Related papers: Skolemisation for Intuitionistic Linear Logic
In recent work, we proved that the domain recursion inference rule makes domain-lifted inference possible on several relational probability models (RPMs) for which the best known time complexity used to be exponential. We also identified…
Chain-of-thought distillation is a powerful technique for transferring reasoning abilities from large language models (LLMs) to smaller student models. Previous methods typically require the student to mimic the step-by-step rationale…
We employ a recently developed methodology -- called "structural refinement" -- to extract nested sequent systems for a sizable class of intuitionistic modal logics from their respective labelled sequent systems. This method can be seen as…
With the continuous advancement of reasoning abilities in Large Language Models (LLMs), their application to scientific reasoning tasks has gained significant research attention. Current research primarily emphasizes boosting LLMs'…
Formalized mathematics has recently garnered significant attention for its ability to assist mathematicians across various fields. Premise retrieval, as a common step in mathematical formalization, has been a challenge, particularly for…
Fractional calculus is a generalization of classical theories of integration and differentiation to arbitrary order (i.e., real or complex numbers). In the last two decades, this new mathematical modeling approach has been widely used to…
We describe a natural deduction formalization of intuitionistic and classical propositional logic in the Isabelle/Pure framework. In contrast to earlier work, where we explored the pedagogical benefits of using a deep embedding approach to…
Rote learning is a memorization technique based on repetition. Many researchers argue that rote learning hinders generalization because it encourages verbatim memorization rather than deeper understanding. This concern extends even to…
In-context learning (ICL) can significantly enhance the complex reasoning capabilities of large language models (LLMs), with the key lying in the selection and ordering of demonstration examples. Previous methods typically relied on simple…
Navigating the complexities of physics reasoning has long been a difficult task for Large Language Models (LLMs), requiring a synthesis of profound conceptual understanding and adept problem-solving techniques. In this study, we investigate…
This thesis introduces the "method of structural refinement", which serves as a means of transforming the relational semantics of a modal and/or constructive logic into an 'economical' proof system by connecting two proof-theoretic…
To improve the performance and explainability of LLM-based natural language reasoning, structured reasoning can be applied to generate explicitly structured proofs. Among different methods for structured reasoning, we specifically focus on…
Linear logic (LL) is a resource-aware, abstract logic programming language that refines both classical and intuitionistic logic. Linear logic semantics is typically presented in one of two ways: by associating each formula with the set of…
An efficient entailment proof system is essential to compositional verification using separation logic. Unfortunately, existing decision procedures are either inexpressive or inefficient. For example, Smallfoot is an efficient procedure but…
These notes present the essentials of first- and second-order monadic logics on strings with introductory purposes. We discuss Monadic First-Order logic and show that it is strictly less expressive than Finite-State Automata, in that it…
We consider the problem of answering queries about formulas of first-order logic based on background knowledge partially represented explicitly as other formulas, and partially represented as examples independently drawn from a fixed…
We consider a typical integration of induction in saturation-based theorem provers and investigate the effects of Skolem symbols occurring in the induction formulas. In a practically relevant setting we establish a Skolem-free…
Owing to the capability of in-context learning, large language models (LLMs) have shown impressive performance across diverse mathematical reasoning benchmarks. However, we find that few-shot demonstrations can sometimes bring negative…
Large Language Models (LLMs) suffer from critical reasoning gaps, including a tendency to hallucinate and poor accuracy in classifying logical fallacies. This limitation stems from their default System 1 processing, which is fast and…
This paper shows how to derive nested calculi from labelled calculi for propositional intuitionistic logic and first-order intuitionistic logic with constant domains, thus connecting the general results for labelled calculi with the more…