Logic and Philosophy of Logic

Edited by Aleksandra Samonek (Université Catholique de Louvain, Jagiellonian University, Catholic University of Louvain)
Assistant editors: Mackenzie Marcotte, Sadegh Balal Niaki
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  1. AF-Algebras with Lattice-Ordered K0: Logic and Computation.Daniele Mundici - forthcoming - Annals of Pure and Applied Logic:103182.
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  2. Maximal Towers and Ultrafilter Bases in Computability Theory.Steffen Lempp, Joseph S. Miller, André Nies & Mariya I. Soskova - forthcoming - Journal of Symbolic Logic:1-20.
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    Logics
     Classical Logic
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  3. Distality rank.Roland Walker - forthcoming - Journal of Symbolic Logic:1-32.
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  4. On the Proof Complexity of Logics of Bounded Branching.Emil Jeřábek - 2023 - Annals of Pure and Applied Logic 174 (1):103181.
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  5. The Two Halves of Disjunctive Correctness.Cezary Cieslinski, Mateusz Lelyk & Bartosz Wcislo - forthcoming - Journal of Mathematical Logic.
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  6. Cohen-Like First Order Structures.Ziemowit Kostana - 2023 - Annals of Pure and Applied Logic 174 (1):103172.
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     Classical Logic
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    Paradoxes
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     Paradoxes, Misc    		Logical Semantics and Logical TruthHistory of Logic
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  7. Trial and Error Mathematics: Dialectical Systems and Completions of Theories.Luca San Mauro, Jacopo Amidei, Uri Andrews, Duccio Pianigiani & Andrea Sorbi - 2019 - Journal of Logic and Computation 1 (29):157-184.
    This paper is part of a project that is based on the notion of a dialectical system, introduced by Magari as a way of capturing trial and error mathematics. In Amidei et al. (2016, Rev. Symb. Logic, 9, 1–26) and Amidei et al. (2016, Rev. Symb. Logic, 9, 299–324), we investigated the expressive and computational power of dialectical systems, and we compared them to a new class of systems, that of quasi-dialectical systems, that enrich Magari’s systems with a natural mechanism (...)
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  8. Non-Stationary Support Iterations of Prikry Forcings and Restrictions of Ultrapower Embeddings to the Ground Model.Moti Gitik & Eyal Kaplan - 2023 - Annals of Pure and Applied Logic 174 (1):103164.
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  9. Huge Reflection.Joan Bagaria & Philipp Lücke - 2023 - Annals of Pure and Applied Logic 174 (1):103171.
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     Classical Logic
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    Paradoxes
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     Paradoxes, Misc    		Logical Semantics and Logical TruthHistory of Logic
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  10. Admissibility of Π2-Inference Rules: Interpolation, Model Completion, and Contact Algebras.Nick Bezhanishvili, Luca Carai, Silvio Ghilardi & Lucia Landi - 2023 - Annals of Pure and Applied Logic 174 (1):103169.
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    Logics
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  11. The Poset of All Logics II: Leibniz Classes and Hierarchy.R. Jansana & T. Moraschini - forthcoming - Journal of Symbolic Logic:1-39.
    A Leibniz class is a class of logics closed under the formation of term-equivalent logics, compatible expansions, and non-indexed products of sets of logics. We study the complete lattice of all Leibniz classes, called the Leibniz hierarchy. In particular, it is proved that the classes of truth-equational and assertional logics are meet-prime in the Leibniz hierarchy, while the classes of protoalgebraic and equivalential logics are meet-reducible. However, the last two classes are shown to be determined by Leibniz conditions consisting of (...)
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    Paradoxes
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     Paradoxes, Misc    		Logical Semantics and Logical TruthHistory of Logic
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  12. Incompatible Bounded Category Forcing Axioms.David Asperó & Matteo Viale - 2022 - Journal of Mathematical Logic 22 (2).
    We introduce bounded category forcing axioms for well-behaved classes Γ. These are strong forms of bounded forcing axioms which completely decide the theory of some initial segment of the universe...
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    Paradoxes
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     Paradoxes, Misc    		Logical Semantics and Logical TruthHistory of Logic
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  13. Strong Compactness and the Ultrapower Axiom I: The Least Strongly Compact Cardinal.Gabriel Goldberg - 2022 - Journal of Mathematical Logic 22 (2).
    The Ultrapower Axiom is a combinatorial principle concerning the structure of large cardinals that is true in all known canonical inner models of set theory. A longstanding test question for inner...
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  14. Forcing the Σ31-Separation Property.Stefan Hoffelner - 2022 - Journal of Mathematical Logic 22 (2).
    We generically construct a model in which the Σ31-separation property is true, i.e. every pair of disjoint Σ31-sets can be separated by a Δ31-definable set. This answers an old question from the pr...
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    Logics
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    Paradoxes
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     Paradoxes, Misc    		Logical Semantics and Logical TruthHistory of Logic
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  15. Structural Reflection, Shrewd Cardinals and the Size of the Continuum.Philipp Lücke - 2022 - Journal of Mathematical Logic 22 (2).
    Motivated by results of Bagaria, Magidor and Väänänen, we study characterizations of large cardinal properties through reflection principles for classes of structures. More specifically, we aim to...
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    Logics
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     Paradoxes, Misc    		Logical Semantics and Logical TruthHistory of Logic
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  16. Definable Completeness of P-Minimal Fields and Applications.Pablo Cubides Kovacsics & Françoise Delon - 2022 - Journal of Mathematical Logic 22 (2).
    We show that every definable nested family of closed and bounded subsets of a P-minimal field K has nonempty intersection. As an application we answer a question of Darnière and Halupczok showing t...
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  17. Frege’s Ontological Diagram Completed.David Makinson - forthcoming - Logica Universalis:1-7.
    In a letter of 1891, Frege drew a diagram to illustrate his logical ontology. We observe that it omits features that play an important role in his thought on the matter, propose an extension of the diagram to include them, and compare with a diagram of the ontology of current first-order logic.
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  18. The Bounds of Transcendental Logic.S. Kovač - forthcoming - History and Philosophy of Logic:1-4.
    There is a persistent line of research attesting to the relevance of Kant’s philosophy for the development of modern logic and for the foundations of logical primitive concepts and structures. This...
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  19. On Equational Completeness Theorems.Tommaso Moraschini - forthcoming - Journal of Symbolic Logic:1-54.
    A logic is said to admit an equational completeness theorem when it can be interpreted into the equational consequence relative to some class of algebras. We characterize logics admitting an equational completeness theorem that are either locally tabular or have some tautology. In particular, it is shown that a protoalgebraic logic admits an equational completeness theorem precisely when it has two distinct logically equivalent formulas. While the problem of determining whether a logic admits an equational completeness theorem is shown to (...)
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  20. Quantifier Elimination on Some Pseudo-Algebraically Closed Valued Fields.Jizhan Hong - 2023 - Annals of Pure and Applied Logic 174 (1):103170.
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  21. The Permutations with Non-Fixed Points and the Sequences with Length of a Set.J. Nuntasri & P. Vejjajiva - forthcoming - Journal of Symbolic Logic:1-14.
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  22. Revisiting the Conditional Construal of Conditional Probability.Jakub Węgrecki & Leszek Wroński - forthcoming - Logic and Logical Philosophy.
    We show how to extend any finite probability space into another finite one which satisfies the conditional construal of conditional probability for the original propositions, given some maximal allowed degree of nesting of the conditional. This mitigates the force of the well-known triviality results.
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  23. Logic and Phenomenology: Wittgenstein / Ramsey / Schlick in Colour-Exclusion.Mihai Ometiță - 2017 - In Marcos Silva (ed.), Colours in the Development of Wittgenstein’s Philosophy. London, UK: pp. 127-159.
    The paper argues, in a nutshell, that Wittgenstein’s reconsideration, after Ramsey’s review, of the Tractatus provides the rationale for the methodological reflections from the former’s manuscripts, which are less sceptical than Schlick’s, on the viability of a phenomenological philosophy. The argument proceeds like this. Section 1 exposes a charge against a Tractarian account of logical syntax: for Ramsey, early Wittgenstein holds unjustifiably that any proposition taken to exhibit logical impossibility, like the impossibility of a fleck of two colours, is analysable (...)
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  24. Bounded-Depth Frege Complexity of Tseitin Formulas for All Graphs.Nicola Galesi, Dmitry Itsykson, Artur Riazanov & Anastasia Sofronova - 2023 - Annals of Pure and Applied Logic 174 (1):103166.
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  25. Constructive Strong Regularity and the Extension Property of a Compactification.Giovanni Curi - 2023 - Annals of Pure and Applied Logic 174 (1):103154.
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  26. Wittgenstein and the Problem of Phenomenology [PhD Diss.].Mihai Ometiță - 2016 - Dissertation, University of East Anglia
    Wittgenstein’s mention of the term “phenomenology” in his writings from the middle period has long been regarded as puzzling by interpreters. It is striking to see him concerned with that philosophical approach, generally regarded as foreign to the tradition of Russell and Frege, in which Wittgenstein’s thought is commonly taken to have primarily developed. On the basis of partially unpublished material from Wittgenstein’s Nachlass, the thesis provides a reconstruction of the rationale and fate of his conception of phenomenology, which he (...)
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  27. Extensional Realizability and Choice for Dependent Types in Intuitionistic Set Theory.Emanuele Frittaion - forthcoming - Journal of Symbolic Logic:1-31.
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  28. Affine Logic for Constructive Mathematics.Michael Shulman - forthcoming - Bulletin of Symbolic Logic:1-51.
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  29. Arbitrary Public Announcement Logic with Memory.Alexandru Baltag, Aybüke Özgün & Ana Lucia Vargas Sandoval - forthcoming - Journal of Philosophical Logic:1-58.
    We introduce Arbitrary Public Announcement Logic with Memory, obtained by adding to the models a ‘memory’ of the initial states, representing the information before any communication took place, and adding to the syntax operators that can access this memory. We show that APALM is recursively axiomatizable. We present a complete recursive axiomatization, that includes a natural finitary rule, and study this logic’s expressivity and the appropriate notion of bisimulation. We then examine Group Announcement Logic with Memory, the extension of APALM (...)
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  30. On Zardini’s Rules for Multiplicative Quantification as the Source of Contra(di)Ctions.Uwe Petersen - forthcoming - Review of Symbolic Logic:1-10.
    Certain instances of contraction are provable in Zardini’s system $\mathbf {IK}^\omega $ which causes triviality once a truth predicate and suitable fixed points are available.
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  31. Strong Homomorphisms, Category Theory, and Semantic Paradox.Jonathan Wolfgram & Roy T. Cook - forthcoming - Review of Symbolic Logic:1-24.
    In this essay we introduce a new tool for studying the patterns of sentential reference within the framework introduced in [2] and known as the language of paradox $\mathcal {L}_{\mathsf {P}}$ : strong $\mathcal {L}_{\mathsf {P}}$ -homomorphisms. In particular, we show that strong $\mathcal {L}_{\mathsf {P}}$ -homomorphisms between $\mathcal {L}_{\mathsf {P}}$ constructions preserve paradoxicality, many earlier results regarding the paradoxicality of $\mathcal {L}_{\mathsf {P}}$ constructions can be recast as special cases of our central result regarding strong $\mathcal {L}_{\mathsf {P}}$ -homomorphisms, (...)
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  32. Logic and African Philosophy: Seminal Essays on African Systems of Thought: J. Chimakonam, Editor. Delaware, Vernon Press, 2020, Xiv + 326 Pp., 16 Plts, €48, ISBN: 978-1-62273-882-3.E. Ofuasia - 2021 - History and Philosophy of Logic 43 (3):303-305.
    Logic and African Philosophy: Seminal Essays on African Systems of Thought is an edited work by Jonathan Chimakonam who is affiliated to the Philosophy Department at the University of Pretoria, Sou...
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  33. Computational Complexity of Hybrid Interval Temporal Logics.Przemysław Andrzej Wałęga - 2023 - Annals of Pure and Applied Logic 174 (1):103165.
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  34. Pa Relative to an Enumeration Oracle.Jun le Goh, Iskander Sh Kalimullin, Joseph S. Miller & Mariya I. Soskova - forthcoming - Journal of Symbolic Logic:1-27.
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  35. The G4i Analogue of a G3i Sequent Calculus.Rosalie Iemhoff - forthcoming - Studia Logica:1-14.
    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 (...)
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  36. Enumerating Teams in First-Order Team Logics.Anselm Haak, Arne Meier, Fabian Müller & Heribert Vollmer - forthcoming - Annals of Pure and Applied Logic:103163.
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  37. Twist Structures and Nelson Conuclei.Manuela Busaniche, Nikolaos Galatos & Miguel Andrés Marcos - 2022 - Studia Logica 110 (4):949-987.
    Motivated by Kalman residuated lattices, Nelson residuated lattices and Nelson paraconsistent residuated lattices, we provide a natural common generalization of them. Nelson conucleus algebras unify these examples and further extend them to the non-commutative setting. We study their structure, establish a representation theorem for them in terms of twist structures and conuclei that results in a categorical adjunction, and explore situations where the representation is actually an isomorphism. In the latter case, the adjunction is elevated to a categorical equivalence. By (...)
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  38. An Analysis of Poly-connexivity.Luis Estrada-González - 2022 - Studia Logica 110 (4):925-947.
    Francez has suggested that connexivity can be predicated of connectives other than the conditional, in particular conjunction and disjunction. Since connexivity is not any connection between antecedents and consequents—there might be other connections among them, such as relevance—, my question here is whether Francez’s conjunction and disjunction can properly be called ‘connexive’. I analyze three ways in which those connectives may somehow inherit connexivity from the conditional by standing in certain relations to it. I will show that Francez’s connectives fail (...)
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  39. On Extracting Variable Herbrand Disjunctions.Andrei Sipoş - 2022 - Studia Logica 110 (4):1115-1134.
    Some quantitative results obtained by proof mining take the form of Herbrand disjunctions that may depend on additional parameters. We attempt to elucidate this fact through an extension to first-order arithmetic of the proof of Herbrand’s theorem due to Gerhardy and Kohlenbach which uses the functional interpretation.
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  40. Generalizing Deontic Action Logic.Alessandro Giordani & Matteo Pascucci - 2022 - Studia Logica 110 (4):989-1033.
    We introduce a multimodal framework of deontic action logic which encodes the interaction between two fundamental procedures in normative reasoning: conceptual classification and deontic classification. The expressive power of the framework is noteworthy, since it combines insights from agency logic and dynamic logic, allowing for a representation of many kinds of normative conflicts. We provide a semantic characterization for three axiomatic systems of increasing strength, showing how our approach can be modularly extended in order to get different levels of analysis (...)
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  41. Correction to: The Hahn Embedding Theorem for a Class of Residuated Semigroups.Sándor Jenei - 2022 - Studia Logica 110 (4):1135-1135.
    A Correction to this paper has been published: 10.1007/s11225-020-09933-y.
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  42. Group Representation for Even and Odd Involutive Commutative Residuated Chains.Sándor Jenei - 2022 - Studia Logica 110 (4):881-922.
    For odd and for even involutive, commutative residuated chains a representation theorem is presented in this paper by means of direct systems of abelian o-groups equipped with further structure. This generalizes the corresponding result of J. M. Dunnabout finite Sugihara monoids.
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  43. Correction to: Group Representation for Even and Odd Involutive Commutative Residuated Chains.Sándor Jenei - 2022 - Studia Logica 110 (4):923-924.
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  44. What is a Relevant Connective?Shawn Standefer - 2022 - Journal of Philosophical Logic 51 (4):919-950.
    There appears to be few, if any, limits on what sorts of logical connectives can be added to a given logic. One source of potential limitations is the motivating ideology associated with a logic. While extraneous to the logic, the motivating ideology is often important for the development of formal and philosophical work on that logic, as is the case with intuitionistic logic. One family of logics for which the philosophical ideology is important is the family of relevant logics. In (...)
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  45. A Unified Logic for Contingency and Accident.Jie Fan - 2022 - Journal of Philosophical Logic 51 (4):693-720.
    As shown in Fan, there are some similarities/resemblances between contingency and accident. Given this, one may naturally ask if we can unify the two operators to manifest all of their similarities/resemblances. In this article, instead of looking at the interactions between the two operators like in Fan, we turn our attention to the resemblances between the two operators. We extend the unification method in Fan to the current setting. The main results include some model-theoretical ones, such as expressivity, frame definability, (...)
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  46. Designing Paradoxes: A Revision-theoretic Approach.Ming Hsiung - 2022 - Journal of Philosophical Logic 51 (4):739-789.
    According to the revision theory of truth, the binary sequences generated by the paradoxical sentences in revision sequence are always unstable. In this paper, we work backwards, trying to reconstruct the paradoxical sentences from some of their binary sequences. We give a general procedure of constructing paradoxes with specific binary sequences through some typical examples. Particularly, we construct what Herzberger called “unstable statements with unpredictably complicated variations in truth value.” Besides, we also construct those paradoxes with infinitely many finite primary (...)
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  47. Higher-Order Logic and Disquotational Truth.Lavinia Picollo & Thomas Schindler - 2022 - Journal of Philosophical Logic 51 (4):879-918.
    Truth predicates are widely believed to be capable of serving a certain logical or quasi-logical function. There is little consensus, however, on the exact nature of this function. We offer a series of formal results in support of the thesis that disquotational truth is a device to simulate higher-order resources in a first-order setting. More specifically, we show that any theory formulated in a higher-order language can be naturally and conservatively interpreted in a first-order theory with a disquotational truth or (...)
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  48. Paraconsistent Metatheory: New Proofs with Old Tools.Guillermo Badia, Zach Weber & Patrick Girard - 2022 - Journal of Philosophical Logic 51 (4):825-856.
    This paper is a step toward showing what is achievable using non-classical metatheory—particularly, a substructural paraconsistent framework. What standard results, or analogues thereof, from the classical metatheory of first order logic can be obtained? We reconstruct some of the originals proofs for Completeness, Löwenheim-Skolem and Compactness theorems in the context of a substructural logic with the naive comprehension schema. The main result is that paraconsistent metatheory can ‘re-capture’ versions of standard theorems, given suitable restrictions and background assumptions; but the shift (...)
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  49. Smooth Infinitesimals in the Metaphysical Foundation of Spacetime Theories.Lu Chen - 2022 - Journal of Philosophical Logic 51 (4):857-877.
    I propose a theory of space with infinitesimal regions called smooth infinitesimal geometry based on certain algebraic objects, which regiments a mode of reasoning heuristically used by geometricists and physicists. I argue that SIG has the following utilities. It provides a simple metaphysics of vector fields and tangent space that are otherwise perplexing. A tangent space can be considered an infinitesimal region of space. It generalizes a standard implementation of spacetime algebraicism called Einstein algebras. It solves the long-standing problem of (...)
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  50. Taking Up Thagard’s Challenge: A Formal Model of Conceptual Revision.Sena Bozdag & Matteo De Benedetto - 2022 - Journal of Philosophical Logic 51 (4):791-824.
    Thagard presented a framework for conceptual change in science based on conceptual systems. Thagard challenged belief revision theorists, claiming that traditional belief-revision systems are able to model only the two most conservative types of changes in his framework, but not the more radical ones. The main aim of this work is to take up Thagard’s challenge, presenting a belief-revision-like system able to mirror radical types of conceptual change. We will do that with a conceptual revision system, i.e. a belief-revision-like system (...)
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