Related papers: Superposition as a logical glue
We describe a "top down" approach for automated theorem proving (ATP). Researchers might usefully investigate the forms of the theorems mathematicians use in practice, carefully examine how they differ and are proved in practice, and code…
Data integration is considered a classic research field and a pressing need within the information science community. Ontologies play a critical role in such a process by providing well-consolidated support to link and semantically…
Non-classical logics are used in a wide spectrum of disciplines, including artificial intelligence, computer science, mathematics, and philosophy. The de-facto standard infrastructure for automated theorem proving, the TPTP World, currently…
In order to work with mathematical content in computer systems, it is necessary to represent it in formal languages. Ideally, these are supported by tools that verify the correctness of the content, allow computing with it, and produce…
Incrementality is ubiquitous in human-human interaction and beneficial for human-computer interaction. It has been a topic of research in different parts of the NLP community, mostly with focus on the specific topic at hand even though…
Formal logic has often been seen as uniquely placed to analyze mathematical argumentation. While formal logic is certainly necessary for a complete understanding of mathematical practice, it is not sufficient. Important aspects of…
This paper is a reflexion on the computability of natural language semantics. It does not contain a new model or new results in the formal semantics of natural language: it is rather a computational analysis of the logical models and…
This paper explores the relationship of artificial intelligence to the task of resolving open questions in mathematics. We first present an updated version of a traditional argument that limitative results from computability and complexity…
Logicians study and apply a multiplicity of various logical systems. Consequently, there is necessity to build foundations and common grounds for all these systems. This is done in metalogic. Like metamathematics studies formalized…
Across languages, numeral systems vary widely in how they construct and combine numbers. While humans consistently learn to navigate this diversity, large language models (LLMs) struggle with linguistic-mathematical puzzles involving…
This article describes a prototype implementation of a web interface for the Matita proof assistant. The interface supports all basic functionalities of the local Gtk interface, but takes advantage of the markup to enrich the document with…
A logic is presented for reasoning on iterated sequences of formulae over some given base language. The considered sequences, or "schemata", are defined inductively, on some algebraic structure (for instance the natural numbers, the lists,…
We present a modification of the superposition calculus that is meant to generate consequences of sets of first-order axioms. This approach is proven to be sound and deductive-complete in the presence of redundancy elimination rules,…
Software tools of Automated Reasoning are too sophisticated for general use in mathematics education and respective reasoning, while Lucas-Interpretation provides a general concept for integrating such tools into educational software with…
We examine whether self-supervised language modeling applied to mathematical formulas enables logical reasoning. We suggest several logical reasoning tasks that can be used to evaluate language models trained on formal mathematical…
The next-token prediction (NTP) objective trains language models to predict a single token at each step, even though many continuations can express the same meaning. For example, in the sentence ``this sticker can be placed here'',…
In argumentative discourse, persuasion is often achieved by refuting or attacking others arguments. Attacking is not always straightforward and often comprise complex rhetorical moves such that arguers might agree with a logic of an…
Business documents often contain substantial tabular and textual information with numerical values, requiring mathematical reasoning for effective document understanding. While Small Language Models (SLMs) still struggle at this task,…
The study of finite automata and regular languages is a privileged meeting point of algebra and logic. Since the work of Buchi, regular languages have been classified according to their descriptive complexity, i.e. the type of logical…
To appear in Theory and Practice of Logic Programming (TPLP). Dynamic systems play a central role in fields such as planning, verification, and databases. Fragmented throughout these fields, we find a multitude of languages to formally…