Related papers: Interaction Graphs: Multiplicatives
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…
Recent findings in neuroscience suggest that the human brain represents information in a geometric structure (for instance, through conceptual spaces). In order to communicate, we flatten the complex representation of entities and their…
We present a game semantics for Linear Logic, in which formulas denote games and proofs denote winning strategies. We show that our semantics yields a categorical model of Linear Logic and prove full completeness for Multiplicative Linear…
In this thesis we present a semantic representation formalism based on directed graphs and explore its linguistic adequacy and explanatory benefits in the semantics of plurality and quantification. Our graph language covers the essentials…
We demonstrate a deep learning framework which is inherently based in the highly expressive language of relational logic, enabling to, among other things, capture arbitrarily complex graph structures. We show how Graph Neural Networks and…
The notion of homomorphism indistinguishability offers a combinatorial framework for characterizing equivalence relations of graphs, in particular equivalences in counting logics within finite model theory. That is, for certain graph…
We introduce a complete many-valued semantics for two normal lattice-based modal logics. This semantics is based on reflexive many-valued graphs. We discuss an interpretation and possible applications of this logical framework in the…
We develop a new, intrinsic, computationally friendly approach to Lie coalgebras through graph coalgebras, which are new and likely to be of independent interest. Our graph coalgebraic approach has advantages both in finding relations…
We present the theory of multifunctions applied to graphs. Its interesting feature is that walks are recognized as iterations. We consider the graphs with arbitrary number of vertices which are determined by multifunctions. The mutually…
In this paper we investigate two logics from an algebraic point of view. The two logics are: MALL (multiplicative-additive Linear Logic) and LL (classical Linear Logic). Both logics turn out to be strongly algebraizable in the sense of Blok…
The Resource $\lambda$-calculus is a variation of the $\lambda$-calculus where arguments can be superposed and must be linearly used. Hence it is a model for linear and non-deterministic programming languages, and the target language of…
Metabolic networks, formed by a series of metabolic pathways, are made of intracellular and extracellular reactions that determine the biochemical properties of a cell, and by a set of interactions that guide and regulate the activity of…
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…
Large language models (LLMs) are being increasingly explored for graph tasks. Despite their remarkable success in text-based tasks, LLMs' capabilities in understanding explicit graph structures remain limited, particularly with large…
Knowledge graphs (KGs) have gained prominence for their ability to learn representations for uni-relational facts. Recently, research has focused on modeling hyper-relational facts, which move beyond the restriction of uni-relational facts…
Game semantics extends the Curry-Howard isomorphism to a three-way correspondence: proofs, programs, strategies. But the universe of strategies goes beyond intuitionistic logics and lambda calculus, to capture stateful programs. In this…
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…
Distributed representations (such as those based on embeddings) and discrete representations (such as those based on logic) have complementary strengths. We explore one possible approach to combining these two kinds of representations. We…
Linear Logic refines Intuitionnistic Logic by taking into account the resources used during the proof and program computation. In the past decades, it has been extended to various frameworks. The most famous are indexed linear logics which…
The relational semantics of linear logic is a powerful framework for defining resource-aware models of the $\lambda$-calculus. However, its quantitative aspects are not reflected in the preorders and equational theories induced by these…