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  Subjects -> PHILOSOPHY (Total: 762 journals)
Showing 1 - 135 of 135 Journals sorted by number of followers
Philosophical Review     Full-text available via subscription   (Followers: 72)
Ethics     Full-text available via subscription   (Followers: 69)
European Journal of Philosophy     Hybrid Journal   (Followers: 68)
Journal of Political Philosophy     Hybrid Journal   (Followers: 65)
Mind     Hybrid Journal   (Followers: 64)
Australasian Journal of Philosophy     Hybrid Journal   (Followers: 58)
Philosophy & Public Affairs     Hybrid Journal   (Followers: 57)
International Journal for Philosophy of Religion     Hybrid Journal   (Followers: 52)
Contemporary Political Theory     Hybrid Journal   (Followers: 52)
Nous     Hybrid Journal   (Followers: 52)
Journal of the History of Philosophy     Full-text available via subscription   (Followers: 48)
Philosophical Quarterly     Hybrid Journal   (Followers: 47)
British Journal for the History of Philosophy     Hybrid Journal   (Followers: 43)
Journal of Applied Philosophy     Hybrid Journal   (Followers: 43)
American Journal of Theology & Philosophy     Full-text available via subscription   (Followers: 42)
British Journal for the Philosophy of Science     Hybrid Journal   (Followers: 40)
Journal of Moral Philosophy     Hybrid Journal   (Followers: 37)
Analysis     Hybrid Journal   (Followers: 37)
Philosophy and Phenomenological Research     Hybrid Journal   (Followers: 36)
Philosophy of Science     Full-text available via subscription   (Followers: 33)
Journal of Medical Ethics     Partially Free   (Followers: 32)
Erkenntnis     Hybrid Journal   (Followers: 31)
Philosophy and Literature     Full-text available via subscription   (Followers: 31)
Continental Philosophy Review     Partially Free   (Followers: 28)
Inquiry : An Interdisciplinary Journal of Philosophy     Hybrid Journal   (Followers: 28)
Journal of Social Philosophy     Hybrid Journal   (Followers: 27)
Journal of Ethics & Social Philosophy     Open Access   (Followers: 27)
Constellations     Hybrid Journal   (Followers: 27)
Canadian Journal of Philosophy     Full-text available via subscription   (Followers: 25)
Social Philosophy and Policy     Full-text available via subscription   (Followers: 25)
Ethical Theory and Moral Practice     Hybrid Journal   (Followers: 24)
British Journal of Aesthetics     Hybrid Journal   (Followers: 23)
Journal of Law, Medicine & Ethics     Hybrid Journal   (Followers: 23)
Philosophy & Social Criticism     Hybrid Journal   (Followers: 22)
Philosophical Studies     Hybrid Journal   (Followers: 22)
Linguistics and Philosophy     Hybrid Journal   (Followers: 22)
Philosophy and Rhetoric     Full-text available via subscription   (Followers: 21)
The Heythrop Journal     Hybrid Journal   (Followers: 21)
Philosophy Compass     Hybrid Journal   (Followers: 19)
BMC Medical Ethics     Open Access   (Followers: 19)
Biology and Philosophy     Hybrid Journal   (Followers: 18)
Journal of Medical Ethics and History of Medicine     Open Access   (Followers: 18)
Philosophy     Full-text available via subscription   (Followers: 17)
Philosophers' Imprint     Open Access   (Followers: 17)
Jurisprudence     Hybrid Journal   (Followers: 17)
Assuming Gender     Open Access   (Followers: 16)
Mouseion: Journal of the Classical Association of Canada     Full-text available via subscription   (Followers: 16)
Journal of the Philosophy of History     Hybrid Journal   (Followers: 16)
Pragmatics & Cognition     Hybrid Journal   (Followers: 16)
Philosophy East and West     Full-text available via subscription   (Followers: 15)
International Studies in the Philosophy of Science     Hybrid Journal   (Followers: 15)
Bioethics Research Notes     Full-text available via subscription   (Followers: 15)
Midwest Studies In Philosophy     Hybrid Journal   (Followers: 14)
Journal of Media Ethics : Exploring Questions of Media Morality     Hybrid Journal   (Followers: 14)
Episteme     Hybrid Journal   (Followers: 14)
Phronesis : A journal for Ancient Philosophy     Hybrid Journal   (Followers: 13)
Social Epistemology: A Journal of Knowledge, Culture and Policy     Hybrid Journal   (Followers: 13)
Philosophy & Technology     Hybrid Journal   (Followers: 13)
Review of Philosophy and Psychology     Hybrid Journal   (Followers: 13)
Pragmatics and Society     Hybrid Journal   (Followers: 12)
Reformed Theological Review, The     Full-text available via subscription   (Followers: 12)
Ethical Perspectives     Full-text available via subscription   (Followers: 12)
Journal of Indian Philosophy     Hybrid Journal   (Followers: 12)
Journal of Global Ethics     Hybrid Journal   (Followers: 12)
Journal of Chinese Philosophy     Hybrid Journal   (Followers: 12)
Philosophy of Photography     Hybrid Journal   (Followers: 11)
Philosophy, Psychiatry, & Psychology     Full-text available via subscription   (Followers: 11)
Open Journal of Philosophy     Open Access   (Followers: 11)
Utilitas     Hybrid Journal   (Followers: 11)
Estudos Bíblicos     Open Access   (Followers: 11)
Dao : A Journal of Comparative Philosophy     Hybrid Journal   (Followers: 11)
Pacific Philosophical Quarterly     Hybrid Journal   (Followers: 10)
Kennedy Institute of Ethics Journal     Full-text available via subscription   (Followers: 10)
Metaphor and Symbol     Hybrid Journal   (Followers: 10)
Polis : The Journal of the Society for Greek Political Thought     Hybrid Journal   (Followers: 10)
HTS Theological Studies     Open Access   (Followers: 9)
Journal of Philosophical Logic     Hybrid Journal   (Followers: 9)
Film-Philosophy Journal     Open Access   (Followers: 9)
Journal of the Gilded Age and Progressive Era     Full-text available via subscription   (Followers: 9)
Research in Phenomenology     Hybrid Journal   (Followers: 9)
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences     Full-text available via subscription   (Followers: 9)
Philosophical Books     Hybrid Journal   (Followers: 8)
Philosophia     Hybrid Journal   (Followers: 8)
Diogenes     Hybrid Journal   (Followers: 8)
Philosophical Perspectives     Hybrid Journal   (Followers: 8)
Myth & Symbol     Hybrid Journal   (Followers: 8)
Nordic Journal of Aesthetics     Open Access   (Followers: 7)
Journal of Speculative Philosophy     Full-text available via subscription   (Followers: 7)
Metaphilosophy     Hybrid Journal   (Followers: 7)
African Journal of Business Ethics     Open Access   (Followers: 7)
Medicine, Health Care and Philosophy     Hybrid Journal   (Followers: 7)
SubStance     Full-text available via subscription   (Followers: 7)
Contagion : Journal of Violence, Mimesis, and Culture     Full-text available via subscription   (Followers: 7)
Philosophical Issues     Hybrid Journal   (Followers: 7)
Contributions to the History of Concepts     Full-text available via subscription   (Followers: 7)
International Journal of Philosophical Studies     Hybrid Journal   (Followers: 7)
The Southern Journal of Philosophy     Hybrid Journal   (Followers: 6)
Philosophical Explorations: An International Journal for the Philosophy of Mind and Action     Hybrid Journal   (Followers: 6)
Axiomathes     Hybrid Journal   (Followers: 6)
Philosophical Investigations     Hybrid Journal   (Followers: 6)
Contemporary Chinese Thought     Full-text available via subscription   (Followers: 6)
Dialogue Canadian Philosophical Review/Revue canadienne de philosophie     Full-text available via subscription   (Followers: 6)
History and Philosophy of Logic     Hybrid Journal   (Followers: 6)
Think     Full-text available via subscription   (Followers: 6)
Philosophical Magazine Letters     Hybrid Journal   (Followers: 6)
Zeitschrift für philosophische Forschung     Full-text available via subscription   (Followers: 6)
Journal of Critical Realism     Hybrid Journal   (Followers: 5)
Journal of Empirical Research on Human Research Ethics     Full-text available via subscription   (Followers: 5)
Endeavour     Hybrid Journal   (Followers: 5)
Australasian Catholic Record, The     Full-text available via subscription   (Followers: 5)
Journal of Nietzsche Studies     Full-text available via subscription   (Followers: 5)
Critical Horizons     Hybrid Journal   (Followers: 5)
Aisthesis     Open Access   (Followers: 5)
Philosophical Papers     Hybrid Journal   (Followers: 5)
Review of Contemporary Philosophy     Full-text available via subscription   (Followers: 5)
International Journal of the Platonic Tradition     Open Access   (Followers: 5)
Zeitschrift für Religions- und Geistesgeschichte     Hybrid Journal   (Followers: 5)
Bochumer Philosophisches Jahrbuch für Antike und Mittelalter     Hybrid Journal   (Followers: 4)
Transactions of the Charles S. Peirce Society     Full-text available via subscription   (Followers: 4)
Journal of Theoretical & Philosophical Psychology     Full-text available via subscription   (Followers: 4)
National Catholic Bioethics Quarterly     Hybrid Journal   (Followers: 4)
The Philosophical Forum     Hybrid Journal   (Followers: 4)
Royal Institute of Philosophy Supplements     Full-text available via subscription   (Followers: 4)
Church Heritage     Full-text available via subscription   (Followers: 4)
Franciscan Studies     Full-text available via subscription   (Followers: 4)
South African Journal of Philosophy = Suid-Afrikaanse Tydskrif vir Wysbegeerte     Hybrid Journal   (Followers: 4)
Hume Studies     Full-text available via subscription   (Followers: 4)
Philosophy in Review     Open Access   (Followers: 4)
Australian Humanist, The     Full-text available via subscription   (Followers: 3)
Journal of Religion and Business Ethics     Open Access   (Followers: 3)
Studia Logica     Hybrid Journal   (Followers: 3)
The Pluralist     Full-text available via subscription   (Followers: 3)
Recherches de Théologie et Philosophie Médiévales     Full-text available via subscription   (Followers: 3)
Russell : the Journal of Bertrand Russell Studies     Full-text available via subscription   (Followers: 3)
Studies in Philology     Full-text available via subscription   (Followers: 3)
CR : The New Centennial Review     Full-text available via subscription   (Followers: 3)
Utopian Studies     Full-text available via subscription   (Followers: 3)
Kantian Review     Full-text available via subscription   (Followers: 3)
Bulletin de Philosophie Medievale     Full-text available via subscription   (Followers: 3)
Topoi     Hybrid Journal   (Followers: 3)
Bijdragen     Full-text available via subscription   (Followers: 3)
International Journal for the Study of Skepticism     Hybrid Journal   (Followers: 2)
International Journal of Žižek Studies     Open Access   (Followers: 2)
Empedocles : European Journal for the Philosophy of Communication     Hybrid Journal   (Followers: 2)
Horizonte : Revista de Estudos de Teologia e Ciências da Religião     Open Access   (Followers: 2)
Cultura : International Journal of Philosophy of Culture and Axiology     Open Access   (Followers: 2)
Erasmus Studies     Hybrid Journal   (Followers: 2)
Socioaffective Neuroscience and Psychology     Open Access   (Followers: 2)
Between the Species     Open Access   (Followers: 2)
Journal of Friends of Lutheran Archives     Full-text available via subscription   (Followers: 2)
Journal of Scottish Philosophy     Hybrid Journal   (Followers: 2)
Poiesis & Praxis : International Journal of Technology Assessment and Ethics of Science     Open Access   (Followers: 2)
Journal of Aesthetic Education     Full-text available via subscription   (Followers: 2)
Sartre Studies International     Full-text available via subscription   (Followers: 2)
Quaestio     Full-text available via subscription   (Followers: 2)
Grazer Philosophische Studien     Full-text available via subscription   (Followers: 2)
Kriterion: Revista de Filosofia     Open Access   (Followers: 2)
Philosophy & Theory in Biology     Open Access   (Followers: 2)
Australian Journal of Parapsychology     Full-text available via subscription   (Followers: 2)
Éthique publique     Open Access   (Followers: 1)
Noesis     Open Access   (Followers: 1)
Philosophia Scientiæ     Open Access   (Followers: 1)
Revue Philosophique de Louvain     Full-text available via subscription   (Followers: 1)
Nóema     Open Access   (Followers: 1)
International Journal of Social Quality     Full-text available via subscription   (Followers: 1)
Revista Latinoamericana de Filosofía     Open Access   (Followers: 1)
PAN: Philosophy Activism Nature     Full-text available via subscription   (Followers: 1)
Temporalités     Open Access   (Followers: 1)
Le Portique     Open Access   (Followers: 1)
Ethische Perspectieven     Full-text available via subscription   (Followers: 1)
Journal of Humanistic Mathematics     Open Access   (Followers: 1)
Laval théologique et philosophique     Full-text available via subscription   (Followers: 1)
Revue d’études benthamiennes     Open Access   (Followers: 1)
Eleutheria     Open Access   (Followers: 1)
Husserl Studies     Hybrid Journal   (Followers: 1)
Veritas : Revista de Filosofí­a y Teología     Open Access   (Followers: 1)
Hobbes Studies     Hybrid Journal   (Followers: 1)
Collingwood and British Idealism Studies     Full-text available via subscription  
Grotiana     Hybrid Journal  
Signos Filosóficos     Open Access  
Eidos     Open Access  
Cinta de Moebio     Open Access  
Cuyo Anuario de Filosofía Argentina y Americana     Open Access  
Tópicos. Revista de Filosofía de Santa Fe     Open Access  
Rhuthmos     Open Access  
Philosophiques     Open Access  
Ramon Llull Journal of Applied Ethics     Open Access  
Studia Philosophica Estonica     Open Access  
Synthesis (La Plata)     Open Access  
Revista de Filosofia     Open Access  
Alpha (Osorno)     Open Access  
Circe de clásicos y modernos     Open Access  
Estudios de Filosofía Práctica e Historia de las Ideas     Open Access  
Doctor virtualis     Open Access  
Humanidades Médicas     Open Access  
Methodos     Open Access  
Labyrinthe     Open Access  
Astérion     Open Access  
Trans/Form/Ação - Revista de Filosofia     Open Access  
Russian Studies in Philosophy     Full-text available via subscription  

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Studia Logica
Journal Prestige (SJR): 0.353
Citation Impact (citeScore): 1
Number of Followers: 3  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1572-8730 - ISSN (Online) 0039-3215
Published by Springer-Verlag Homepage  [2467 journals]
  • Correction to: A Modal View on Resource-Bounded Propositional Logics

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      PubDate: 2022-12-01
       
  • Logics of Order and Related Notions

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      Abstract: Abstract The aim of the paper is twofold. First, we want to recapture the genesis of the logics of order. The origin of this notion is traced back to the work of Jerzy Kotas, Roman Suszko, Richard Routley and Robert K. Meyer. A further development of the theory of logics of order is presented in the papers of Jacek K. Kabziński. Quite contemporarily, this notion gained in significance in the papers of Carles Noguera and Petr Cintula. Logics of order are named there logics of weak implications. They play a crucial role in their monograph (Noguera and Cintula Logic and Implication. An Introduction to the General Algebraic Study of Non-Classical Logics, Trends in Logic 57, Springer, Berlin, 2021). But, more importantly, the other goal is to define some subclasses of the logics of order in reference to later results of Jacek K. Kabziński and Michael Dunn. The original conception of implication is due to Kabziński. Implication is a stronger notion than the notion of the connective of order aka weak implication. As a result, the three subclasses of logics of order are isolated: logics of implication, logics of symmetry, and tonoidal logics. These notions are uniformly defined and investigated from various viewpoints in terms of consequence operations. The emphasis is put on their semantics.
      PubDate: 2022-12-01
       
  • On Relative Principal Congruences in Term Quasivarieties

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      Abstract: Abstract Let \({\mathcal {K}}\) be a quasivariety. We say that \({\mathcal {K}}\) is a term quasivariety if there exist an operation of arity zero e and a family of binary terms \(\{t_i\}_{i\in I}\) such that for every \(A \in {\mathcal {K}}\) , \(\theta \) a \({\mathcal {K}}\) -congruence of A and \(a,b\in A\) the following condition is satisfied: \((a,b)\in \theta \) if and only if \((t_{i}(a,b),e) \in \theta \) for every \(i\in I\) . In this paper we study term quasivarieties. For every \(A\in {\mathcal {K}}\) and \(a,b\in A\) we present a description for the smallest \({\mathcal {K}}\) -congruence containing the pair (a, b). We apply this result in order to characterize \({\mathcal {K}}\) -compatible functions on A (i.e., functions which preserve all the \({\mathcal {K}}\) -congruences of A) and we give two applications of this property: (1) we give necessary conditions on \({\mathcal {K}}\) for which for every \(A \in {\mathcal {K}}\) the \({\mathcal {K}}\) -compatible functions on A coincides with a polynomial over finite subsets of A; (2) we give a method to build up \({\mathcal {K}}\) -compatible functions.
      PubDate: 2022-12-01
       
  • Natural Deduction Systems for Intuitionistic Logic with Identity

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      Abstract: Abstract The aim of the paper is to present two natural deduction systems for Intuitionistic Sentential Calculus with Identity (ISCI); a syntactically motivated \(\mathsf {ND}^1_{\mathsf {ISCI}}\) and a semantically motivated \(\mathsf {ND}^2_{\mathsf {ISCI}}\) . The formulation of \(\mathsf {ND}^1_{\mathsf {ISCI}}\) is based on the axiomatic formulation of ISCI. Its rules cannot be straightforwardly classified as introduction or elimination rules; ISCI-specific rules are based on axioms characterizing the identity connective. The system does not enjoy the standard subformula property, but due to the normalization procedure non-subformulas can label only leaves of proofs. In \(\mathsf {ND}^2_{\mathsf {ISCI}}\) , we propose only two general identity-related rules, in reference to the treatment of the identity connective in First-Order Logic.
      PubDate: 2022-12-01
       
  • The G4i Analogue of a G3i Sequent Calculus

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      Abstract: Abstract This paper provides a method to obtain terminating analytic calculi for a large class of intuitionistic modal logics. For a given logic L with a cut-free calculus G that is an extension of G3ip the method produces a terminating analytic calculus that is an extension of G4ip and equivalent to G. G4ip was introduced by Roy Dyckhoff in 1992 as a terminating analogue of the calculus G3ip for intuitionistic propositional logic. Thus this paper can be viewed as an extension of Dyckhoff’s work to intuitionistic modal logic.
      PubDate: 2022-12-01
       
  • On the Proof Theory of Infinitary Modal Logic

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      Abstract: Abstract The article deals with infinitary modal logic. We first discuss the difficulties related to the development of a satisfactory proof theory and then we show how to overcome these problems by introducing a labelled sequent calculus which is sound and complete with respect to Kripke semantics. We establish the structural properties of the system, namely admissibility of the structural rules and of the cut rule. Finally, we show how to embed common knowledge in the infinitary calculus and we discuss first-order extensions of infinitary modal logic.
      PubDate: 2022-12-01
       
  • The Quantified Argument Calculus with Two- and Three-valued
           Truth-valuational Semantics

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      Abstract: Abstract We introduce a two-valued and a three-valued truth-valuational substitutional semantics for the Quantified Argument Calculus (Quarc). We then prove that the 2-valid arguments are identical to the 3-valid ones with strict-to-tolerant validity. Next, we introduce a Lemmon-style Natural Deduction system and prove the completeness of Quarc on both two- and three-valued versions, adapting Lindenbaum’s Lemma to truth-valuational semantics. We proceed to investigate the relations of three-valued Quarc and the Predicate Calculus (PC). Adding a logical predicate T to Quarc, true of all singular arguments, allows us to represent PC quantification in Quarc and translate PC into Quarc, preserving validity. Introducing a weak existential quantifier into PC allows us to translate Quarc into PC, also preserving validity. However, unlike the translated systems, neither extended system can have a sound and complete proof system with Cut, supporting the claim that these are basically different calculi.
      PubDate: 2022-11-25
       
  • Kapsner Complementation: An Algebraic Take on Kapsner Strong Logics

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      Abstract: Abstract Kapsner strong logics, originally studied in the context of connexive logics, are those in which all formulas of the form \(A\rightarrow \lnot A\) or \(\lnot A\rightarrow A\) are unsatisfiable, and in any model at most one of \(A\rightarrow B, A\rightarrow \lnot B\) is satisfied. In this paper, such logics are studied algebraically by means of algebraic structures in which negation is modeled by an operator \(\lnot \) s.t. any element a is incomparable with \(\lnot a\) . A range of properties which are (in)compatible with such operators are studied, and examples are given; finally, the question of which further operators can be added to such structures is broached.
      PubDate: 2022-11-25
       
  • On Categorical Equivalence of Weak Monadic Residuated Distributive
           

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      Abstract: Abstract The category \(\mathbb {DRDL}{'}\) , whose objects are c-differential residuated distributive lattices satisfying the condition \(\textbf{CK}\) , is the image of the category \(\mathbb {RDL}\) , whose objects are residuated distributive lattices, under the categorical equivalence \(\textbf{K}\) that is constructed in Castiglioni et al. (Stud Log 90:93–124, 2008). In this paper, we introduce weak monadic residuated lattices and study some of their subvarieties. In particular, we use the functor \(\textbf{K}\) to relate the category \(\mathbb {WMRDL}\) , whose objects are weak monadic residuated distributive lattices, and the category \(\mathbb {WMDRDL}{'}\) , whose objects are pairs formed by an object of \(\mathbb {DRDL}{'}\) and a center weak universal quantifier.
      PubDate: 2022-11-25
       
  • Infinitary Action Logic with Multiplexing

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      Abstract: Abstract Infinitary action logic can be naturally expanded by adding exponential and subexponential modalities from linear logic. In this article we shall develop infinitary action logic with a subexponential that allows multiplexing (instead of contraction). Both non-commutative and commutative versions of this logic will be considered, presented as infinitary sequent calculi. We shall prove cut admissibility for these calculi, and estimate the complexity of the corresponding derivability problems: in both cases it will turn out to be between complete first-order arithmetic and the \(\omega ^\omega \) level of the hyperarithmetical hierarchy. Here the complexity upper bound is much lower than that for the system with a subexponential that allows contraction. The complexity lower bound in turn is much higher than that for infinitary action logic.
      PubDate: 2022-11-21
       
  • The Categorical Equivalence Between Domains and Interpolative Generalized
           Closure Spaces

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      Abstract: Abstract Closure space has been proven to be a useful tool to restructure lattices and various order structures. This paper aims to provide an approach to characterizing domains by means of closure spaces. The notion of an interpolative generalized closure space is presented and shown to generate exactly domains, and the notion of an approximable mapping between interpolative generalized closure spaces is identified to represent Scott continuous functions between domains. These produce a category equivalent to that of domains with Scott continuous functions. Meanwhile, some important subclasses of domains are discussed, such as algebraic domains, L-domains, bounded-complete domains, and continuous lattices. Conditions are presented which, when fulfilled by an interpolative generalized closure space, make the generated domain fulfill some restrictive conditions.
      PubDate: 2022-11-15
       
  • Finite Model Property in Weakly Transitive Tense Logics

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      Abstract: Abstract The finite model property (FMP) in weakly transitive tense logics is explored. Let \(\mathbb {S}=[\textsf{wK}_t\textsf{4}, \textsf{K}_t\textsf{4}]\) be the interval of tense logics between \(\textsf{wK}_t\textsf{4}\) and \(\textsf{K}_t\textsf{4}\) . We introduce the modal formula \(\textrm{t}_0^n\) for each \(n\ge 1\) . Within the class of all weakly transitive frames, \(\textrm{t}_0^n\) defines the class of all frames in which every cluster has at most n irreflexive points. For each \(n\ge 1\) , we define the interval \(\mathbb {S}_n=[\textsf{wK}_t\textsf{4T}_0^{n+1}, \textsf{wK}_t\textsf{4T}_0^{n}]\) which is a subset of \(\mathbb {S}\) . There are \(2^{\aleph _0}\) logics in \(\mathbb {S}_n\) lacking the FMP, and there are \(2^{\aleph _0}\) logics in \(\mathbb {S}_n\) having the FMP. Then we explore the FMP in finitely alternative tense logics \(L_{n,m}=L\oplus \{\textrm{Alt}_n^F, \textrm{Alt}_m^P\}\) with \(n,m\ge 0\) and \(L\in \mathbb {S}\) . For all \(k\ge 0\) and \(n,m\ge 1\) , we define intervals \(\mathbb {F}^k_{n,m}\) , \(\mathbb {P}^k_{n,m}\) and \(\mathbb {S}^k_{n,m}\) of tense logics. The number of logics lacking the FMP in them is either 0 or \(2^{\aleph _0}\) , and the number of logics having the FMP in them is either finite or \(2^{\aleph _0}\) .
      PubDate: 2022-11-15
       
  • Hereditarily Structurally Complete Intermediate Logics: Citkin’s
           Theorem Via Duality

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      Abstract: Abstract A deductive system is said to be structurally complete if its admissible rules are derivable. In addition, it is called hereditarily structurally complete if all its extensions are structurally complete. Citkin (1978) proved that an intermediate logic is hereditarily structurally complete if and only if the variety of Heyting algebras associated with it omits five finite algebras. Despite its importance in the theory of admissible rules, a direct proof of Citkin’s theorem is not widely accessible. In this paper we offer a self-contained proof of Citkin’s theorem, based on Esakia duality and the method of subframe formulas. As a corollary, we obtain a short proof of Citkin’s 2019 characterization of hereditarily structurally complete positive logics.
      PubDate: 2022-11-02
       
  • There are Infinitely Many Mersenne Prime Numbers. Applications of
           Rasiowa–Sikorski Lemma in Arithmetic (II)

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      Abstract: Abstract The paper is concerned with the old conjecture that there are infinitely many Mersenne primes. It is shown in the work that this conjecture is true in the standard model of arithmetic. The proof refers to the general approach to first–order logic based on Rasiowa-Sikorski Lemma and the derived notion of a Rasiowa–Sikorski set. This approach was developed in the papers [2–4]. This work is a companion piece to [4].
      PubDate: 2022-10-25
       
  • Hilbert Algebras with Hilbert–Galois Connections

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      Abstract: Abstract In this paper we introduce Hilbert algebras with Hilbert–Galois connections (HilGC-algebras) and we study the Hilbert–Galois connections defined in Heyting algebras, called HGC-algebras. We assign a categorical duality between the category HilGC-algebras with Hilbert homomorphisms that commutes with Hilbert–Galois connections and Hilbert spaces with certain binary relations and whose morphisms are special functional relations. We also prove a categorical duality between the category of Heyting Galois algebras with Heyting homomorphisms that commutes with Hilbert–Galois connections and the category of spectral Heyting spaces endowed with a binary relation with certain special continuous maps.
      PubDate: 2022-10-25
       
  • The Twin Primes Conjecture is True in the Standard Model of Peano
           Arithmetic: Applications of Rasiowa–Sikorski Lemma in Arithmetic (I)

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      Abstract: Abstract The paper is concerned with the old conjecture that there are infinitely many twin primes. In the paper we show that this conjecture is true, that is, it is true in the standard model of arithmetic. The proof is based on Rasiowa–Sikorski Lemma. The key role are played by the derived notion of a Rasiowa–Sikorski set and the method of forcing adjusted to arbitrary first–order languages. This approach was developed in the papers Czelakowski [4, 5]. The central idea consists in constructing an appropriate countable model \(\textbf{A}\) of Peano arithmetic by means of a Rasiowa–Sikorski set. This model validates the twin prime conjecture. Since \(\textbf{A}\) is elementarily equivalent to the standard model, the conjecture follows. Thus the standard model validates the twin primes conjecture. More generally, it is shown that de Polignac’s conjecture has a positive solution. The paper employs methods borrowed from the contemporary mathematical logic. Such a ’logical’ approach may be viewed as a useful addition to the dominant methodology in number theory based on mathematical analysis.
      PubDate: 2022-10-25
       
  • Notes on Models of (Partial) Kripke–Feferman Truth

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      Abstract: Abstract This article investigates models of axiomatizations related to the semantic conception of truth presented by Kripke (J Philos 72(19):690–716, 1975), the so-called fixed-point semantics. Among the various proof systems devised as a proof-theoretic characterization of the fixed-point semantics, in recent years two alternatives have received particular attention: classical systems (i.e., systems based on classical logic) and nonclassical systems (i.e., systems based on some nonclassical logic). The present article, building on Halbach and Nicolai (J Philos Log 47(2):227–257, 2018), shows that there is a sense in which classical and nonclassical theories (in suitable variants) have the same models.
      PubDate: 2022-10-15
       
  • Linear L-Algebras and Prime Factorization

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      Abstract: Abstract A complete recursive description of noetherian linear KL-algebras is given. L-algebras form a quantum structure that occurs in algebraic logic, combinatorial group theory, measure theory, geometry, and in connection with solutions to the Yang-Baxter equation. It is proved that the self-similar closure of a noetherian linear KL-algebra is determined by its partially ordered set of primes, and that its elements admit a unique factorization by a decreasing sequence of prime elements.
      PubDate: 2022-10-14
       
  • Modal Companions of $$K4^{+}$$

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      Abstract: Abstract We study modal companions of \(K4^+\) , the strictly positive fragment of K4. We partially find the boundary between all normal extensions of K4 and modal companions of \(K4^+\) among them. We also show that there is no greatest modal companion of \(K4^+\) .
      PubDate: 2022-10-01
      DOI: 10.1007/s11225-022-10001-w
       
  • Loop-Check Specification for a Sequent Calculus of Temporal Logic

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      Abstract: Abstract In our previous work we have introduced loop-type sequent calculi for propositional linear discrete tense logic and proved that these calculi are sound and complete. Decision procedures using the calculi have been constructed for the considered logic. In the present paper we restrict ourselves to the logic with the unary temporal operators “next” and “henceforth always”. Proof-theory of the sequent calculus of this logic is considered, focusing on loop specification in backward proof-search. We describe cyclic sequents and prove that any loop consists of only cyclic sequents. A class of sequents for which backward proof-search do not require loop-check is presented. It is shown how sequents can be coded by binary strings that are used in backward proof-search for the sake of more efficient loop-check.
      PubDate: 2022-08-30
      DOI: 10.1007/s11225-022-10010-9
       
 
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