Related papers: Intuitionistic Layered Graph Logic: Semantics and …
We derive an intuitionistic version of G\"odel-L\"ob modal logic ($\sf{GL}$) in the style of Simpson, via proof theoretic techniques. We recover a labelled system, $\sf{\ell IGL}$, by restricting a non-wellfounded labelled system for…
Knowledge graph (KG) reasoning is becoming increasingly popular in both academia and industry. Conventional KG reasoning based on symbolic logic is deterministic, with reasoning results being explainable, while modern embedding-based…
We show that intuitionistic logic is deductively equivalent to Connexive Heyting Logic (CHL), hereby introduced as an example of a strong connexive logic with intuitive semantics. We use the reverse algebraisation paradigm: CHL is presented…
Inductive logic reasoning is a fundamental task in graph analysis, which aims to generalize patterns from data. This task has been extensively studied for traditional graph representations, such as knowledge graphs (KGs), using techniques…
In this paper we present a formalization of Intuitionistic Propositional Logic in the Lean proof assistant. Our approach focuses on verifying two completeness proofs for the studied logical system, as well as exploring the relation between…
Recent progress in large language models has renewed interest in how multi-step reasoning is represented internally. While prior work often treats reasoning as a linear chain, many reasoning problems are more naturally modeled as directed…
In-context learning (ICL) enhances large language models (LLMs) by incorporating demonstration examples, yet its effectiveness heavily depends on the quality of selected examples. Current methods typically use text embeddings to measure…
Stone-type duality theorems, which relate algebraic and relational/topological models, are important tools in logic because -- in addition to elegant abstraction -- they strengthen soundness and completeness to a categorical equivalence,…
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…
The intersection type assignment system has been designed directly as deductive system for assigning formulae of the implicative and conjunctive fragment of the intuitionistic logic to terms of lambda-calculus. But its relation with 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) 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…
The Lambek calculus is a substructural logic known to be closely related to the formal language theory: on the one hand, it is used for generating formal languages by means of categorial grammars and, on the other hand, it has formal…
While context-free grammars are characterized by a simple proof-theoretic grammatical formalism namely categorial grammar and its logic the Lambek calculus, no such characterizations were known for tree-adjoining grammars, and even for any…
We introduce the notion of coherent graphs, and show how those can be used to define dynamic semantics for Multiplicative Linear Logic (MLL) extended with non-determinism. Thanks to the use of a coherence relation rather than mere formal…
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…
We focus on a conversational question answering task which combines the challenges of understanding questions in context and reasoning over evidence gathered from heterogeneous sources like text, knowledge graphs, tables, and infoboxes. Our…
Reasoning over knowledge graphs (KGs) is a challenging task that requires a deep understanding of the complex relationships between entities and the underlying logic of their relations. Current approaches rely on learning geometries to…
We propose a graph-based extension of Boolean logic called Boolean Graph Logic (BGL). Construing formula trees as the cotrees of cographs, we may state semantic notions such as evaluation and entailment in purely graph-theoretic terms,…
Integrated Gradients (IG) is a common explainability technique to address the black-box problem of neural networks. Integrated gradients assumes continuous data. Graphs are discrete structures making IG ill-suited to graphs. In this work,…