Related papers: Proof Generation from Delta-Decisions
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…
This work explores the application of deep learning, a machine learning technique that uses deep neural networks (DNN) in its core, to an automated theorem proving (ATP) problem. To this end, we construct a statistical model which…
This paper examines two related problems that are central to developing an autonomous decision-making agent, such as a robot. Both problems require generating structured representafions from a database of unstructured declarative knowledge…
Recent research increasingly brings to question the appropriateness of using predictive tools in complex, real-world tasks. While a growing body of work has explored ways to improve value alignment in these tools, comparatively less work…
Large Language Models (LLMs) have demonstrated significant potential in generating mathematical proofs. However, a persistent challenge is that LLMs occasionally make mistakes, while even a minor mistake can invalidate an entire proof.…
Existing algorithms for explaining the outputs of image classifiers are based on a variety of approaches and produce explanations that frequently lack formal rigour. On the other hand, logic-based explanations are formally and rigorously…
The need for rigorous process composition is encountered in many situations pertaining to the development and analysis of complex systems. We discuss the use of Classical Linear Logic (CLL) for correct-by-construction resource-based process…
Model checking is a technique to automatically assess whether a model of the behaviour of a system meets its requirements. Evidence explaining why the behaviour does (not) meet its requirements is essential for the user to understand the…
Recently, with the chain of thought (CoT) prompting, large language models (LLMs), e.g., GPT-3, have shown strong reasoning ability in several natural language processing tasks such as arithmetic, commonsense, and logical reasoning.…
Evaluating an explanation's faithfulness is desired for many reasons such as trust, interpretability and diagnosing the sources of model's errors. In this work, which focuses on the NLI task, we introduce the methodology of…
We introduce a non-wellfounded proof system for intuitionistic logic extended with inductive and co-inductive definitions, based on a syntax in which fixpoint formulas are annotated with explicit variables for ordinals. We explore the…
Ensuring the reliability of Large Language Models (LLMs) in complex reasoning tasks remains a formidable challenge, particularly in scenarios that demand precise mathematical calculations and knowledge-intensive open-domain generation. In…
This paper provides a set of cut-free complete sequent-style calculi for deontic STIT ('See To It That') logics used to formally reason about choice-making, obligations, and norms in a multi-agent setting. We leverage these calculi to write…
The coalgebraic $\mu$-calculus provides a generic semantic framework for fixpoint logics over systems whose branching type goes beyond the standard relational setup, e.g. probabilistic, weighted, or game-based. Previous work on the…
Many of the recent capabilities demonstrated by Large Language Models (LLMs) arise primarily from their ability to exploit contextual information. In this paper, we explore ways to improve reasoning capabilities of LLMs through (1)…
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 shown promising results in automating formal verification. However, existing approaches treat proof generation as a static, end-to-end prediction over source code, relying on limited verifier feedback and…
Proof-theoretic methods are developed for subsystems of Johansson's logic obtained by extending the positive fragment of intuitionistic logic with weak negations. These methods are exploited to establish properties of the logical systems.…
Legal Artificial Intelligence (LegalAI) has achieved notable advances in automating judicial decision-making with the support of Large Language Models (LLMs). However, existing legal LLMs still struggle to generate reliable and…
While Large Language Models (LLMs) have demonstrated strong math reasoning abilities through Reinforcement Learning with *Verifiable Rewards* (RLVR), many advanced mathematical problems are proof-based, with no guaranteed way to determine…