Related papers: Graph Logics with Rational Relations
This thesis investigates the central role of homomorphism problems (structure-preserving maps) in two complementary domains: database querying over finite, graph-shaped data, and constraint solving over (potentially infinite) structures.…
Graph data is ubiquitous in the physical world, and it has always been a challenge to efficiently model graph structures using a unified paradigm for the understanding and reasoning on various graphs. Moreover, in the era of large language…
Recent advances in the integration of deep learning with automated theorem proving have centered around the representation of logical formulae as inputs to deep learning systems. In particular, there has been a growing interest in adapting…
To appear in Theory and Practice of Logic Programming (TPLP). Tabling is a commonly used technique in logic programming for avoiding cyclic behavior of logic programs and enabling more declarative program definitions. Furthermore, tabling…
Graph-structured combinatorial challenges are inherently difficult due to their nonlinear and intricate nature, often rendering traditional computational methods ineffective or expensive. However, these challenges can be more naturally…
This paper introduces epistemic graphs as a generalization of the epistemic approach to probabilistic argumentation. In these graphs, an argument can be believed or disbelieved up to a given degree, thus providing a more fine--grained…
Relational properties arise in many settings: relating two versions of a program that use different data representations, noninterference properties for security, etc. The main ingredient of relational verification, relating aligned pairs…
Justification theory is a unifying framework for semantics of non-monotonic logics. It is built on the notion of a justification, which intuitively is a graph that explains the truth value of certain facts in a structure. Knowledge…
This paper explores relational syllogistic logics, a family of logical systems related to reasoning about relations in extensions of the classical syllogistic. These are all decidable logical systems. We prove completeness theorems and…
Graphs are fundamental data structures which concisely capture the relational structure in many important real-world domains, such as knowledge graphs, physical and social interactions, language, and chemistry. Here we introduce a powerful…
Human beings are fundamentally sociable -- that we generally organize our social lives in terms of relations with other people. Understanding social relations from an image has great potential for intelligent systems such as social chatbots…
While large language models (LLMs) have made significant progress in processing and reasoning over knowledge graphs, current methods suffer from a high non-retrieval rate. This limitation reduces the accuracy of answering questions based on…
For some geometric graph classes, tractability of testing first-order formulas is precisely characterised by the graph parameter twin-width. This was first proved for interval graphs among others in [BCKKLT, IPEC '22], where the equivalence…
We try to bring to light some combinatorial structure underlying formal proofs in logic. We do this through the study of the Craig Interpolation Theorem which is properly a statement about the structure of formal derivations. We show that…
Syntax connects words to each other in very specific ways. Two words are syntactically connected if they depend directly on each other. Syntactic connections usually happen within a sentence. Gathering all those connection across several…
Traditionally, graph algorithms get a single graph as input, and then they should decide if this graph satisfies a certain property $\Phi$. What happens if this question is modified in a way that we get a possibly infinite family of graphs…
Graph-based modeling plays a fundamental role in many areas of computer science. In this paper, we introduce systems of graph formulas with variables for specifying graph properties; this notion generalizes the graph formulas introduced in…
We investigate families of infinite automata for context-sensitive languages. An infinite automaton is an infinite labeled graph with two sets of initial and final vertices. Its language is the set of all words labelling a path from an…
The literature on word-representable graphs is quite rich, and a number of variations of the original definition have been proposed over the years. We are initiating a systematic study of such variations based on formal languages. In our…
We present results concerning the expressiveness and decidability of a popular graph learning formalism, graph neural networks (GNNs), exploiting connections with logic. We use a family of recently-discovered decidable logics involving…