Article
Mathematics
Asadollah Fallahi, James Gordon Raftery
Summary: In this article, we exhibit infinitely many semisimple varieties of semilinear De Morgan monoids that are not tabular, but have only tabular proper subvarieties. Thus, the addition of the axiom (p -> q) proves (q -> p) in the extension of relevance logic, resulting in infinitely many pretabular axiomatic extensions regardless of the presence or absence of Ackermann constants.
Article
Logic
Jared Warren
Summary: The article discusses the options for responding to the revenge liar sentence and argues in favor of the meaningless strategy. The author provides a detailed exploration of various response approaches and concludes that the meaningless strategy is as effective as other methods in dealing with the revenge paradox.
JOURNAL OF PHILOSOPHICAL LOGIC
(2023)
Article
Computer Science, Artificial Intelligence
Zeming Chen, Qiyue Gao
Summary: The recent advancements in large language models have demonstrated their remarkable capabilities across various language tasks and domains, challenging traditional understanding of symbolic and logical reasoning. This paper summarizes works on improving monotonicity reasoning through neural networks and deep learning, showcasing different methods and discussing their advantages and limitations. It also focuses on analyzing the ability of large-scale general-purpose language models to perform monotonicity reasoning.
JOURNAL OF LOGIC LANGUAGE AND INFORMATION
(2023)
Article
Computer Science, Artificial Intelligence
Hoang Nga Nguyen, Abdur Rakib
Summary: This paper presents a logic for reasoning about coalitional ability under resource constraints in the probabilistic setting. The authors extend Resource-bounded Alternating-time Temporal Logic (RB-ATL) with probabilistic reasoning and provide a standard algorithm for model-checking. They implement the algorithm and present experimental results using increasingly complex multi-agent model-checking problems.
JOURNAL OF LOGIC LANGUAGE AND INFORMATION
(2023)
Article
Mathematics
A. N. Rybalov
Summary: This paper investigates the generic decidability of word problems in finitely generated semigroups with certain conditions, and provides examples to support the conclusion.
Article
Logic
Alexander De Klerck, Leander Vignero, Lorenz Demey
Summary: In this paper, the study of Aristotelian diagrams in logical geometry is formalized using category theory. Different categories are built and evaluated based on their ability to generalize previous work and their category-theoretical properties. The most promising category is identified, which can significantly enhance further research effectiveness in logical geometry.
LOGICA UNIVERSALIS
(2023)
Article
Mathematics
Fengkui Ju
Summary: This paper presents a logic for conditional weak ontic necessity in branching time and discusses its consequences and comparisons with related works.
Article
Mathematics
Yang Song, Hitoshi Omori, Jonas R. B. Arenhart, Satoshi Tojo
Summary: In this paper, the author discusses JC Beall's new interpretation of Weak Kleene logic and proposes an alternative semantic framework to enrich the interpretation. The paper also offers a new interpretation of the logic of Catuskoti using the on-topic/off-topic divide, based on Beall's proposal. Furthermore, a general result is presented to make sense of a family of infectious logics in terms of Beall's on-topic/off-topic reading.
Article
Computer Science, Artificial Intelligence
Alok Debanth, Manish Shrivastava
Summary: This paper presents a computational algebraic representation of Hindi syntax and demonstrates its application in various syntactic structures.
JOURNAL OF LOGIC LANGUAGE AND INFORMATION
(2023)
Article
Mathematics
James S. Barnes, Jun Le Goh, Richard A. Shore
Summary: This paper examines the complexity of Halin's theorem and similar results in terms of computable and proof theoretic complexity. It finds that these theorems are more complicated than standard compactness arguments and belong to the theorems of hyperarithmetic analysis, which imply the ability to iterate the Turing jump along any computable well ordering. Several important logical principles in this class have been extensively studied and only one purely mathematical example was previously known. The work presented in this paper provides many more examples and answers an open question in reverse mathematics.
JOURNAL OF MATHEMATICAL LOGIC
(2023)
Article
Computer Science, Artificial Intelligence
Shalom Lappin
Summary: This article discusses large language models (LLMs) that drive chatbots and other AI systems, providing a comprehensive assessment of the capabilities and limitations of LLMs. It presents both the arguments against LLMs and the compelling criticisms of these models.
JOURNAL OF LOGIC LANGUAGE AND INFORMATION
(2023)
Article
Computer Science, Artificial Intelligence
Satoru Niki
Summary: This paper investigates subsystems of Kamide's logics, focusing on a system in which double negation behaves as the negation of minimal logic. It explores the phenomenon of these systems proving contradictions but being non-trivial by examining the negation inconsistency and embeddability of contradictions from other systems. Additionally, an informational interpretation of negation is attempted using H. Wansing's dimathematical framework.
JOURNAL OF LOGIC LANGUAGE AND INFORMATION
(2023)
Article
Mathematics
Juan Manuel Cornejo, Hernn Javier San Martin, Valeria Sigal
Summary: This paper introduces the definition and characteristics of integral subresiduated lattice ordered commutative monoids, studies the properties of its submodels, and presents a logic with algebraic semantics.
Article
Mathematics
Luis Estrada-Gonzalez, Ricardo Arturo Nicolas-Francisco
Summary: This paper explores two ways of obtaining connexive logic, either by assigning special properties to the conditional or to the negation. It provides a characterization of connexive negation and discusses the ancient view on connexive logics.
Article
Mathematics
S. V. Pchelintsev, O. V. Shashkov
Summary: It has been proven that a singular superalgebra with a 2-dimensional even part is isomorphic to a superalgebra B2|3(phi, xi, psi). Particularly, there are no infinite-dimensional simple singular superalgebras with a 2-dimensional even part. It has been shown that if a singular superalgebra contains an odd left annihilator, then it contains a nondegenerate switch. Lastly, it has been established that for any number N >= 5, except the numbers 6, 7, 8, 11, there exist singular superalgebras with a switch of dimension N. For the numbers N = 6, 7, 8, 11, there do not exist singular N-dimensional superalgebras with a switch.
Article
Mathematics
A. A. Onoprienko
Summary: This paper examines the joint logic of problems and propositions QHC introduced by S. A. Melikhov, as well as intuitionistic modal logic QH4, and considers their immersion into classical first-order predicate logic. An analog of the Lowenheim-Skolem theorem on the existence of countable elementary submodels for QHC and QH4 is established.
Article
Logic
MIGUEL MORENO
JOURNAL OF SYMBOLIC LOGIC
(2023)
Article
Logic
Soren Brinck Knudstorp
Summary: This paper studies the formal properties of modal information logics (MILs) and solves their open problems regarding axiomatization and decidability. The results have significant implications for modeling information theory and are linked to the study of Lambek Calculus.
JOURNAL OF PHILOSOPHICAL LOGIC
(2023)
Article
Mathematics
A. S. Zakharov
Summary: We consider a class of generalized derivations related to the problem of adding unity to an algebra with generalized derivation and searching for envelopes for Novikov-Poisson algebras. We specify conditions for the existence of the localization of an algebra with ternary derivation, as well as conditions for constructing a Novikov-Poisson algebra and a Jordan superalgebra given an algebra with ternary derivation. Finally, we establish the connection between the simplicity of an algebra with Bresar generalized derivation and the simplicity of the appropriate Novikov algebra.
Article
Mathematics
Juvenal Murwanashyaka
Summary: In this article, we present a method to interpret concatenation theories in arithmetical theories without coding sequences by using 2 x 2 matrices with determinant 1 to represent binary strings.
ARCHIVE FOR MATHEMATICAL LOGIC
(2023)
