Related papers: Refinement Types for Logical Frameworks and Their …

Large Language Models (LLMs) are so powerful that they sometimes learn correlations between labels and features that are irrelevant to the task, leading to poor generalization on out-of-distribution data. We propose explanation-based…

The prevalence of fake news on social media demands automated fact-checking systems to provide accurate verdicts with faithful explanations. However, existing large language model (LLM)-based approaches ignore deceptive misinformation…

The advancement of Large Language Models (LLMs) has greatly improved our ability to process complex language. However, accurately detecting logical fallacies remains a significant challenge. This study presents a novel and effective prompt…

Intuitionistic grammar logics fuse constructive and multi-modal reasoning while permitting the use of converse modalities, serving as a generalization of standard intuitionistic modal logics. In this paper, we provide definitions of these…

In this paper we investigate the relationships between a multipreferential semantics for defeasible reasoning in knowledge representation and a multilayer neural network model. Weighted knowledge bases for a simple description logic with…

We generalize the notion of proof term to the realm of transfinite reduction. Proof terms represent reductions in the first-order term format, thereby facilitating their formal analysis. We show that any transfinite reduction can be…

Value independence is enormously beneficial for reasoning about software systems at scale. These benefits carry over into the world of formal verification. Reasoning about programs algebraically is a simple affair in a proof assistant,…

Large Language Models (LLMs) are often used as automated judges to evaluate text, but their effectiveness can be hindered by various unintentional biases. We propose using linear classifying probes, trained by leveraging differences between…

Language models (LMs) have recently shown remarkable performance on reasoning tasks by explicitly generating intermediate inferences, e.g., chain-of-thought prompting. However, these intermediate inference steps may be inappropriate…

We present the design, implementation, and foundation of a verifier for higher-order functional programs with generics and recursive data types. Our system supports proving safety and termination using preconditions, postconditions and…

In this position paper, we propose a reasoning framework that can model the reasoning process underlying natural language inferences. The framework is based on the semantic tableau method, a well-studied proof system in formal logic. Like…

We present a type inference algorithm for lambda-terms in Elementary Affine Logic using linear constraints. We prove that the algorithm is correct and complete.

Convincing someone of the truth value of a premise requires understanding and articulating the core logical structure of the argument which proves or disproves the premise. Understanding the logical structure of an argument refers to…

Human explanations of natural language, rationales, form a tool to assess whether models learn a label for the right reasons or rely on dataset-specific shortcuts. Sufficiency is a common metric for estimating the informativeness of…

Despite the increasing effectiveness of language models, their reasoning capabilities remain underdeveloped. In particular, causal reasoning through counterfactual question answering is lacking. This work aims to bridge this gap. We first…

Iteratively improving and repairing source code with large language models (LLMs), known as refinement, has emerged as a popular way of generating programs that would be too complex to construct in one shot. Given a bank of test cases,…

We describe a type system with mixed linear and non-linear recursive types called LNL-FPC (the linear/non-linear fixpoint calculus). The type system supports linear typing, which enhances the safety properties of programs, but also supports…

This paper presents a type theory with a form of equality reflection: provable equalities can be used to coerce the type of a term. Coercions and other annotations, including implicit arguments, are dropped during reduction of terms. We…

Recent advances in large language models (LLMs) have yielded impressive performance on various tasks, yet they often depend on high-quality feedback that can be costly. Self-refinement methods attempt to leverage LLMs' internal evaluation…

Software and hardware architectures are prone to modifications. We demonstrate how a mathematically founded powerful refinement calculus for a class of architectures, namely pipe and filter architectures, can be used to modify a system in a…