Related papers: Layered Clause Selection for Theory Reasoning

We study a well-known technique of using absoluteness for giving choice-free proofs to some statements which are known to be provable with the axiom of choice. The idea is to reduce the problem to an inner model where the axiom of choice…

This paper describes a procedure that system developers can follow to translate typical mathematical representations of linearized control systems into logic theories. These theories are then used to verify system requirements and find…

Taxonomies are hierarchical knowledge graphs crucial for recommendation systems, and web applications. As data grows, expanding taxonomies is essential, but existing methods face key challenges: (1) discriminative models struggle with…

Motivated by applications in automated verification of higher-order functional programs, we develop a notion of constrained Horn clauses in higher-order logic and a decision problem concerning their satisfiability. We show that, although…

Concept Induction refers to the problem of creating complex Description Logic class descriptions (i.e., TBox axioms) from instance examples (i.e., ABox data). In this paper we look particularly at the case where both a set of positive and a…

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…

This paper introduces ThoughtProbe, a novel inference time framework that leverages the hidden reasoning features of Large Language Models (LLMs) to improve their reasoning performance. Unlike previous works that manipulate the hidden…

We present a method for using standard techniques from satisfiability checking to automatically verify and discover theorems in an area of economic theory known as ranking sets of objects. The key question in this area, which has important…

A major challenge in applying machine learning to automated theorem proving is the scarcity of training data, which is a key ingredient in training successful deep learning models. To tackle this problem, we propose an approach that relies…

Protecting privileged communications and data from disclosure is paramount for legal teams. Unrestricted legal advice, such as attorney-client communications or litigation strategy. are vital to the legal process and are exempt from…

Very large commonsense knowledge bases (KBs) often have thousands to millions of axioms, of which relatively few are relevant for answering any given query. A large number of irrelevant axioms can easily overwhelm resolution-based theorem…

This paper presents a novel approach termed Layer-of-Thoughts Prompting (LoT), which utilizes constraint hierarchies to filter and refine candidate responses to a given query. By integrating these constraints, our method enables a…

Recent advancements in Chain-of-Thought prompting have facilitated significant breakthroughs for Large Language Models (LLMs) in complex reasoning tasks. Current research enhances the reasoning performance of LLMs by sampling multiple…

We present a system for the investigation of computational properties of categorial grammar parsing based on a labelled analytic tableaux theorem prover. This proof method allows us to take a modular approach, in which the basic grammar can…

In theorem proving, the task of selecting useful premises from a large library to unlock the proof of a given conjecture is crucially important. This presents a challenge for all theorem provers, especially the ones based on language…

Recent advances in automated theorem proving leverages language models to explore expanded search spaces by step-by-step proof generation. However, such approaches are usually based on short-sighted heuristics (e.g., log probability or…

Vampire proves theorems completely automatically in first- and higher-order logic extended with theories. Proof checking is increasingly demanded to consolidate user trust in Vampires output. We describe ongoing efforts in reconstructing…

Large Language Models (LLMs) are often used as automated judges to evaluate text, but their effectiveness can be hindered by various unintentional biases. We propose using linear classifying probes, trained by leveraging differences between…

We address generating theorems from a given set of axioms, without proof goal, aiming at value from a mathematical point of view or as lemmas for automated proving. As benchmark, we convert a fragment of the Metamath database set.mm. Our…

Recent advancements in large language models (LLMs) have sparked considerable interest in automated theorem proving and a prominent line of research integrates stepwise LLM-based provers into tree search. In this paper, we introduce a novel…