Related papers: On Graph Refutation for Relational Inclusions
The Calculus of Conjunctive Queries (CCQ) has foundational status in database theory. A celebrated theorem of Chandra and Merlin states that CCQ query inclusion is decidable. Its proof transforms logical formulas to graphs: each query has a…
The syntax of modal graphs is defined in terms of the continuous cut and broken cut following Charles Peirce's notation in the gamma part of his graphical logic of existential graphs. Graphical calculi for normal modal logics are developed…
In this paper, author uses set theory to construct a logic model of abstract figure from binary relation. Based on the uniform quantified structure, author gives two logic system for graph traversal and graph coloring respectively, moreover…
Motivated by the definition of the edge elimination polynomial of a graph we define the covered components polynomial counting spanning subgraphs with respect to their number of components, edges and covered components. We prove a…
The question of whether or not any zero torsion linear map on a non abelian real Lie algebra g is necessarily an extension of some CR-structure is considered and answered in the negative. Two examples are provided, one in the negative and…
Current methods for textual analysis rely on data annotated within predefined ontologies, often embedding human bias within black-box models. Despite achieving near-perfect performance, these approaches exploit unstructured, linear pattern…
A broader definition of generalized truncations of graphs is introduced followed by an exploration of some standard concepts and parameters with regard to generalized truncations.
We employ the theory of canonical extensions to study residuation algebras whose associated relational structures are functional, i.e., for which the ternary relations associated to the expanded operations admit an interpretation as…
We study the semantics of a resource-sensitive extension of the lambda calculus in a canonical reflexive object of a category of sets and relations, a relational version of Scott's original model of the pure lambda calculus. This calculus…
In recent work, the authors developed a simple method of constructing topological spaces from certain well-behaved partially ordered sets -- those coming from sequences of relations between finite sets. This method associates a given poset…
Graphs can represent relational information among entities and graph structures are widely used in many intelligent tasks such as search, recommendation, and question answering. However, most of the graph-structured data in practice suffers…
In this paper we study possibilities of interpolation and symbol elimination in extensions of a theory $\mathcal{T}_0$ with additional function symbols whose properties are axiomatised using a set of clauses. We analyze situations in which…
Proof schemata are infinite sequences of proofs which are defined inductively. In this paper we present a general framework for schemata of terms, formulas and unifiers and define a resolution calculus for schemata of quantifier-free…
Knowledge graphs (KGs) are inherently incomplete because of incomplete world knowledge and bias in what is the input to the KG. Additionally, world knowledge constantly expands and evolves, making existing facts deprecated or introducing…
The \emph{fractional matching preclusion number} of a graph $G$, denoted by $fmp(G)$, is the minimum number of edges whose deletion results in a graph that has no fractional perfect matchings. In this paper, we first give some sharp upper…
Fractional calculus is the calculus of differentiation and integration of non-integer orders. In a recently paper (Annals of Physics 323 (2008) 2756-2778), the Fundamental Theorem of Fractional Calculus is highlighted. Based on this…
This article describes a method to build syntactical dependencies starting from the phrase structure parsing process. The goal is to obtain all the information needed for a detailled semantical analysis. Interaction Grammars are used for…
We study the reverse mathematics and computability of countable graph theory, obtaining the following results. The principle that every countable graph has a connected component is equivalent to $\mathsf{ACA}_0$ over $\mathsf{RCA}_0$. The…
The purpose of this paper is to develop a "calculus" on graphs that allows graph theory to have new connections to analysis. For example, our framework gives rise to many new partial differential equations on graphs, most notably a new…
We answer some questions about graphs which are reducts of countable models of Anti-Foundation, obtained by considering the binary relation of double-membership $x\in y\in x$. We show that there are continuum-many such graphs, and study…