Related papers: Online Generation of Proofs Without Words
The set theory relations \in, \backslash, \Delta, \cap, and \cup have corollaries in subspace relations. Geometric Algebra is introduced as the ideal framework to explore these subspace operations. The relations \in, \backslash, and \Delta…
"How to generate a sentence" is the most critical and difficult problem in all the natural language processing technologies. In this paper, we present a new approach to explain the generation process of a sentence from the perspective of…
We present a light formalism for proofs that encodes their inferential structure, along with a system that transforms these representations into flow-chart diagrams. Such diagrams should improve the comprehensibility of proofs. We discuss…
We present IntelliProof, an interactive system for analyzing argumentative essays through LLMs. IntelliProof structures an essay as an argumentation graph, where claims are represented as nodes, supporting evidence is attached as node…
Two distinct algorithms are presented to extract (schemata of) resolution proofs from closed tableaux for propositional schemata. The first one handles the most efficient version of the tableau calculus but generates very complex…
Geometric (Clifford) algebra provides an efficient mathematical language for describing physical problems. We formulate general relativity in this language. The resulting formalism combines the efficiency of differential forms with the…
Grammar-based sentence generation has been thoroughly explored for Context-Free Grammars (CFGs), but remains unsolved for recognition-based approaches such as Parsing Expression Grammars (PEGs). Lacking tool support, language designers…
Fact verification based on structured data is challenging as it requires models to understand both natural language and symbolic operations performed over tables. Although pre-trained language models have demonstrated a strong capability in…
The Agora system is a prototypical Wiki for formal mathematics: a web-based system for collaborating on formal mathematics, intended to support informal documentation of formal developments. This system requires a reusable proof editor…
We explore the application of transformer-based language models to automated theorem proving. This work is motivated by the possibility that a major limitation of automated theorem provers compared to humans -- the generation of original…
This is a survey on the geometry of warped products, without, or essentially with only soft, calculation. Somewhere in the paper, the goal was to give a synthetic account since existing approaches are rather analytic. Somewhere else, we…
Knowledge graphs (KGs) have the advantage of providing fine-grained detail for question-answering systems. Unfortunately, building a reliable KG is time-consuming and expensive as it requires human intervention. To overcome this issue, we…
We study the proof scheme "proof by example" in which a general statement can be proved by verifying it for a single example. This strategy can indeed work if the statement in question is an algebraic identity and the example is "generic".…
LLM-generated explanations can make technical content more accessible, but there is a ceiling on what they can support interactively. Because LLM outputs are static text, they cannot be executed or stepped through. We argue that grounding…
Proposed is a program for what we call Geometric Arithmetic, based on our works on non-abelian zeta functions and non-abelian class field theory. Key words are stability and adelic intersection-cohomology theory.
In various subjects, there exist compact and consistent relationships between input and output parameters. Discovering the relationships, or namely compact laws, in a data set is of great interest in many fields, such as physics, chemistry,…
We consider the task of automated theorem proving, a key AI task. Deep learning has shown promise for training theorem provers, but there are limited human-written theorems and proofs available for supervised learning. To address this…
Designing software systems for Geometric Computing applications can be a challenging task. Software engineers typically use software abstractions to hide and manage the high complexity of such systems. Without the presence of a unifying…
Recent work by Clark et al. (2020) shows that transformers can act as 'soft theorem provers' by answering questions over explicitly provided knowledge in natural language. In our work, we take a step closer to emulating formal theorem…
The traditional view of evidence in mathematics is that evidence is just proof and proof is just derivation. There are good reasons for thinking that this view should be rejected: it misrepresents both historical and current mathematical…