Logic and Philosophy of Logic

Edited by Aleksandra Samonek (Université Catholique de Louvain, Jagiellonian University, Catholic University of Louvain)
Assistant editor: Sadegh Balal Niaki (University of Western Ontario)
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  1. Large Cardinals Beyond Choice.Joan Bagaria, Peter Koellner & W. Hugh Woodin - forthcoming - Bulletin of Symbolic Logic:1-57.
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    Logics
     Classical Logic
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  2. Exponential Constructible Functions in P-Minimal Structures.Saskia Chambille, Pablo Cubides Kovacsics & Eva Leenknegt - forthcoming - Journal of Mathematical Logic.
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  3. Computable Aspects of the Bachmann-Howard Principle.Anton Freund - forthcoming - Journal of Mathematical Logic.
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  4. Discrete Metric Spaces: Structure, Enumeration, and 0-1 Laws.Dhruv Mubayi & Caroline Terry - forthcoming - Journal of Symbolic Logic:1-33.
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  5. A Critical Examination of the Historical Origins of Connexive Logic.Wolfgang Lenzen - forthcoming - History and Philosophy of Logic:1-20.
    It is often assumed that Aristotle, Boethius, Chrysippus, and other ancient logicians advocated a connexive conception of implication according to which no proposition entails, or is entailed by, i...
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  6. Alethic Reference.Lavinia Picollo - forthcoming - Journal of Philosophical Logic:1-22.
    I put forward precise and appealing notions of reference, self-reference, and well-foundedness for sentences of the language of first-order Peano arithmetic extended with a truth predicate. These notions are intended to play a central role in the study of the reference patterns that underlie expressions leading to semantic paradox and, thus, in the construction of philosophically well-motivated semantic theories of truth.
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  7. Lyndon Interpolation Theorem of Instantial Neighborhood Logic - Constructively Via a Sequent Calculus.Junhua Yu - forthcoming - Annals of Pure and Applied Logic:102721.
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  8. Cut Elimination in Hypersequent Calculus for Some Logics of Linear Time.Andrzej Indrzejczak - forthcoming - Review of Symbolic Logic:1-20.
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  9. On Morita Equivalence and Interpretability.Paul Anh Mceldowney - forthcoming - Review of Symbolic Logic:1-28.
    In a recent article, Barrett & Halvorson define a notion of equivalence for first-order theories, which they call “Morita equivalence.” To argue that Morita equivalence is a reasonable measure of “theoretical equivalence,” they make use of the claim that Morita extensions “say no more” than the theories they are extending. The goal of this article is to challenge this central claim by raising objections to their argument for it and by showing why there is good reason to think that the (...)
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    Logical Semantics and Logical TruthHistory of Logic
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  10. Subordination Tarski Algebras.Sergio A. Celani - 2019 - Journal of Applied Non-Classical Logics 29 (3):288-306.
    ABSTRACTIn this work we will study Tarski algebras endowed with a subordination, called subordination Tarski algebras. We will define the notion of round filters, and we will study the class of irr...
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  11. Belnap-Dunn Semantics for Natural Implicative Expansions of Kleene's Strong Three-Valued Matrix II. Only One Designated Value.Gemma Robles, Francisco Salto & José M. Méndez - 2019 - Journal of Applied Non-Classical Logics 29 (3):307-325.
    ABSTRACTThis paper is a sequel to ‘Belnap-Dunn semantics for natural implicative expansions of Kleene's strong three-valued matrix with two designated values’, where a ‘bivalent’ Belnap-Dunn semant...
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  12. Indefinite Abductive Explanations.Luciano Caroprese & Ester Zumpano - 2019 - Journal of Applied Non-Classical Logics 29 (3):233-254.
    ABSTRACTThis paper stems from previous works of the authors in which a new measure of the simplicity of an explanation based on its degree of arbitrariness is proposed: The more the explanation is...
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  13. Axiomatic and Dual Systems for Constructive Necessity, a Formally Verified Equivalence.Lourdes del Carmen González-Huesca, Favio E. Miranda-Perea & P. Selene Linares-Arévalo - 2019 - Journal of Applied Non-Classical Logics 29 (3):255-287.
    ABSTRACTWe present a proof of the equivalence between two deductive systems for constructive necessity, namely an axiomatic characterisation inspired by Hakli and Negri's system of derivations from...
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  14. Non-Constructive Procedural Theory of Propositional Problems and the Equivalence of Solutions.Ivo Pezlar - 2019 - In Igor Sedlár & Martin Blicha (eds.), The Logica Yearbook 2018. London: College Publications. pp. 197-210.
    We approach the topic of solution equivalence of propositional problems from the perspective of non-constructive procedural theory of problems based on Transparent Intensional Logic (TIL). The answer we put forward is that two solutions are equivalent if and only if they have equivalent solution concepts. Solution concepts can be understood as a generalization of the notion of proof objects from the Curry-Howard isomorphism.
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  15. Aristotle in Prussian Gymnasiums: Why the Texts of the Ancient Philosopher Became Popular for Teaching Logic.Maxim Demin - forthcoming - History and Philosophy of Logic:1-15.
    During the nineteenth century, German philosophy developed from a type of general knowledge to an academic discipline at the university. Changes across disciplines to the philosophy of science and...
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  16. Corrigendum to “Model-Completions for Abelian Lattice-Ordered Groups with Finitely Many Disjoint Elements” [Ann. Pure Appl. Logic 170 673–698]. [REVIEW]Philip Scowcroft - forthcoming - Annals of Pure and Applied Logic:102720.
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  17. $$\Hbox {Venn}{I{O1}}$$ Venn I o 1 : A Diagram System for Universe Without Boundary.Reetu Bhattacharjee, Mihir Kr Chakraborty & Lopamudra Choudhury - forthcoming - Logica Universalis.
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  18. $$Hbox {Venn}{I{O1}}$$: A Diagram System for Universe Without Boundary.Reetu Bhattacharjee, Mihir Kr Chakraborty & Lopamudra Choudhury - forthcoming - Logica Universalis:1-58.
    A new diagram system \ where properties are fundamental and an object exists only w.r.t a property is presented. This work modifies both in syntax and semantics the system \ proposed by Choudhury and Chakraborty to picturise and address issues connected with open universe. Semantics for the current system is given. Soundness and completeness w.r.t the semantics are established.
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  19. Modelling Last-Act Attempted Crime in Criminal Law.Jiraporn Pooksook, Phan Minh Dung, Ken Satoh & Giovanni Sartor - forthcoming - Journal of Applied Non-Classical Logics:1-31.
    ABSTRACTIn the court of law, a person can be punished for attempting to commit a crime. An open issue in the study of Artificial Intelligence and Law is whether the law of attempts could be formall...
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  20. Strong Density of Definable Types and Closed Ordered Differential Fields.Quentin Brouette, Pablo Cubides Kovacsics & Françoise Point - forthcoming - Journal of Symbolic Logic:1-19.
    The following strong form of density of definable types is introduced for theories T admitting a fibered dimension function d: given a model M of T and a definable set X ⊆ M n, there is a definable type p in X, definable over a code for X and of the same d-dimension as X. Both o-minimal theories and the theory of closed ordered differential fields are shown to have this property. As an application, we derive a new proof of (...)
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  21. The Dp-Rank of Abelian Groups.Yatir Halevi & Daniel Palacín - forthcoming - Journal of Symbolic Logic:1-30.
    An equation to compute the dp-rank of any abelian group is given. It is also shown that its dp-rank, or more generally that of any one-based group, agrees with its Vapnik–Chervonenkis density. Furthermore, strong abelian groups are characterised to be precisely those abelian groups A such that there are only finitely many primes p such that the group A / pA is infinite and for every prime p, there are only finitely many natural numbers n such that $\left[p]/\left[p]$ is infinite. (...)
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  22. Two Proofs of the Algebraic Completeness Theorem for Multilattice Logic.Oleg Grigoriev & Yaroslav Petrukhin - forthcoming - Journal of Applied Non-Classical Logics:1-24.
    Shramko [. Truth, falsehood, information and beyond: The American plan generalized. In K. Bimbo, J. Michael Dunn on information based logics, outstanding contributions to logic...
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  23. The Large Structures of Grothendieck Founded on Finite Order Arithmetic.Colin Mclarty - forthcoming - Review of Symbolic Logic:1-30.
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  24. Raymond Smullyan, A Beginner’s Further Guide to Mathematical Logic.Morten Heine Sørensen - forthcoming - Studia Logica:1-3.
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  25. A Note on Strong Axiomatization of Gödel Justification Logic.Nicholas Pischke - forthcoming - Studia Logica:1-38.
    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 operators, one can therefore not only reason about modal effects on propositions but also about dynamics inside the justifications themselves. We (...)
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  26. Frege on Referentiality and Julius Caesar in Grundgesetze §10.Bruno Bentzen - forthcoming - Notre Dame Journal of Formal Logic.
    This paper aims to answer the question of whether or not Frege's solution limited to value-ranges and truth-values proposed to resolve the "problem of indeterminacy of reference" in section 10 of Grundgesetze is a violation of his principle of complete determination, which states that a predicate must be defined to apply for all objects in general. Closely related to this doubt is the common allegation that Frege was unable to solve a persistent version of the Caesar problem for value-ranges. It (...)
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  27. Separating the Fan Theorem and Its Weakenings II.Robert S. Lubarsky - forthcoming - Journal of Symbolic Logic:1-28.
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  28. Regular Tree Languages in the First Two Levels of the Borel Hierarchy.Filippo Cavallari - 2019 - Bulletin of Symbolic Logic 25 (2):221-222.
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  29. Self-Embeddings of Models of Peano Arithmetic.Saeideh Bahrami - 2019 - Bulletin of Symbolic Logic 25 (2):217-218.
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  30. A Theory of Stationary Trees and the Balanced Baumgartner–Hajnal–Todorcevic Theorem for Trees.Ari Meir Brodsky - 2019 - Bulletin of Symbolic Logic 25 (2):219-219.
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  31. Self-Similarity in the Foundations.Paul K. Gorbow - 2019 - Bulletin of Symbolic Logic 25 (2):216-217.
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  32. Creatures and Cardinals.Lukas Daniel Klausner - 2019 - Bulletin of Symbolic Logic 25 (2):218-219.
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  33. Completeness of Finite-Rank Differential Varieties.William D. Simmons - 2019 - Bulletin of Symbolic Logic 25 (2):220-221.
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  34. New Directions for Neo-Logicism.Aaron Thomas-Bolduc - 2019 - Bulletin of Symbolic Logic 25 (2):219-220.
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  35. Indirect Proof and Inversions of Syllogisms.Roy Dyckhoff - 2019 - Bulletin of Symbolic Logic 25 (2):196-207.
    By considering the new notion of the inverses of syllogisms such as Barbara and Celarent, we show how the rule of Indirect Proof, in the form used by Aristotle, may be dispensed with, in a system comprising four basic rules of subalternation or conversion and six basic syllogisms.
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  36. Vaught’s Two-Cardinal Theorem and Notions of Minimality in Continuous Logic.Victoria Noquez - 2019 - Bulletin of Symbolic Logic 25 (2):215-216.
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  37. Explicit Computational Paths in Type Theory.Arthur Freitas Ramos - 2019 - Bulletin of Symbolic Logic 25 (2):213-214.
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  38. Formalization of Context-Free Language Theory.Marcus Vinícius Midena Ramos - 2019 - Bulletin of Symbolic Logic 25 (2):214-214.
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  39. Some Applications of Set Theory to Model Theory.Douglas Ulrich - 2019 - Bulletin of Symbolic Logic 25 (2):214-215.
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  40. Foundations of Online Structure Theory.Nikolay Bazhenov, Rod Downey, Iskander Kalimullin & Alexander Melnikov - 2019 - Bulletin of Symbolic Logic 25 (2):141-181.
    The survey contains a detailed discussion of methods and results in the new emerging area of online “punctual” structure theory. We also state several open problems.
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  41. A Conjectural Classification of Strongly Dependent Fields.Yatir Halevi, Assaf Hasson & Franziska Jahnke - 2019 - Bulletin of Symbolic Logic 25 (2):182-195.
    We survey the history of Shelah’s conjecture on strongly dependent fields, give an equivalent formulation in terms of a classification of strongly dependent fields and prove that the conjecture implies that every strongly dependent field has finite dp-rank.
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  42. An Extension of a Theorem of Zermelo.Jouko Väänänen - 2019 - Bulletin of Symbolic Logic 25 (2):208-212.
    We show that if $$ satisfies the first-order Zermelo–Fraenkel axioms of set theory when the membership relation is ${ \in _1}$ and also when the membership relation is ${ \in _2}$, and in both cases the formulas are allowed to contain both ${ \in _1}$ and ${ \in _2}$, then $\left \cong \left$, and the isomorphism is definable in $$. This extends Zermelo’s 1930 theorem in [6].
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  43. Agglomerative Algebras.Jeremy Goodman - 2019 - Journal of Philosophical Logic 48 (4):631-648.
    This paper investigates a generalization of Boolean algebras which I call agglomerative algebras. It also outlines two conceptions of propositions according to which they form an agglomerative algebra but not a Boolean algebra with respect to conjunction and negation.
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  44. Reasoning About Arbitrary Natural Numbers From a Carnapian Perspective.Leon Horsten & Stanislav O. Speranski - 2019 - Journal of Philosophical Logic 48 (4):685-707.
    Inspired by Kit Fine’s theory of arbitrary objects, we explore some ways in which the generic structure of the natural numbers can be presented. Following a suggestion of Saul Kripke’s, we discuss how basic facts and questions about this generic structure can be expressed in the framework of Carnapian quantified modal logic.
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  45. Six Problems in Pure Inductive Logic.J. B. Paris & A. Vencovská - 2019 - Journal of Philosophical Logic 48 (4):731-747.
    We present six significant open problems in Pure Inductive Logic, together with their background and current status, with the intention of raising awareness and leading ultimately to their resolution.
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  46. A New Game Equivalence, its Logic and Algebra.Johan van Benthem, Nick Bezhanishvili & Sebastian Enqvist - 2019 - Journal of Philosophical Logic 48 (4):649-684.
    We present a new notion of game equivalence that captures basic powers of interacting players. We provide a representation theorem, a complete logic, and a new game algebra for basic powers. In doing so, we establish connections with imperfect information games and epistemic logic. We also identify some new open problems concerning logic and games.
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  47. Holism, Meaning Similarity and Inferential Space—a Measurement Theoretic Approach.Eli Dresner - 2019 - Journal of Philosophical Logic 48 (4):611-630.
    Proponents of meaning holism often invoke notions of meaning similarity and semantic spatiality in order to counter accusations that holism renders language unstable and chaotic. However, talk of such notions often falls short of being explicit and formal. In this paper I present an algebraically couched theory of inferential similarity and spatiality, motivated by measurement theory, and I apply it to the discussion of meaning holism. I argue that the proposed theory offers new and improved conceptual resources for facing the (...)
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  48. On Generalization of Definitional Equivalence to Non-Disjoint Languages.Koen Lefever & Gergely Székely - 2019 - Journal of Philosophical Logic 48 (4):709-729.
    For simplicity, most of the literature introduces the concept of definitional equivalence only for disjoint languages. In a recent paper, Barrett and Halvorson introduce a straightforward generalization to non-disjoint languages and they show that their generalization is not equivalent to intertranslatability in general. In this paper, we show that their generalization is not transitive and hence it is not an equivalence relation. Then we introduce another formalization of definitional equivalence due to Andréka and Németi which is equivalent to the Barrett–Halvorson (...)
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  49. Adding a Nonreflecting Weakly Compact Set.Brent Cody - 2019 - Notre Dame Journal of Formal Logic 60 (3):503-521.
    For n<ω, we say that theΠn1-reflection principle holds at κ and write Refln if and only if κ is a Πn1-indescribable cardinal and every Πn1-indescribable subset of κ has a Πn1-indescribable proper initial segment. The Πn1-reflection principle Refln generalizes a certain stationary reflection principle and implies that κ is Πn1-indescribable of order ω. We define a forcing which shows that the converse of this implication can be false in the case n=1; that is, we show that κ being Π11-indescribable of (...)
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  50. Martin-Löf Randomness Implies Multiple Recurrence in Effectively Closed Sets.Rodney G. Downey, Satyadev Nandakumar & André Nies - 2019 - Notre Dame Journal of Formal Logic 60 (3):491-502.
    This work contributes to the program of studying effective versions of “almost-everywhere” theorems in analysis and ergodic theory via algorithmic randomness. Consider the setting of Cantor space {0,1}N with the uniform measure and the usual shift. We determine the level of randomness needed for a point so that multiple recurrence in the sense of Furstenberg into effectively closed sets P of positive measure holds for iterations starting at the point. This means that for each k∈N there is an n such (...)
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