Article
Mathematics
Shaun Allison, Assaf Shani
Summary: A Polish group G is considered tame if the corresponding orbit equivalence relation is Borel under any continuous action of G. Solecki provided a characterization for when G is tame, for the case when G = Pi(n)gamma(n) where gamma(n) is a countable abelian group. Ding and Gao showed that the orbit equivalence relation for such G must be potentially Pi(0)(6), conjecturing that the optimal bound could be Pi(0)(3).
JOURNAL OF MATHEMATICAL LOGIC
(2023)
Article
Computer Science, Artificial Intelligence
Gene Louis Kim, Mandar Juvekar, Junis Ekmekciu, Viet Duong, Lenhart Schubert
Summary: This paper describes the foundation and systematization of natural logic-like monotonic inference using unscoped episodic logical forms (ULFs). It extends the inference manager to address limitations of the naive system by incorporating lexical information, considering multiple scopings, and matching against the goal using English.
JOURNAL OF LOGIC LANGUAGE AND INFORMATION
(2023)
Article
Logic
Balthasar Grabmayr
Summary: There is a gap between metamathematical theorems and their philosophical interpretations, and the philosophical force of these theorems heavily relies on the belief that they do not depend on contingencies regarding formalisation choices. The paper aims to provide metamathematical facts that support this belief and extends previous work by establishing invariant versions of important theorems that are not affected by choices of notation systems and numberings.
JOURNAL OF PHILOSOPHICAL LOGIC
(2023)
Article
Logic
William Troiani
Summary: This article describes how finite colimits can be described using the internal language of a topos, provided the topos allows countably infinite colimits. The article points out the differences between set theory and the internal language, and provides solutions to these differences.
LOGICA UNIVERSALIS
(2023)
Article
Computer Science, Software Engineering
Amelie Gheerbrant, Leonid Libkin, Alexandra Rogova, Cristina Sirangelo
Summary: This paper investigates the problem of answering database queries over incomplete data. By exploring the complexity of certain answers and efficiently answering queries outside the usual classes, the paper proposes a method of rewriting queries as Datalog and first-order queries. The study shows that certain answers can be expressed in Datalog for a well-behaved class of queries, making them tractable in data complexity.
THEORY AND PRACTICE OF LOGIC PROGRAMMING
(2023)
Article
Logic
Eric Raidl, Gilberto Gomes
Summary: This paper investigates the logical behavior of implicative conditionals in natural language. The implicative conditional strengthens the strict conditional while allowing for the possibility of the antecedent and contradictory of the consequent. The paper explores the logical properties of this conditional in a reflexive normal Kripke semantics and provides an axiomatic system that proves to be sound and complete.
JOURNAL OF PHILOSOPHICAL LOGIC
(2023)
Article
Mathematics, Applied
Daniil Kozhemiachenko, Liubov Vashentseva
Summary: This paper discusses the limitations of the traditional approach of using the necessity modality $\Box$ to model knowledge and belief in the Belnap-Dunn logic framework. It introduces a nonstandard modality $\blacksquare$ to address these limitations and formalizes knowledge, belief, unknown truth, and ignorance. The paper provides a Kripke-frame-based semantics and a sound and complete analytic cut system for the introduced modalities, as well as demonstrates the non-definability and definability of certain classes of frames using $\blacksquare$.
LOGIC JOURNAL OF THE IGPL
(2023)
Article
Computer Science, Theory & Methods
Alexander Gheorghiu, David J. Pym
Summary: This paper presents a comprehensive programme for decomposing proof systems of non-classical logics into proof systems of other logics using an algebra of constraints. By enriching simpler proof systems with constraints, proof systems for target logics can be recovered. The aim is to provide a tool for uniform and modular treatment of proof theory and establish a bridge between semantics logics and their proof theory.
JOURNAL OF LOGIC AND COMPUTATION
(2023)
Article
Computer Science, Theory & Methods
Tiago M. L. de Veras, Arthur F. Ramos, Ruy J. G. B. de Queiroz, Anjolina G. de Oliveira
Summary: This paper demonstrates how to formalize the concept of computational paths as equalities between two terms of the same type using a labelled deduction system. With this formalization, the fundamental groupoid of a path-connected type and the concept of isomorphism between types are constructed. It is also shown that computational paths determine a weak category and a weak groupoid.
JOURNAL OF LOGIC AND COMPUTATION
(2023)
Article
Mathematics
S. A. Drobyshevich
Summary: This article studies the extensions of four independent intuitionistic modal logics, finding that the extensions of HKN and HKUn have normal companions, while the extensions of HKP and HKIm have normal companions only if they satisfy a certain law of double negation, and the addition of this law affects the expressive capacities of the logic. It is noteworthy that the extensions of HKP and HKIm have normal companions only if they are definitionally equivalent to the extensions of HKN and HKUn, respectively.
Article
Computer Science, Theory & Methods
Jiachao Wu, Hengfei Li
Summary: This study explores the underlying commons in existing higher-order argumentation framework (HO-AF) semantics and examines their role in semantic research. By introducing the notion of renovation sets and using them to represent and compare semantics built in different approaches, we demonstrate a method of using renovation sets to study HO-AFs.
JOURNAL OF LOGIC AND COMPUTATION
(2023)
Article
Computer Science, Theory & Methods
Leandro Fiorini Aurichi, Lucas Silva Sinzato Real
Summary: This paper investigates the problem of unfriendly partitions in graphs, seeking the minimum cardinality of a graph that satisfies certain criteria and has no unfriendly partitions. The authors found counterexamples by studying graphs with uncountably many vertices, and concluded that this value may vary across different models of set theory.
JOURNAL OF LOGIC AND COMPUTATION
(2023)
Article
Mathematics
Elliot Kaplan, Christoph Kesting
Summary: This study proves a dichotomy for o-minimal fields R expanded by a T-convex valuation ring and a compatible monomial group. It demonstrates that if T is power bounded, then this expansion of R is model complete, has a distal theory, and the definable sets are geometrically tame. However, if R defines an exponential function, then the natural numbers can be externally definable in our expansion, precluding any sort of model-theoretic tameness.
MATHEMATICAL LOGIC QUARTERLY
(2023)
Article
Computer Science, Artificial Intelligence
Reto Gubelmann, Ioannis Katis, Christina Niklaus, Siegfried Handschuh
Summary: This article highlights the dominance of Transformer-based Pre-Trained Language Models in the field of Natural Language Inference (NLI) and identifies two gaps in the current dataset landscape. To address these gaps, the authors propose the introduction of a dataset developed in argumentative writing research and a new dataset based on syllogistic logic. The promises of ChatGPT are also explored. The results show that the new datasets pose a challenge to existing methods and models, including ChatGPT, and that fine-tuning only yields partly satisfactory results.
JOURNAL OF LOGIC LANGUAGE AND INFORMATION
(2023)
Article
Mathematics
Roland Omanadze, Irakli Chitaia
Summary: In this paper, we study the bQ(1)-degrees of c.e. sets using properties of simple sets. We prove several results, including the existence of a simple set C such that C <=(1) A and C <=(1) B when A is a simple set and A <=(bQ1) B, the non-upper semilattice property of c.e. bQ(1)-degrees, the non-density of c.e. b(Q1)-degrees, and the upward density of c.e. b(Q1)-degrees.
MATHEMATICAL LOGIC QUARTERLY
(2023)
Article
Computer Science, Theory & Methods
Ronald Fagin
Summary: This paper utilizes three case studies from IBM to demonstrate the importance and value of applying theory to practice. These case studies cover different fields, including object ranking, data exchange, and real-valued logic, showcasing the interaction between theoreticians and system builders and the benefits of their collaboration.
JOURNAL OF LOGIC AND COMPUTATION
(2023)
Article
Mathematics
Ashutosh Kumar, Saharon Shelah
Summary: It is shown in this study that in the context of ZFC, there exists a relatively consistent scenario where a non-meager set of real numbers X exists. For every non-meager subset Y of X, there are distinct elements x, y, z in Y such that z is computable from the Turing join of x and y.
JOURNAL OF MATHEMATICAL LOGIC
(2023)
Article
Logic
Pablo Caballero, Pablo Valencia
Summary: This paper introduces Hans Reichenbach's three-valued propositional logic RQML developed in 1944 and develops a corresponding calculus Q calculus using First Degree Entailment logic (FDE). By proving the soundness and completeness of Q calculus with respect to RQML semantics, we are able to apply it to analyze causal anomalies.
JOURNAL OF PHILOSOPHICAL LOGIC
(2023)
Article
Mathematics, Applied
Agustin L. Nagy, William J. Zuluaga Botero
Summary: This paper introduces various $I$-modal ririgs and characterizes the congruence lattice of its members using $I$-filters. It provides a description of $I$-filter generation and presents an axiomatic presentation for the variety generated by chains of the subvariety of contractive $I$-modal ririgs. Finally, it introduces a Hilbert-style calculus for a logic with $I$-modal ririgs as an equivalent algebraic semantics and proves the parametrized local deduction-detachment theorem for such a logic.
LOGIC JOURNAL OF THE IGPL
(2023)
Article
Mathematics, Applied
Petar Iliev
Summary: The study demonstrates that the $n$-density and bounded $n$-width of Kripke frames can be defined using Sahlqvist formulae with either a linear number of propositional variables or with polynomial length formulae containing a logarithmic number of variables. However, it is shown that this exponential decrease in the number of variables takes the definition outside the class of Sahlqvist formulae.
LOGIC JOURNAL OF THE IGPL
(2023)
