Related papers: Maximality in finite-valued Lukasiewicz logics def…

The classical zero-one law for first-order logic on random graphs says that for any first-order sentence $\phi$ in the theory of graphs, as n approaches infinity, the probability that the random graph G(n, p) satisfies $\phi$ approaches…

We show that on graphs with n vertices, the 2-dimensional Weisfeiler-Leman algorithm requires at most O(n^2/log(n)) iterations to reach stabilization. This in particular shows that the previously best, trivial upper bound of O(n^2) is…

The theorem like Pontryagin's maximum principle for multiple integrals is proved. Unlike the usual maximum principle, the maximum should be taken not over all matrices, but only on matrices of rank one. Examples are given.

In the first part, after showing that the most natural approach to define an order on sets of conformal classes fails, we define a nontrivial order $\leq_2$ on the set of conformal classes of compact Cauchy slabs with fixed past boundary…

The multi-valued logic of {\L}ukasiewicz is a substructural logic that has been widely studied and has many interesting properties. It is classical, in the sense that it admits the axiom schema of double negation, [DNE]. However, our…

If $R$ is a valuation domain of maximal ideal $P$ with a maximal immediate extension of finite rank it is proven that there exists a finite sequence of prime ideals $P=L_0\supset L_1\supset...\supset L_m\supseteq 0$ such that…

In this paper, we present an experiment of our randomized hints strategy of automated reasoning for yielding Axiom(5) from Axiom(1)(2)(3)(4) of Infinite-Valued Lukasiewicz Logic. In the experiment, we randomly generated a set of hints with…

We study elementary modal logics, i.e. modal logic considered over first-order definable classes of frames. The classical semantics of modal logic allows infinite structures, but often practical applications require to restrict our…

Let $E$ be an arbitrary directed graph and let $L$ be the Leavitt path algebra of the graph $E$ over a field $K$. The necessary and sufficient con- ditions are given to assure the existence of a maximal ideal in $L$ and also the necessary…

This paper introduces Logical Credal Networks, an expressive probabilistic logic that generalizes many prior models that combine logic and probability. Given imprecise information represented by probability bounds and conditional…

A main property of support vector machines consists in the fact that only a small portion of the training data is significant to determine the maximum margin separating hyperplane in the feature space, the so called support vectors. In a…

General and legal domain LLMs have demonstrated strong performance in various tasks of LegalAI. However, the current evaluations of these LLMs in LegalAI are defined by the experts of computer science, lacking consistency with the logic of…

We characterize several large cardinal notions by model-theoretic properties of extensions of first-order logic. We show that $\Pi_n$-strong cardinals, and, as a corollary, ``Ord is Woodin" and weak Vop\v{e}nka's Principle, are…

Provability logics are modal or polymodal systems designed for modeling the behavior of G\"odel's provability predicate in arithmetical theories and its natural extensions. If \Lambda is any ordinal, the G\"odel-L\"ob calculus GLP(\Lambda)…

In [1] the authors showed some basic properties of a pre-order that arose in combinatorial number theory, namely the finite embeddability between sets of natural numbers, and they presented its generalization to ultrafilters, which is…

In this paper we develop a variational method for the Loewner equation in higher dimensions. As a result we obtain a version of Pontryagin's maximum principle from optimal control theory for the Loewner equation in several complex…

Let $\{X_{k,i};i\geq 1,k\geq 1\}$ be an array of i.i.d. random variables and let $\{p_n;n\geq 1\}$ be a sequence of positive integers such that $n/p_n$ is bounded away from 0 and $\infty$. For $W_n=\max_{1\leq i<j\leq…

Large Language Models (LLMs) are expected to be predictable and trustworthy to support reliable decision-making systems. Yet current LLMs often show inconsistencies in their judgments. In this work, we examine logical preference consistency…

A classical result of Erd\H{o}s and Gallai determines the maximum size $m(n,\nu)$ of a graph $G$ of order $n$ and matching number $\nu n$. We show that $G$ has factorially many maximum matchings provided that its size is sufficiently close…

We review the notion of (finitary) filter pair as a tool for creating and analyzing logics. A filter pair can be seen as a presentation of a logic, given by presenting its lattice of theories as the image of a lattice homomorphism, with…