Related papers: Deriving Theorems in Implicational Linear Logic, D…

Recently, there has been considerable progress on designing algorithms with provable guarantees -- typically using linear algebraic methods -- for parameter learning in latent variable models. But designing provable algorithms for inference…

First-order logic (FOL) reasoning, which involves sequential deduction, is pivotal for intelligent systems and serves as a valuable task for evaluating reasoning capabilities, particularly in chain-of-thought (CoT) contexts. Existing…

We introduce LeanConjecturer, a pipeline for automatically generating university-level mathematical conjectures in Lean 4 using Large Language Models (LLMs). Our hybrid approach combines rule-based context extraction with LLM-based theorem…

Two lines of approaches are adopted for complex reasoning with LLMs. One line of work prompts LLMs with various reasoning structures, while the structural outputs can be naturally regarded as intermediate reasoning steps. Another line of…

Large Language Models (LLMs) have demonstrated significant promise in formal theorem proving. In this study, we investigate the ability of LLMs to discover novel theorems and produce verified proofs. We propose a pipeline called…

We investigate how large language models can be used as research tools in scientific computing while preserving mathematical rigor. We propose a human-in-the-loop workflow for interactive theorem proving and discovery with LLMs. Human…

Lambda calculus is the basis of functional programming and higher order proof assistants. However, little is known about combinatorial properties of lambda terms, in particular, about their asymptotic distribution and random generation.…

Despite their linguistic competence, Large Language Models (LLMs) often struggle to reason reliably and flexibly. To identify these shortcomings, we introduce the Non-Linear Reasoning (NLR) dataset, a collection of 55 unique, hand-designed…

A logic program is an executable specification. For example, merge sort in pure Prolog is a logical formula, yet shows creditable performance on long linked lists. But such executable specifications are a compromise: the logic is distorted…

Prolog is a well known declarative programming language based on propositional Horn formulas. It is useful in various areas, including artificial intelligence, automated theorem proving, mathematical logic and so on. An active research area…

This paper presents a Prolog-based reasoning module to generate counterfactual explanations given the predictions computed by a black-box classifier. The proposed symbolic reasoning module can also resolve what-if queries using the…

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…

Automated theorem provers and formal proof assistants are general reasoning systems that are in theory capable of proving arbitrarily hard theorems, thus solving arbitrary problems reducible to mathematics and logical reasoning. In…

We design a proof system for propositional classical logic that integrates two languages for Boolean functions: standard conjunction-disjunction-negation and binary decision trees. We give two reasons to do so. The first is…

Argumentation problems are concerned with determining the acceptability of a set of arguments from their relational structure. When the available information is uncertain, probabilistic argumentation frameworks provide modelling tools to…

The problem-solving in automated theorem proving (ATP) can be interpreted as a search problem where the prover constructs a proof tree step by step. In this paper, we propose a deep reinforcement learning algorithm for proof search in…

The application of Large Language Models to Question Answering has shown great promise, but important challenges such as hallucinations and erroneous reasoning arise when using these models, particularly in knowledge-intensive,…

Large Language Models (LLMs) with reasoning are trained to iteratively generate and refine their answers before finalizing them, which can help with applications to mathematics and code generation. We apply code generation with reasoning…

A natural approach to software quality assurance consists in writing unit tests securing programmer-declared code invariants. Throughout the literature a great body of work has been devoted to tools and techniques automating this…

Inductive reasoning is a core problem-solving capacity: humans can identify underlying principles from a few examples, which robustly generalize to novel scenarios. Recent work evaluates large language models (LLMs) on inductive reasoning…