Related papers: Graph Logics with Rational Relations
Graphs, as a relational data structure, have been widely used for various application scenarios, like molecule design and recommender systems. Recently, large language models (LLMs) are reorganizing in the AI community for their expected…
We present a form of algebraic reasoning for computational objects which are expressed as graphs. Edges describe the flow of data between primitive operations which are represented by vertices. These graphs have an interface made of…
Regular logic can be regarded as the internal language of regular categories, but the logic itself is generally not given a categorical treatment. In this paper, we understand the syntax and proof rules of regular logic in terms of the free…
Graph reachability is the task of understanding whether two distinct points in a graph are interconnected by arcs to which in general a semantic is attached. Reachability has plenty of applications, ranging from motion planning to routing.…
Graph theory provides a language for studying the structure of relations, and it is often used to study interactions over time too. However, it poorly captures the both temporal and structural nature of interactions, that calls for a…
We introduced a methodology to efficiently exploit natural-language expressed biomedical knowledge for repurposing existing drugs towards diseases for which they were not initially intended. Leveraging on developments in Computational…
Regular path queries (RPQs) select nodes connected by some path in a graph. The edge labels of such a path have to form a word that matches a given regular expression. We investigate the evaluation of RPQs with an additional constraint that…
Non-normal modal logics, interpreted on neighbourhood models which generalise the usual relational semantics, have found application in several areas, such as epistemic, deontic, and coalitional reasoning. We present here preliminary…
Logic languages based on the theory of rational, possibly infinite, trees have much appeal in that rational trees allow for faster unification (due to the safe omission of the occurs-check) and increased expressivity (cyclic terms can…
The Int_reg-problem of a combinatorial problem P asks, given a nondeterministic automaton M as input, whether the language L(M) accepted by M contains any positive instance of the problem P. We consider the Int_reg-problem for a number of…
We introduce a refutation graph calculus for classical first-order predicate logic, which is an extension of previous ones for binary relations. One reduces logical consequence to establishing that a constructed graph has empty extension,…
In knowledge-intensive tasks, especially in high-stakes domains like medicine and law, it is critical not only to retrieve relevant information but also to provide causal reasoning and explainability. Large language models (LLMs) have…
We demonstrate that graph-based models are fully capable of representing higher-order interactions, and have a long history of being used for precisely this purpose. This stands in contrast to a common claim in the recent literature on…
Human syntactic structures are usually represented as graphs. Much research has focused on the mapping between such graphs and linguistic sequences, but less attention has been paid to the shapes of the graphs themselves: their topologies.…
Graphs are fundamental objects that find widespread applications across computer science and beyond. Graph Theory has yielded deep insights about structural properties of various families of graphs, which are leveraged in the design and…
We study a general class of recurrence relations that appear in the application of a matrix diagonalization procedure. We find general closed formula and determine analytical properties of the solutions. We finally apply these findings in…
Monadic decomposibility --- the ability to determine whether a formula in a given logical theory can be decomposed into a boolean combination of monadic formulas --- is a powerful tool for devising a decision procedure for a given logical…
Understanding the uncertainty in large language model (LLM) explanations is important for evaluating their faithfulness and reasoning consistency, and thus provides insights into the reliability of LLM's output regarding a question. In this…
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…
We present the basic ideas of forms (a generalization of Ehresmann's sketches) and their theories and models, more explicitly than in previous expositions. Forms provide the ability to specify mathematical structures and data types in any…