Related papers: A correspondence problem for mathematical proof
We give a formalization of the notion of test purpose based on (suitably restricted) Message Sequence Charts. We define the validity of test cases with respect to such a formal test purpose and provide a simple decision procedure for…
The ability to find correspondences in visual data is the essence of most computer vision tasks. But what are the right correspondences? The task of visual correspondence is well defined for two different images of same object instance. In…
Libraries of formal proofs are an important part of our mathematical heritage, but their usability and sustainability is poor. Indeed, each library is specific to a proof system, sometimes even to some version of this system. Thus, a…
The concept of paradeduction is presented in order to justify that we can overlook contradictory information taking into account only what is consistent. Besides that, paradeduction is used to show that there is a way to transform any…
A new generation of AI models generates step-by-step reasoning text before producing an answer. This text appears to offer a human-readable window into their computation process, and is increasingly relied upon for transparency and…
We consider the problem of translating high-level textual descriptions to formal representations in technical documentation as part of an effort to model the meaning of such documentation. We focus specifically on the problem of learning…
We study a conservative extension of classical propositional logic distinguishing between four modes of statement: a proposition may be affirmed or denied, and it may be strong or classical. Proofs of strong propositions must be…
The recently developed proof of Fermat's Last Theorem is very lengthy and difficult, so much so as to be beyond all but a small body of specialists. While certainly of value in the developments that resulted, that proof could not be, nor…
We examine the practicality for a user of using Answer Set Programming (ASP) for representing logical formalisms. We choose as an example a formalism aiming at capturing causal explanations from causal information. We provide an…
Chain-of-Thought reasoning has emerged as a powerful approach for solving complex mathematical and logical problems. However, it can often veer off track through incorrect or unsubstantiated inferences. Formal mathematical reasoning, which…
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…
As deep neural models in NLP become more complex, and as a consequence opaque, the necessity to interpret them becomes greater. A burgeoning interest has emerged in rationalizing explanations to provide short and coherent justifications for…
Scientific fact-checking aims to determine the veracity of scientific claims by retrieving and analysing evidence from research literature. The problem is inherently more complex than general fact-checking since it must accommodate the…
This paper engages the question "Does the consistency of a set of axioms entail the existence of a model in which they are satisfied?" within the frame of the Frege-Hilbert controversy. The question is related historically to the…
This paper develops a formal account of causal explanation, grounded in a theory of conversational pragmatics, and inspired by the interventionist idea that explanation is about asking and answering what-if-things-had-been-different…
The bilateralist approach to logical consequence maintains that judgments of different qualities should be taken into account in determining what-follows-from-what. We argue that such an approach may be actualized by a two-dimensional…
The proof identity problem asks: When are two proofs the same? The question naturally occurs when one reflects on mathematical practice. The problem understandably can be seen as a challenge for mathematical logic, and indeed various…
Languages vary widely in how meanings map to word forms. These mappings have been found to support efficient communication; however, this theory does not account for systematic relations within word forms. We examine how a restricted set of…
Given a class C of word languages, the C-separation problem asks for an algorithm that, given as input two regular languages, decides whether there exists a third language in C containing the first language, while being disjoint from the…
As transformers have gained prominence in natural language processing, some researchers have investigated theoretically what problems they can and cannot solve, by treating problems as formal languages. Exploring such questions can help…