Related papers: Uniform Interpolation in provability logics

We present a variation of Maehara's method to construct Craig-Lyndon interpolants for the three-valued propositional logic of here and there (HT), also known as G\"odel's $G_3$, a superintuitionistic logic of importance in logic…

This paper introduces a uniform substitution calculus for differential refinement logic dRL. The logic dRL extends the differential dynamic logic dL such that one can simultaneously reason about properties of and relations between hybrid…

In this paper we investigate the parallelization of two modular algorithms. In fact, we consider the modular computation of Gr\"obner bases (resp. standard bases) and the modular computation of the associated primes of a zero-dimensional…

We give a necessary and sufficient graph-theoretic characterization of toric ideals of graphs that are unimodular. As a direct consequence, we provide the structure of unimodular graphs by proving that the incidence matrix of a graph $G$ is…

This paper studies the proof of Collatz conjecture for some set of sequence of odd numbers with infinite number of elements. These set generalized to the set which contains all positive odd integers. This extension assumed to be the proof…

We ask questions generalizing uniform versions of conjectures of Mordell and Lang and combining them with the Morton--Silverman conjecture on preperiodic points. We prove a few results relating different versions of such questions.

In the first part, in the local non archimedean case, we consider distributions on GL(n+1) which are invariant under the adjoint action of GL(n). We conjecture that such distributions are invariant by transposition. This would imply…

The quasi-normal modal logic GLS is a provability logic formalizing the arithmetical truth. Kushida (2020) gave a sequent calculus for GLS and proved the cut-elimination theorem. This paper introduces semantical characterizations of GLS and…

We say that a Kripke model is a GL-model if the accessibility relation $\prec$ is transitive and converse well-founded. We say that a Kripke model is a D-model if it is obtained by attaching infinitely many worlds $t_1, t_2, \ldots$, and…

In this paper we prove a Robinson consistency theorem for a class of many-sorted hybrid logics as a consequence of an Omitting Types Theorem. An important corollary of this result is an interpolation theorem.

In these lecture notes, we first recall the connection between graph neural networks, Weisfeiler-Lehman tests and logics such as first-order logic and graded modal logic. We then present a modal logic in which counting modalities appear in…

The present work aims to give a unity of logic via standard sequential, unpolarized games. Specifically, our vision is that there must be mathematically precise concepts of linear refinement and intuitionistic restriction of logic such that…

We present a sequent calculus for the weak Grzegorczyk logic Go allowing non-well-founded proofs and obtain the cut-elimination theorem for it by constructing a continuous cut-elimination mapping acting on these proofs.

We construct a Gr\"obner Basis of the relation ideal of a polynomial, give an interpolation formula for the basis elements and explain the connection of the interpolation formula to the Buchberger--M\"oller algorithm. We present a situation…

Let $(G,\pmb{+})$ be any given semimodule over a discrete semiring $(R,+,\cdot)$ with a finite coloring, say $G=B_1\cup\dotsm\cup B_q$. By establishing a Regional Multiple Recurrence Theorem for semimodules, we prove that one of the colors…

Craig's interpolation theorem (Craig 1957) is an important theorem known for propositional logic and first-order logic. It says that if a logical formula $\beta$ logically follows from a formula $\alpha$, then there is a formula $\gamma$,…

We study the first-order primal infon logic. It is the core of the policy language DKAL. We provide Gentzen-style calculi for two versions of this logic that are not equivalent. For both versions we investigate the semantics: one of them is…

A unified Gentzen-style framework for until-free propositional linear-time temporal logic is introduced. The proposed framework, based on infinitary rules and rules for primitive negation, can handle uniformly both a single-succedent…

The complex method of interpolation, going back to Calder\'on and Coifman et al., on the one hand, and the Alexander-Wermer-Slodkowski theorem on polynomial hulls with convex fibers, on the other hand, are generalized to a method of…

The classical Gagliardo-Nirenberg inequality, known as an interpolation inequality, involves Lebesgue norms of functions and their derivatives. We established an interpolation lemma to connect Lebesgue and H\"older spaces, thus extending…