Article
Logic
Daniel Dohrn
Summary: The translation discusses the comparison between actual possibilities and mere possibilities, as well as the principle of "what is actual is possible." It also proposes restrictions on the validity of this principle when the accessibility of possibilities is contextually restricted.
JOURNAL OF PHILOSOPHICAL LOGIC
(2023)
Article
Mathematics
Bruno Jacinto, Javier Belastegui
Summary: This paper introduces and defends the Synonymy account, which proposes that two theories are synonymous and equivalent if they have the same propositions and entailment relations, as well as a commitment to the truth of the same propositions. It further demonstrates how this account provides a better understanding of the debate between Quineans and noneists, and compares favorably to other competing accounts.
Article
Mathematics
Heinrich Wansing, Hitoshi Omori
Summary: This article introduces the rapid growth of the community researching connexive logics and the issues with terminology used in the field. The aim is to contribute towards unifying and reducing the terminology, making it easier for external scholars to understand the field.
Article
Mathematics
Angelina Ilic-Stepic, Zoran Ognjanovic, Aleksandar Perovic
Summary: The paper introduces a new approach to intuitionistic formalization of reasoning about probability, utilizing Kripke models and a measure function satisfying specific conditions. In order to achieve strong completeness, an infinitary inference rule with a countable set of premises is introduced. The main technical results are proofs of strong completeness and decidability.
Article
Mathematics
Ivan Chajda, Helmut Laenger, Jan Paseka
Summary: A Kleene lattice and Kleene poset are distributive lattices and posets equipped with an antitone involution, which have important mathematical properties. This paper investigates how to construct Kleene lattices and Kleene posets from given distributive lattices or posets using a construction method, and studies their representability and extensions.
Article
Computer Science, Theory & Methods
Yukihiro Oda, James Brotherston, Makoto Tatsuta
Summary: This paper investigates the cut-elimination in cyclic proof systems, focusing on the case of first-order logic with inductive definitions. By providing a specific example, it demonstrates that the use of cut rule is not possible in the cyclic proof system.
JOURNAL OF LOGIC AND COMPUTATION
(2023)
Article
Ethics
Jim Hutchinson
Summary: Frege's systematic conception of science, which emphasizes the Simplicity Requirement, has a significant influence on his work. Acknowledging the central role of this requirement helps illuminate several aspects of his work in new ways.
HISTORY AND PHILOSOPHY OF LOGIC
(2023)
Article
Mathematics
Yushiro Aoki
Summary: We define a property of forcing notions and prove the existence of a model in which this property holds and the continuum hypothesis is negated, while the Cichon-Blass diagram of cardinal invariants matches that of the Cohen model. As a consequence, the forcing axiom and the forcing axiom for sigma-centered forcing notions are shown to be independent of each other.
MATHEMATICAL LOGIC QUARTERLY
(2023)
Article
Mathematics
Matteo Tesi
Summary: This paper presents a purely syntactic analysis of infinitary logic with infinite sequents. It discusses sequent calculi for classical and intuitionistic infinitary logic, which have good structural properties and allow sequents to possibly contain infinitely many formulas. A cut admissibility proof is proposed using a new strategy and a new inductive parameter. The paper concludes by discussing related issues and potential themes for future research.
MATHEMATICAL LOGIC QUARTERLY
(2023)
Article
Computer Science, Theory & Methods
David Makinson
Summary: This article discusses Sir William Hamilton's proposal to extend the traditional categorical logic and the quantification approach he intended. It also examines how commentators have primarily focused on the distributive perspective and how the use of selection functions in third-order logic can provide a more sophisticated representation.
JOURNAL OF LOGIC AND COMPUTATION
(2023)
Article
Mathematics, Applied
Pierre Touchard
Summary: In this article, we demonstrate that the burden of a Henselian valued field can be determined based on the burden of its residue field and value group, following the Ax-Kochen-Ershov principle. To establish this, we establish that the burden of such a field is equivalent to the burden of its leading term structure. These findings extend the work of Chernikov and Simon in [11].
ANNALS OF PURE AND APPLIED LOGIC
(2023)
Article
Mathematics
A. Rodriguez Fanlo
Summary: The aim of this paper is to extend and improve two of the main model-theoretic results by Hrushovski in the context of piecewise hyperdefinable sets, namely the existence of Lie models and the Stabilizer Theorem. This study also includes a systematic investigation of the structure of piecewise hyperdefinable sets, particularly focusing on their logic topologies.
JOURNAL OF MATHEMATICAL LOGIC
(2023)
Article
Logic
Giuseppina Barbieri, Giangiacomo Gerla
Summary: This article addresses the question of a suitable measure theory in Euclidean point-free geometry and outlines some possible solutions. The proposed measures, which are positive and invariant with respect to movements, are based on the concept of infinitesimal masses, i.e. masses whose associated supports form a sequence of finer and finer partitions.
LOGIC AND LOGICAL PHILOSOPHY
(2023)
Correction
Mathematics
Fedor Pakhomov, James Walsh
Summary: We have fixed a gap in a proof in our paper entitled Reducing omega-model reflection to iterated syntactic reflection.
JOURNAL OF MATHEMATICAL LOGIC
(2023)
Article
Mathematics, Applied
Pavel Naumov, Jia Tao
Summary: The article examines two types of responsibility, seeing-to-it responsibility and counterfactual responsibility, in strategic games with imperfect information. It demonstrates that counterfactual responsibility can be defined through seeing-to-it responsibility, but not the other way around. Additionally, the article presents a comprehensive and sound bimodal logical system that captures the interaction between the seeing-to-it modality and the individual ex ante knowledge modality.
ANNALS OF PURE AND APPLIED LOGIC
(2023)
Article
Mathematics, Applied
Dylan Bellier, Massimo Benerecetti, Dario Della Monica, Fabio Mogavero
Summary: The author introduces the limitations of Independence Friendly Logic (IF) and proposes an extension called Alternating Dependence/Independence Friendly Logic (ADIF) to overcome these limitations. ADIF has a stronger expressive power and introduces a new semantics that solves some of the problems of IF.
ANNALS OF PURE AND APPLIED LOGIC
(2023)
Article
Logic
Paolo Maffezioli
Summary: This article provides a mereological analysis of Zeno of Sidon's objection to the principles in Euclid's Elements, specifically the claim that there are no common segments of straight lines and circumferences. The objection centers around the proof that the diameter cuts the circle in half, and Posidonius attempts to prove the bisection without relying on Zeno's principle. The author demonstrates that Posidonius' proof is flawed as it fails to consider cases where one circumference is a proper part of the other, leading to the conclusion that the bisection either false or presupposes Zeno's principle as Zeno claimed.
LOGIC AND LOGICAL PHILOSOPHY
(2023)
Article
Mathematics
James Freitag, Remi Jaoui, Rahim Moosa
Summary: This paper demonstrates that in the theory of differentially closed fields of characteristic zero, if p is a complete type of Lascar rank at least 2 in S(A), then there exists a pair of realizations a(1), a(2) such that p has a nonalgebraic forking extension over Aa(1)a(2). Furthermore, if A is contained in the field of constants, then p already has a nonalgebraic forking extension over Aa(1). The results are also formulated in a more general setting.
JOURNAL OF MATHEMATICAL LOGIC
(2023)
Article
Mathematics, Applied
Grigory Olkhovikov, Guillermo Badia, Reihane Zoghifard
Summary: This study extends the main result of [1] to the first-order intuitionistic logic and demonstrates that it is a maximal abstract logic in terms of expressive power, satisfying a certain form of compactness, the Tarski union property, and preservation under simulations. A similar result is also applicable to the intuitionistic logic of constant domains.
ANNALS OF PURE AND APPLIED LOGIC
(2023)
Article
Mathematics, Applied
Alexi Block Gorman
Summary: This paper provides a complete characterization of the expansion of a complete o-minimal theory by a unary predicate that selects a divisible, dense, and codense group and determines whether it has a model companion. The motivation for this result comes from recent works on the existence of model companions and preservation results for neostability properties. The paper includes examples in which the predicate is an additive subgroup of a real ordered vector space and a multiplicative subgroup of the nonzero elements of an o-minimal expansion of a real closed field. The paper concludes with a discussion on the lack of preservation for certain properties when passing to the model companion.
ANNALS OF PURE AND APPLIED LOGIC
(2023)
