Related papers: Coherent Interaction Graphs
The original idea of proof nets can be formulated by means of interaction nets syntax. Additional machinery as switching, jumps and graph connectivity is needed in order to ensure correspondence between a proof structure and a correct proof…
We introduce a graph-theoretical representation of proofs of multiplicative linear logic which yields both a denotational semantics and a notion of truth. For this, we use a locative approach (in the sense of ludics) related to game…
We devise an algorithm to generate propositions that objectively instantiate graphs supporting coherence-driven inference. We also benchmark the ability of large language models (LLMs) to reconstruct coherence graphs from (a simple…
Interaction graphs were introduced as a general, uniform, construction of dynamic models of linear logic, encompassing all "Geometry of Interaction" (GoI) constructions introduced so far. This series of work was inspired from Girard's…
In (hyper)coherence semantics, proofs/terms are cliques in (hyper)graphs. Intuitively, vertices represent results of computations and the edge relation witnesses the ability of being assembled into a same piece of data or a same (strongly)…
Proof nets are a syntax for linear logic proofs which gives a coarser notion of proof equivalence with respect to syntactic equality together with an intuitive geometrical representation of proofs. In this paper we give an alternative…
Models of complex systems are widely used in the physical and social sciences, and the concept of layering, typically building upon graph-theoretic structure, is a common feature. We describe an intuitionistic substructural logic called…
Recent advances in test-time scaling have enabled Large Language Models (LLMs) to display sophisticated reasoning abilities via extended Chain-of-Thought (CoT) generation. Despite their potential, these Reasoning LLMs (RLMs) often…
Large language models (LLMs) are increasingly used for text-rich graph machine learning tasks such as node classification in high-impact domains like fraud detection and recommendation systems. Yet, despite a surge of interest, the field…
Linear logic has provided new perspectives on proof-theory, denotational semantics and the study of programming languages. One of its main successes are proof-nets, canonical representations of proofs that lie at the intersection between…
This work deals with the challenge of learning and reasoning over multi-hop question answering (QA). We propose a graph reasoning network based on the semantic structure of the sentences to learn cross paragraph reasoning paths and find the…
The Geometry of Interaction purpose is to give a semantic of proofs or programs accounting for their dynamics. The initial presentation, translated as an algebraic weighting of paths in proofnets, led to a better characterization of the…
Large language models (LLMs) have demonstrated remarkable success across a wide range of tasks; however, they still encounter challenges in reasoning tasks that require understanding and inferring relationships between distinct pieces of…
Large language models (LLMs) have shown promise in table Question Answering (Table QA). However, extending these capabilities to multi-table QA remains challenging due to unreliable schema linking across complex tables. Existing methods…
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…
Handsome proof nets were introduced by Retor\'e as a syntax for multiplicative linear logic. These proof nets are defined by means of cographs (graphs representing formulas) equipped with a vertices partition satisfying simple topological…
Coherence with respect to Kelly-Mac Lane graphs is proved for categories that correspond to the multiplicative fragment without constant propositions of classical linear first-order predicate logic without or with mix. To obtain this…
Differentiable Logics are deployed in neuro-symbolic learning tasks as a way of embedding logical constraints in the training objective of neural networks. A differentiable logic consists of a syntax to write logical properties and a…
We have designed a new logic programming language called LM (Linear Meld) for programming graph-based algorithms in a declarative fashion. Our language is based on linear logic, an expressive logical system where logical facts can be…
Large Language Models (LLMs) have demonstrated remarkable capabilities in text generation and understanding, yet their reliance on implicit, unstructured knowledge often leads to factual inaccuracies and limited interpretability. Knowledge…