Related papers: Mathematical Knowledge Bases as Grammar-Compressed…
One often sees a sharp distinction in mathematics between descriptions from the outside and from the inside. Think of defining a set in the plane through an algebraic equation, or dynamically as the closure of the orbit of some point under…
The automated proof search system and decidability for logic of correlated knowledge is presented in this paper. The core of the proof system is the sequent calculus with the properties of soundness, completeness, admissibility of cut and…
The development of logic has largely been through the 'deductive' paradigm: conclusions are inferred from established premisses. However, the use of logic in the context of both human and machine reasoning is typically through the dual…
Currently used metrics for assessing summarization algorithms do not account for whether summaries are factually consistent with source documents. We propose a weakly-supervised, model-based approach for verifying factual consistency and…
In this paper, we introduce a set of tools for providing user-friendly explanations in an explanation-based constraint programming system. The idea is to represent the constraints of a problem as an hierarchy (a tree). Users are then…
As large language models (LLMs) are increasing integrated into fact-checking pipelines, formal logic is often proposed as a rigorous means by which to mitigate bias, errors and hallucinations in these models' outputs. For example, some…
It is well-known that the size of propositional classical proofs can be huge. Proof theoretical studies discovered exponential gaps between normal or cut free proofs and their respective non-normal proofs. The aim of this work is to study…
We argue for a compositional semantics grounded in a strongly typed ontology that reflects our commonsense view of the world and the way we talk about it in ordinary language. Assuming the existence of such a structure, we show that the…
Human mathematicians are often good at recognizing modular and reusable theorems that make complex mathematical results within reach. In this paper, we propose a novel method called theoREm-from-prooF extrACTOR (REFACTOR) for training…
This vision paper articulates a long-term research agenda for formal methods at the intersection with artificial intelligence, outlining multiple conceptual and technical dimensions and reporting on our ongoing work toward realising this…
Fighting misinformation is a challenging, yet crucial, task. Despite the growing number of experts being involved in manual fact-checking, this activity is time-consuming and cannot keep up with the ever-increasing amount of Fake News…
The Axiom-Based Atlas is a novel framework that structurally represents mathematical theorems as proof vectors over foundational axiom systems. By mapping the logical dependencies of theorems onto vectors indexed by axioms - such as those…
Theorem proving in natural mathematical language - the mixture of symbolic and natural language used by humans - plays a central role in mathematical advances and education, and tests aspects of reasoning that are core to intelligence. Yet…
Compounding is a highly productive word-formation process in some languages that is often problematic for natural language processing applications. In this paper, we investigate whether distributional semantics in the form of word…
Reinforcement learning with evaluation metrics as rewards is widely used to enhance specific capabilities of language models. However, for tasks such as factually consistent summarisation, existing metrics remain underdeveloped, limiting…
We show that context semantics can be fruitfully applied to the quantitative analysis of proof normalization in linear logic. In particular, context semantics lets us define the weight of a proof-net as a measure of its inherent complexity:…
Natural language processing techniques are increasingly applied to identify social trends and predict behavior based on large text collections. Existing methods typically rely on surface lexical and syntactic information. Yet, research in…
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…
Graph-matching metrics such as Smatch are the de facto standard for evaluating neural semantic parsers, yet they capture surface overlap rather than logical equivalence. We reassess evaluation by pairing graph-matching with automated…
Automatically generating debates is a challenging task that requires an understanding of arguments and how to negate or support them. In this work we define debate trees and paths for generating debates while enforcing a high level…