Related papers: Ground interpolation for the theory of equality
Extrapolation -- the ability to make inferences that go beyond the scope of one's experiences -- is a hallmark of human intelligence. By contrast, the generalization exhibited by contemporary neural network algorithms is largely limited to…
In this paper, the problem of matching pairs of correlated random graphs with multi-valued edge attributes is considered. Graph matching problems of this nature arise in several settings of practical interest including social network…
Machine learning models that operate on graph-structured data, such as molecular graphs or social networks, often make accurate predictions but offer little insight into why certain predictions are made. Counterfactual explanations address…
We provide a direct method for proving Craig interpolation for a range of modal and intuitionistic logics, including those containing a "converse" modality. We demonstrate this method for classical tense logic, its extensions with path…
Spline interpolation is a widely used class of methods for solving interpolation problems by constructing smooth interpolants that minimize a regularized energy functional involving the Laplacian operator. While many existing approaches…
Temporal knowledge graph (TKG) reasoning has two settings: interpolation reasoning and extrapolation reasoning. Both of them draw plenty of research interest and have great significance. Methods of the former de-emphasize the temporal…
Graph workloads pose a particularly challenging problem for query optimizers. They typically feature large queries made up of entirely many-to-many joins with complex correlations. This puts significant stress on traditional cardinality…
Flow matching models typically use linear interpolants to define the forward/noise addition process. This, together with the independent coupling between noise and target distributions, yields a vector field which is often non-straight.…
In this paper, we introduce a graph matching method that can account for constraints of arbitrary order, with arbitrary potential functions. Unlike previous decomposition approaches that rely on the graph structures, we introduce a…
We study finite graphs embedded in oriented surfaces by associating a polynomial to it. The tools used in developing a theory of such graph polynomials are algebraic topological while the polynomial itself is inspired from ideas arising in…
We prove the uniform interpolation theorem in modal provability logics GL and Grz by a proof-theoretical method, using analytical and terminating sequent calculi for the logics. The calculus for G\"odel-L\"ob's logic GL is a variant of the…
The aim of this paper is to prove an improved version of the bounded differences inequality for matrix valued functions, by developing the methods of Mackey et al.: "Matrix Concentration Inequalities via the Method of Exchangeable Pairs".…
Craig interpolation in SMT is difficult because, e. g., theory combination and integer cuts introduce mixed literals, i. e., literals containing local symbols from both input formulae. In this paper, we present a scheme to compute Craig…
Equivalence between algebraic equations of motion may be detected by using a $p$-adic method, methods using factorization and linear algebra, or by systematic computer search of suitable Tschirnhausen transformations. Here, we show standard…
Temporal Knowledge Graph Reasoning (TKGR) aims to complete missing factual elements along the timeline. Depending on the temporal position of the query, the task is categorized into interpolation and extrapolation. Existing interpolation…
Interaction nets are a graphical formalism inspired by Linear Logic proof-nets often used for studying higher order rewriting e.g. \Beta-reduction. Traditional presentations of interaction nets are based on graph theory and rely on…
Pitts' proof-theoretic technique for uniform interpolation, which generates uniform interpolants from terminating sequent calculi, has only been applied to logics on an intuitionistic basis through single-succedent sequent calculi. We adapt…
It is well-known that the size of propositional classical proofs can be huge. Proof theoretical studies discovered exponential gaps between normal or cut free proofs and their respective non-normal proofs. The aim of this work is to study…
In this paper we present a proof system that operates on graphs instead of formulas. Starting from the well-known relationship between formulas and cographs, we drop the cograph-conditions and look at arbitrary undirected) graphs. This…
The main purpose of this paper is to construct not only generating functions of the new approach Genocchi type numbers and polynomials but also interpolation function of these numbers and polynomials which are related to a, b, c arbitrary…