Related papers: Improving the Competency of First-Order Ontologies

In a case study we investigate whether off the shelf higher-order theorem provers and model generators can be employed to automate reasoning in and about quantified multimodal logics. In our experiments we exploit the new TPTP…

Empirical methods to examine the capability of Large Language Models (LLMs) to use Automated Theorem Prover (ATP) reasoning strategies are studied. We evaluate the performance of State of the Art models from December 2023 and August 2024 on…

Logical reasoning is a key task for artificial intelligence due to it's role in major downstream tasks such as Question Answering, Summarization. Recent methods in improving the reasoning ability of LLMs fall short in correctly converting a…

Traditional automated theorem provers for first-order logic depend on speed-optimized search and many handcrafted heuristics that are designed to work best over a wide range of domains. Machine learning approaches in literature either…

Automatic (i.e., computer-assisted) theorem proving (ATP) can come in many flavors. This document presents early steps in our effort towards defining object-oriented theorem proving (OOTP) as a new style of ATP. Traditional theorem proving…

Despite recent advances in automating theorem proving in full first-order theories, inductive reasoning still poses a serious challenge to state-of-the-art theorem provers. The reason for that is that in first-order logic induction requires…

We present the Frame-based ontology Design Outlet (FrODO), a novel method and tool for drafting ontologies from competency questions automatically. Competency questions are expressed as natural language and are a common solution for…

We describe a prototype theorem prover, UTP2, developed to match the style of hand-written proof work in the Unifying Theories of Programming semantical framework. This is based on alphabetised predicates in a 2nd-order logic, with a strong…

Similarity in formal argumentation has recently gained attention due to its significance in problems such as argument aggregation in semantics and enthymeme decoding. While existing approaches focus on propositional logic, we address the…

Large language models (LLMs) have achieved remarkable performance on a variety of natural language understanding tasks. However, existing benchmarks are inadequate in measuring the complex logical reasoning capabilities of a model. We…

Undergraduate students of artificial intelligence often struggle with representing knowledge as logical sentences. This is a skill that seems to require extensive practice to obtain, suggesting a teaching strategy that involves the…

Large Language Models (LLMs) are increasingly embedded in enterprise workflows, yet their performance remains highly sensitive to prompt design. Automatic Prompt Optimization (APO) seeks to mitigate this instability, but existing approaches…

Deep learning techniques lie at the heart of several significant AI advances in recent years including object recognition and detection, image captioning, machine translation, speech recognition and synthesis, and playing the game of Go.…

OWL 2 has been standardized by the World Wide Web Consortium (W3C) as a family of ontology languages for the Semantic Web. The most expressive of these languages is OWL 2 Full, but to date no reasoner has been implemented for this language.…

Large Language Models (LLMs) have revolutionized natural language processing, yet they struggle with inconsistent reasoning, particularly in novel domains and complex logical sequences. This research introduces Proof of Thought, a framework…

Automated theorem proving (ATP) is one of the most challenging mathematical reasoning tasks for Large Language Models (LLMs). Most existing LLM-based ATP methods rely on supervised fine-tuning, which results in a limited alignment between…

Humans can develop new theorems to explore broader and more complex mathematical results. While current generative language models (LMs) have achieved significant improvement in automatically proving theorems, their ability to generate new…

Recent advancements in Large Language Models (LLMs) have shifted from explicit Chain-of-Thought (CoT) reasoning to more efficient latent reasoning, where intermediate thoughts are represented as vectors rather than text. However, latent…

We argue that in some KR applications, we want to quantify over sets of concepts formally represented by symbols in the vocabulary. We show that this quantification should be distinguished from second-order quantification and…

This paper aims at carrying out termination proofs for simply typed higher-order calculi automatically by using ordering comparisons. To this end, we introduce the computability path ordering (CPO), a recursive relation on terms obtained by…