Related papers: Logical Relations for Session-Typed Concurrency

Interpolation is an important property of classical and many non-classical logics that has been shown to have interesting applications in computer science and AI. Here we study the Interpolation Property for the the non-monotonic system of…

We present an extension of System F with higher-order context-free session types. The mixture of functional types with session types has proven to be a challenge for type equivalence formalization: whereas functional type equivalence is…

We develop a system for solving logical deduction one-dimensional ordering problems by transforming natural language premises and candidate statements into first-order logic. Building on Heim and Kratzer's syntax-based compositional…

Much recent research has been devoted to modeling effects within type theory. Building on this work, we observe that effectful type theories can provide a foundation on which to build semantics for more complex programming constructs and…

We investigate non-wellfounded proof systems based on parsimonious logic, a weaker variant of linear logic where the exponential modality ! is interpreted as a constructor for streams over finite data. Logical consistency is maintained at a…

In current Large Language Models we can trust the production of smoothly flowing prose on the basis of the principles of machine learning. However, there is no comparably principled basis to justify trust in the content of the text…

Large language models (LLMs) have been shown to be capable of impressive few-shot generalisation to new tasks. However, they still tend to perform poorly on multi-step logical reasoning problems. Here we carry out a comprehensive evaluation…

Large Language Models (LLMs) still struggle with multi-step logical reasoning. Existing approaches either purely refine the reasoning chain in natural language form or attach a symbolic solver as an external module. In this work, we instead…

Analogical reasoning -- the capacity to identify and map structural relationships between different domains -- is fundamental to human cognition and learning. Recent studies have shown that large language models (LLMs) can sometimes match…

This paper proposes the meeting of fuzzy logic with paraconsistency in a very precise and foundational way. Specifically, in this paper we introduce expansions of the fuzzy logic MTL by means of primitive operators for consistency and…

Natural language inference (NLI) aims to determine the logical relationship between two sentences, such as Entailment, Contradiction, and Neutral. In recent years, deep learning models have become a prevailing approach to NLI, but they lack…

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…

Large language model (LLM) based multi-turn dialogue systems often struggle to track dependencies across non-adjacent turns, undermining both consistency and scalability. As conversations lengthen, essential information becomes sparse and…

The proposed framework provides a general model of concurrent imperative programming. Programs are modeled as formal languages and concurrency as an interleaving (or shuffle) operator. This yields a simple and elegant algebra of programs.…

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…

Reasoning large language models (RLLMs) have recently demonstrated remarkable capabilities through structured and multi-step reasoning. While prior research has primarily focused on improving their training and inference strategies, their…

Recently, in order to mix algebraic and logic styles of specification in a uniform framework, the notion of a logic labelled transition system (Logic LTS or LLTS for short) has been introduced and explored. A variety of constructors over…

Probabilistic Logic Programming (PLP), exemplified by Sato and Kameya's PRISM, Poole's ICL, Raedt et al's ProbLog and Vennekens et al's LPAD, is aimed at combining statistical and logical knowledge representation and inference. A key…

Specifications of significant systems can be made short and perspicuous by using abstract data types; data reification can provide a clear, stepwise, development history of programs that use more efficient concrete representations. Data…

Consistency properties of concurrent computations, e.g., sequential consistency, linearizability, or eventual consistency, are essential for devising correct concurrent algorithms. In this paper, we present a logical formalization of such…