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Forthcoming articles
  1. Sergio A. Celani & Daniela Montangie (forthcoming). Hilbert Algebras with a Modal Operator $${\Diamond}$$ ◊. Studia Logica:1-24.
    A Hilbert algebra with supremum is a Hilbert algebra where the associated order is a join-semilattice. This class of algebras is a variety and was studied in Celani and Montangie (2012). In this paper we shall introduce and study the variety of \({H_{\Diamond}^{\vee}}\) -algebras, which are Hilbert algebras with supremum endowed with a modal operator \({\Diamond}\) . We give a topological representation for these algebras using the topological spectral-like representation for Hilbert algebras with supremum given in Celani and Montangie (2012). (...)
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  2. Michael De & Hitoshi Omori (forthcoming). Classical Negation and Expansions of Belnap–Dunn Logic. Studia Logica:1-27.
    We investigate the notion of classical negation from a non-classical perspective. In particular, one aim is to determine what classical negation amounts to in a paracomplete and paraconsistent four-valued setting. We first give a general semantic characterization of classical negation and then consider an axiomatic expansion BD+ of four-valued Belnap–Dunn logic by classical negation. We show the expansion complete and maximal. Finally, we compare BD+ to some related systems found in the literature, specifically a four-valued modal logic of Béziau and (...)
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  3. 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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  4. A. M. Suardiaz A. Quantifier (forthcoming). M. Abad Varieties of Three-Valued. Studia Logica.
     
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  5. Peter Aczel, Benno van den Berg, Johan Granström & Peter Schuster (forthcoming). Are There Enough Injective Sets? Studia Logica.
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  6. Albert J. J. Anglberger & Jonathan Lukic (forthcoming). Hilbert-Style Axiom Systems for the Matrix-Based Logics RMQ − and RMQ. Studia Logica:1-19.
    This paper deals with the axiomatizability problem for the matrix-based logics RMQ − and RMQ *. We present a Hilbert-style axiom system for RMQ −, and a quasi-axiomatization based on it for RMQ *. We further compare these logics to different well-known modal logics, and assess its status as relevance logics.
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  7. 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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  8. Jort M. Bergfeld, Kohei Kishida, Joshua Sack & Shengyang Zhong (forthcoming). Duality for the Logic of Quantum Actions. Studia Logica:1-25.
    In this paper we show a duality between two approaches to represent quantum structures abstractly and to model the logic and dynamics therein. One approach puts forward a “quantum dynamic frame” :2267–2282, 2005), a labelled transition system whose transition relations are intended to represent projections and unitaries on a Hilbert space. The other approach considers a “Piron lattice” , which characterizes the algebra of closed linear subspaces of a Hilbert space. We define categories of these two sorts of structures and (...)
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  9. T. S. Blyth, Jie Fang & Leibo Wang (forthcoming). On Ideals and Congruences of Distributive Demi-P-Algebras. Studia Logica:1-16.
    We identify the \({{}^\star}\) -ideals of a distributive demi-pseudocomplemented algebra L as the kernels of the boolean congruences on L, and show that they form a complete Heyting algebra which is isomorphic to the interval \({[G,\iota]}\) of the congruence lattice of L where G is the Glivenko congruence. We also show that the notions of maximal \({{}^\star}\) -ideal, prime \({{}^\star}\) -ideal, and falsity ideal coincide.
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  10. 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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  11. D. Busneag & M. Ghita (forthcoming). Some Properties of Epimorphisms of Implicative Algebras. Studia Logica.
     
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  12. Mingzhong Cai (forthcoming). Unprovability and Proving Unprovability. Studia Logica:1-20.
    We investigate the “unprovability of unprovability”. Given a sentence P and a fixed base theory T, the unprovability of P is the sentence “ \({T\nvdash P}\) ”. We show that the unprovability of an unprovable true sentence can be “hard to prove”.
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  13. Massimiliano Carrara & Enrico Martino (forthcoming). Grounding Megethology on Plural Reference. Studia Logica:1-15.
    In Mathematics is megethology Lewis reconstructs set theory combining mereology with plural quantification. He introduces megethology, a powerful framework in which one can formulate strong assumptions about the size of the universe of individuals. Within this framework, Lewis develops a structuralist class theory, in which the role of classes is played by individuals. Thus, if mereology and plural quantification are ontologically innocent, as Lewis maintains, he achieves an ontological reduction of classes to individuals. Lewis’work is very attractive. However, the alleged (...)
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  14. Sergio A. Celani (forthcoming). Properties of Saturation in Monotonic Neighbourhood Models and Some Applications. Studia Logica:1-23.
    In this paper we shall discuss properties of saturation in monotonic neighbourhood models and study some applications, like a characterization of compact and modally saturated monotonic models and a characterization of the maximal Hennessy-Milner classes. We shall also show that our notion of modal saturation for monotonic models naturally extends the notion of modal saturation for Kripke models.
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  15. A. V. Chagrov & M. V. Zakharyaschev (forthcoming). Modal Companions of Intermediate Logics: A Survey. Studia Logica.
     
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  16. Petr Cintula & Carles Noguera (forthcoming). A Note on Natural Extensions in Abstract Algebraic Logic. Studia Logica:1-9.
    Transfer theorems are central results in abstract algebraic logic that allow to generalize properties of the lattice of theories of a logic to any algebraic model and its lattice of filters. Their proofs sometimes require the existence of a natural extension of the logic to a bigger set of variables. Constructions of such extensions have been proposed in particular settings in the literature. In this paper we show that these constructions need not always work and propose a wider setting in (...)
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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. Nino B. Cocchiarella (forthcoming). Two Views of the Logic of Plurals and a Reduction of One to the Other. Studia Logica:1-24.
    There are different views of the logic of plurals that are now in circulation, two of which we will compare in this paper. One of these is based on a two-place relation of being among, as in ‘Peter is among the juveniles arrested’. This approach seems to be the one that is discussed the most in philosophical journals today. The other is based on Bertrand Russell’s early notion of a class as many, by which is meant not a class as (...)
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  19. Frank Wolter First Order Common (forthcoming). Knowledge Logics. Studia Logica.
     
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  20. Juan M. Cornejo & Ignacio D. Viglizzo (forthcoming). On Some Semi-Intuitionistic Logics. Studia Logica:1-42.
    Semi-intuitionistic logic is the logic counterpart to semi-Heyting algebras, which were defined by H. P. Sankappanavar as a generalization of Heyting algebras. We present a new, more streamlined set of axioms for semi-intuitionistic logic, which we prove translationally equivalent to the original one. We then study some formulas that define a semi-Heyting implication, and specialize this study to the case in which the formulas use only the lattice operators and the intuitionistic implication. We prove then that all the logics thus (...)
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  21. Juan Manuel Cornejo (forthcoming). The Semi Heyting–Brouwer Logic. Studia Logica:1-23.
    In this paper we introduce a logic that we name semi Heyting–Brouwer logic, \ , in such a way that the variety of double semi-Heyting algebras is its algebraic counterpart. We prove that, up to equivalences by translations, the Heyting–Brouwer logic \ is an axiomatic extension of \ and that the propositional calculi of intuitionistic logic \ and semi-intuitionistic logic \ turn out to be fragments of \.
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  22. Eduardo J. Dubuc & Y. A. Poveda (forthcoming). On the Equivalence Between MV-Algebras and L-Groups with Strong Unit. Studia Logica:1-8.
    In “A new proof of the completeness of the Lukasiewicz axioms” Chang proved that any totally ordered MV-algebra A was isomorphic to the segment \}\) of a totally ordered l-group with strong unit A *. This was done by the simple intuitive idea of putting denumerable copies of A on top of each other . Moreover, he also show that any such group G can be recovered from its segment since \^*}\) , establishing an equivalence of categories. In “Interpretation of (...)
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  23. 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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  24. D. Gabbay & F. Pirri (forthcoming). Special Issue on Combining Logics, Volume 59 (1, 2) Of. Studia Logica.
     
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  25. 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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  26. Sven Ove Hansson (forthcoming). A Monoselective Presentation of AGM Revision. Studia Logica:1-15.
    A new equivalent presentation of AGM revision is introduced, in which a preference-based choice function directly selects one among the potential outcomes of the operation. This model differs from the usual presentations of AGM revision in which the choice function instead delivers a collection of sets whose intersection is the outcome. The new presentation confirms the versatility of AGM revision, but it also lends credibility to the more general model of direct choice among outcomes of which AGM revision is shown (...)
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  27. Simon M. Huttegger & Brian Skyrms (forthcoming). Learning to Transfer Information. Studia Logica.
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  28. Thomas Icard (forthcoming). Exclusion and Containment in Natural Language. Studia Logica.
     
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  29. Jarmo Kontinen (forthcoming). Coherence and Complexity of Quantifier-Free Dependence Logic Formulas. Studia Logica.
     
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  30. Victor N. Krivtsov (forthcoming). Semantical Completeness of First-Order Predicate Logic and the Weak Fan Theorem. Studia Logica:1-16.
    Within a weak system \({{{\sf WKVS}}}\) of intuitionistic analysis one may prove, using the Weak Fan Theorem as an additional axiom, a completeness theorem for intuitionistic first-order predicate logic relative to validity in generalized Beth models as well as a completeness theorem for classical first-order predicate logic relative to validity in intuitionistic structures. Conversely, each of these theorems implies over \({{{\sf WKVS}}}\) the Weak Fan Theorem.
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  31. AgneS Kurucz & Arrow Logic (forthcoming). Infinite Counting. Studia Logica.
     
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  32. Steffen Lewitzka (forthcoming). Denotational Semantics for Modal Systems S3–S5 Extended by Axioms for Propositional Quantifiers and Identity. Studia Logica:1-38.
    There are logics where necessity is defined by means of a given identity connective: \({\square\varphi := \varphi\equiv\top}\) ( \({\top}\) is a tautology). On the other hand, in many standard modal logics the concept of propositional identity (PI) \({\varphi\equiv\psi}\) can be defined by strict equivalence (SE) \({\square(\varphi\leftrightarrow\psi)}\) . All these approaches to modality involve a principle that we call the Collapse Axiom (CA): “There is only one necessary proposition.” In this paper, we consider a notion of PI which relies on the (...)
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  33. Szabolcs Mikulás (forthcoming). Lower Semilattice-Ordered Residuated Semigroups and Substructural Logics. Studia Logica:1-26.
    We look at lower semilattice-ordered residuated semigroups and, in particular, the representable ones, i.e., those that are isomorphic to algebras of binary relations. We will evaluate expressions (terms, sequents, equations, quasi-equations) in representable algebras and give finite axiomatizations for several notions of validity. These results will be applied in the context of substructural logics.
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  34. 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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  35. 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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  36. 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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  37. Hitoshi Omori & Katsuhiko Sano (forthcoming). Generalizing Functional Completeness in Belnap-Dunn Logic. Studia Logica:1-35.
    One of the problems we face in many-valued logic is the difficulty of capturing the intuitive meaning of the connectives introduced through truth tables. At the same time, however, some logics have nice ways to capture the intended meaning of connectives easily, such as four-valued logic studied by Belnap and Dunn. Inspired by Dunn’s discovery, we first describe a mechanical procedure, in expansions of Belnap-Dunn logic, to obtain truth conditions in terms of the behavior of the Truth and the False, (...)
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  38. Federico Pailos & Lucas Rosenblatt (forthcoming). Non-Deterministic Conditionals and Transparent Truth. Studia Logica:1-20.
    Theories where truth is a naive concept fall under the following dilemma: either the theory is subject to Curry’s Paradox, which engenders triviality, or the theory is not trivial but the resulting conditional is too weak. In this paper we explore a number of theories which arguably do not fall under this dilemma. In these theories the conditional is characterized in terms of non-deterministic matrices. These non-deterministic theories are similar to infinitely-valued Łukasiewicz logic in that they are consistent and their (...)
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  39. Arthur Paul Pedersen (forthcoming). An Extension Theorem and a Numerical Representation Theorem for Qualitative Comparative Expectations. Studia Logica.
     
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  40. Dana Piciu & A. Jeflea (forthcoming). Localization of MTL-Algebras. Studia Logica.
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  41. Edoardo Rivello (forthcoming). Cofinally Invariant Sequences and Revision. Studia Logica:1-24.
    Revision sequences are a kind of transfinite sequences which were introduced by Herzberger and Gupta in 1982 (independently) as the main mathematical tool for developing their respective revision theories of truth. We generalise revision sequences to the notion of cofinally invariant sequences, showing that several known facts about Herzberger’s and Gupta’s theories also hold for this more abstract kind of sequences and providing new and more informative proofs of the old results.
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  42. Michael Schippers (forthcoming). Towards a Grammar of Bayesian Coherentism. Studia Logica:1-30.
    One of the integral parts of Bayesian coherentism is the view that the relation of ‘being no less coherent than’ is fully determined by the probabilistic features of the sets of propositions to be ordered. In the last one and a half decades, a variety of probabilistic measures of coherence have been put forward. However, there is large disagreement as to which of these measures best captures the pre-theoretic notion of coherence. This paper contributes to the debate on coherence measures (...)
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  43. 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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  44. Ryo Takemura (forthcoming). Counter-Example Construction with Euler Diagrams. Studia Logica:1-28.
    One of the traditional applications of Euler diagrams is as a representation or counterpart of the usual set-theoretical models of given sentences. However, Euler diagrams have recently been investigated as the counterparts of logical formulas, which constitute formal proofs. Euler diagrams are rigorously defined as syntactic objects, and their inference systems, which are equivalent to some symbolic logical systems, are formalized. Based on this observation, we investigate both counter-model construction and proof-construction in the framework of Euler diagrams. We introduce the (...)
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  45. L. Tatjana & I. Boris (forthcoming). In Databases* T. Studia Logica.
     
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  46. 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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  47. 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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  48. Y. Venema (forthcoming). Meeting Strength in Substructural Logics'. UU Logic Preprint. Studia Logica.
     
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  49. Xue-Ping Wang & Lei-Bo Wang (forthcoming). Congruences and Kernel Ideals on a Subclass of Ockham Algebras. Studia Logica:1-19.
    In this note, it is shown that the set of kernel ideals of a K n, 0-algebra L is a complete Heyting algebra, and the largest congruence on L such that the given kernel ideal as its congruence class is derived and finally, the necessary and sufficient conditions that such a congruence is pro-boolean are given.
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  50. Stefan Wintein & Reinhard A. Muskens (forthcoming). From Bi-Facial Truth to Bi-Facial Proofs. Studia Logica:1-14.
    In their recent paper Bi-facial truth: a case for generalized truth values Zaitsev and Shramko [7] distinguish between an ontological and an epistemic interpretation of classical truth values. By taking the Cartesian product of the two disjoint sets of values thus obtained, they arrive at four generalized truth values and consider two “semi-classical negations” on them. The resulting semantics is used to define three novel logics which are closely related to Belnap’s well-known four valued logic. A syntactic characterization of these (...)
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