Related papers: An Automated Theorem Generator with Theoretical Fo…

We present a~novel approach to the problem of automated theorem proving. Polynomial cost procedures that recognise sentences belonging to a theory are generated on a basis of a set of axioms of the so-called Truncated Predicate Calculus…

In recent years, with the development of deep learning, text generation technology has undergone great changes and provided many kinds of services for human beings, such as restaurant reservation and daily communication. The automatically…

Recently, it is often said that the data used for the pre-training of large language models (LLMs) have been exhausted. This paper proposes a solution to the problem: Automated generation of massive reasonable empirical theorems by forward…

We present Generative Logic (GL), a deterministic architecture that starts from user-supplied axiomatic definitions written in a minimalist Mathematical Programming Language (MPL) and systematically explores a configurable region of their…

Retrieval Augmented Generation (RAG) systems have emerged as a powerful method for enhancing large language models (LLMs) with up-to-date information. However, the retrieval step in RAG can sometimes surface documents containing…

Type-free systems of logic are designed to consistently handle significant instances of self-reference. Some consistent type-free systems also have the feature of allowing the sort of general abstraction or comprehension principle that…

Automated deduction seeks to enable machines to reason with mathematical precision and logical completeness. Classical resolution-based systems, such as Prover9, E, and Vampire, rely on binary inference, which inherently limits multi-clause…

Controlled Text Generation (CTG) aims to produce texts that exhibit specific desired attributes. In this study, we introduce a pluggable CTG framework for Large Language Models (LLMs) named Dynamic Attribute Graphs-based controlled text…

Instruction-tuned large language models have shown remarkable performance in aligning generated text with user intentions across various tasks. However, maintaining human-like discourse structure in the generated text remains a challenging…

Developing the logic necessary to solve mathematical problems or write mathematical proofs is one of the more difficult objectives for large language models (LLMS). Currently, the most popular methods in literature consists of fine-tuning…

Automated Theorem Proving (ATP) deals with the development of computer programs being able to show that some conjectures (queries) are a logical consequence of a set of axioms (facts and rules). There exists several successful ATPs where…

In this paper we study the logical foundations of automated inductive theorem proving. To that aim we first develop a theoretical model that is centered around the difficulty of finding induction axioms which are sufficient for proving a…

Automatic question generation is one of the most challenging tasks of Natural Language Processing. It requires "bidirectional" language processing: firstly, the system has to understand the input text (Natural Language Understanding) and it…

Retrieval-Augmented Generation (RAG) has become a core paradigm for enhancing factual grounding and multi-hop reasoning in Large Language Models (LLMs). Traditional text-based RAG often retrieves logically irrelevant pseudo-evidence, while…

Theorem proving serves as a major testbed for evaluating complex reasoning abilities in large language models (LLMs). However, traditional automated theorem proving (ATP) approaches rely heavily on formal proof systems that poorly align…

Counter-speech generation is at the core of many expert activities, such as fact-checking and hate speech, to counter harmful content. Yet, existing work treats counter-speech generation as pure text generation task, mainly based on Large…

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…

The standard definition generation task requires to automatically produce mono-lingual definitions (e.g., English definitions for English words), but ignores that the generated definitions may also consist of unfamiliar words for language…

In this paper, we study the task of improving the cohesion and coherence of long-form text generated by language models. To this end, we propose RSTGen, a framework that utilises Rhetorical Structure Theory (RST), a classical language…

To assess the knowledge proficiency of a learner, multiple choice question is an efficient and widespread form in standard tests. However, the composition of the multiple choice question, especially the construction of distractors is quite…