Tootfinder

This https://arxiv.org/abs/2304.06186 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csCL_…

Using Large Language Models for (De-)Formalization and Natural Argumentation Exercises for Beginner's Students
We describe two systems currently being developed that use large language models for the automatized correction of (i) exercises in translating back and forth between natural language and the languages of propositional logic and first-order predicate logic and (ii) exercises in writing simple arguments in natural language in non-mathematical scenarios.

This https://arxiv.org/abs/2402.12931 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Epstein Semantics: Characterization, Interpolation, Undefinability, and (In)Completeness
This paper is a mathematical investigation on Epstein semantics. One of the main tools of the present paper is the model-theoretic S-set construction introduced in (Krawczyk 2022). We use it to prove several results: 1) that each Epstein model has uncountably many equivalent Epstein models, 2) that the logic of generalised Epstein models is the S-set invariant fragment of CPL (analogon of the celebrated van Benthem characterization theorem for modal logic), 3) that several sets of Epstein relat…

Stalnaker's Epistemic Logic in Isabelle/HOL
Laura P. Gamboa Guzman (Iowa State University, Ames, Iowa), Kristin Y. Rozier (Iowa State University, Ames, Iowa)
https://arxiv.org/abs/2404.14919

Stalnaker's Epistemic Logic in Isabelle/HOL
The foundations of formal models for epistemic and doxastic logics often rely on certain logical aspects of modal logics such as S4 and S4.2 and their semantics; however, the corresponding mathematical results are often stated in papers or books without including a detailed proof, or a reference to it, that allows the reader to convince themselves about them. We reinforce the foundations of the epistemic logic S4.2 for countably many agents by formalizing its soundness and completeness results …

Two Online Map Matching Algorithms Based on Analytic Hierarchy Process and Fuzzy Logic
Jeremy J. Lin, Tomoro Mochida, Riley C. W. O'Neill, Atsuro Yoshida, Masashi Yamazaki, Akinobu Sasada
https://arxiv.org/abs/2402.11866

Two Online Map Matching Algorithms Based on Analytic Hierarchy Process and Fuzzy Logic
Our aim of this paper is to develop new map matching algorithms and to improve upon previous work. We address two key approaches: Analytic Hierarchy Process (AHP) map matching and fuzzy logic map matching. AHP is a decision-making method that combines mathematical analysis with human judgment, and fuzzy logic is an approach to computing based on the degree of truth and aims at modeling the imprecise modes of reasoning from 0 to 1 rather than the usual boolean logic. Of these algorithms, the way…

Logic in Mathematics and Computer Science
Richard Zach
https://arxiv.org/abs/2404.09033 https://arxiv.org/pdf/2404.09033

Logic in Mathematics and Computer Science
Logic has pride of place in mathematics and its 20th century offshoot, computer science. Modern symbolic logic was developed, in part, as a way to provide a formal framework for mathematics: Frege, Peano, Whitehead and Russell, as well as Hilbert developed systems of logic to formalize mathematics. These systems were meant to serve either as themselves foundational, or at least as formal analogs of mathematical reasoning amenable to mathematical study, e.g., in Hilbert's consistency program. Si…

This https://arxiv.org/abs/2404.09033 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Logic in Mathematics and Computer Science
Logic has pride of place in mathematics and its 20th century offshoot, computer science. Modern symbolic logic was developed, in part, as a way to provide a formal framework for mathematics: Frege, Peano, Whitehead and Russell, as well as Hilbert developed systems of logic to formalize mathematics. These systems were meant to serve either as themselves foundational, or at least as formal analogs of mathematical reasoning amenable to mathematical study, e.g., in Hilbert's consistency program. Si…

This https://arxiv.org/abs/2401.08668 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csIT_…

Thermodynamic Perspectives on Computational Complexity: Exploring the P vs. NP Problem
The resolution of the P vs. NP problem, a cornerstone in computational theory, remains elusive despite extensive exploration through mathematical logic and algorithmic theory. This paper takes a novel approach by integrating information theory, thermodynamics, and computational complexity, offering a comprehensive landscape of interdisciplinary study. We focus on entropy, a concept traditionally linked with uncertainty and disorder, and reinterpret it to assess the complexity of computational p…