Related papers: Polymorphic lemmas and definitions in Lambda Prolo…

Integrating first-order logic constraints (FOLCs) with neural networks is a crucial but challenging problem since it involves modeling intricate correlations to satisfy the constraints. This paper proposes a novel neural layer, LogicMP,…

Large language models (LLMs) have shown strong performance in many reasoning benchmarks. However, recent studies have pointed to memorization, rather than generalization, as one of the leading causes for such performance. LLMs, in fact, are…

The rapid progress in machine learning (ML) has brought forth many large language models (LLMs) that excel in various tasks and areas. These LLMs come with different abilities and costs in terms of computation or pricing. Since the demand…

Human logic has gradually shifted from intuition-driven inference to rigorous formal systems. Motivated by recent advances in large language models (LLMs), we explore whether LLMs exhibit a similar evolution in the underlying logical…

Large Language Models (LLM) have emerged as a tool for robots to generate task plans using common sense reasoning. For the LLM to generate actionable plans, scene context must be provided, often through a map. Recent works have shifted from…

This paper shows the debugging facilities provided by the SLAM system. The SLAM system includes i) a specification language that integrates algebraic specifications and model-based specifications using the object oriented model. Class…

The lambda-PRK-calculus is a typed lambda-calculus that exploits the duality between the notions of proof and refutation to provide a computational interpretation for classical propositional logic. In this work, we extend lambda-PRK to…

System F, the polymorphic lambda calculus, features the principle of impredicativity: polymorphic types may be (explicitly) instantiated at other types, enabling many powerful idioms such as Church encoding and data abstraction.…

Deep and shallow embeddings of non-classical logics in classical higher-order logic have been explored, implemented, and used in various reasoning tools in recent years. This paper presents a method for the simultaneous deployment of deep…

The ability of Large Language Models (LLMs) to perform reasoning tasks such as deduction has been widely investigated in recent years. Yet, their capacity to generate proofs-faithful, human-readable explanations of why conclusions…

Using recent results in topos theory, two systems of higher-order logic are shown to be complete with respect to sheaf models over topological spaces---so-called ``topological semantics''. The first is classical higher-order logic, with…

Convex analysis is a modern branch of mathematics with many applications. As Large Language Models (LLMs) start to automate research-level math and sciences, it is important for LLMs to demonstrate the ability to understand and reason with…

Logical formalisms provide a natural and concise means for specifying and reasoning about preferences. In this paper, we propose lexicographic logic, an extension of classical propositional logic that can express a variety of preferences,…

Large language models (LLMs) have proven to be highly effective for solving complex reasoning tasks. Surprisingly, their capabilities can often be improved by iterating on previously generated solutions. In this context, a reasoning plan…

Most efforts to improve the reasoning capabilities of large language models (LLMs) involve either scaling the number of parameters and the size of training data, or scaling inference computation by letting models generate complex chains of…

We show that any multiple-valued function can be represented by a linear lambda term typed in a second-order polymorphic type system, using two distinct styles. The first is a circuit style, which mimics combinational circuits in switching…

Human reasoning can be understood as a cooperation between the intuitive, associative "System-1" and the deliberative, logical "System-2". For existing System-1-like methods in visual activity understanding, it is crucial to integrate…

Logic is the main formal language to perform automated reasoning, and it is further a human-interpretable language, at least for small formulae. Learning and optimising logic requirements and rules has always been an important problem in…

Large Language Models (LLMs) have shown to be capable of various tasks, yet their capability in interpreting and reasoning over tabular data remains an underexplored area. In this context, this study investigates from three core…

Graph problems are fundamentally challenging for large language models (LLMs). While LLMs excel at processing unstructured text, graph tasks require reasoning over explicit structure, permutation invariance, and computationally complex…