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An introductory formal languages course exposes advanced undergraduate and early graduate students to automata theory, grammars, constructive proofs, computability, and decidability. Programming students find these topics to be challenging…
We argue that in some KR applications, we want to quantify over sets of concepts formally represented by symbols in the vocabulary. We show that this quantification should be distinguished from second-order quantification and…
Human vision is able to compensate imperfections in sensory inputs from the real world by reasoning based on prior knowledge about the world. Machine learning has had a significant impact on computer vision due to its inherent ability in…
As large language models (LLMs) are increasing integrated into fact-checking pipelines, formal logic is often proposed as a rigorous means by which to mitigate bias, errors and hallucinations in these models' outputs. For example, some…
As large language models (LLMs) have become the norm in NLP, demonstrating good performance in generation and reasoning tasks, one of its most fatal disadvantages is the lack of factual correctness. Generating unfactual texts not only leads…
Functional languages have provided major benefits to the verification community. Although features such as purity, a strong type system, and computational abstractions can help guide programmers away from costly errors, these can present…
Isabelle is a generic theorem prover with a fragment of higher-order logic as a metalogic for defining object logics. Isabelle also provides proof terms. We formalize this metalogic and the language of proof terms in Isabelle/HOL, define an…
Large Language Models have significantly advanced natural language processing tasks, but remain prone to generating incorrect or misleading but plausible arguments. This issue, known as hallucination, is particularly concerning in…
By simply composing prompts, developers can prototype novel generative applications with Large Language Models (LLMs). To refine prototypes into products, however, developers must iteratively revise prompts by evaluating outputs to diagnose…
Logic programming has developed as a rich field, built over a logical substratum whose main constituent is a nonclassical form of negation, sometimes coexisting with classical negation. The field has seen the advent of a number of…
We study the semantic foundation of expressive probabilistic programming languages, that support higher-order functions, continuous distributions, and soft constraints (such as Anglican, Church, and Venture). We define a metalanguage (an…
We present a small, formal language for specifying the behavior of simple console I/O programs. The design is driven by the concrete application case of testing interactive Haskell programs written by students. Specifications are…
This paper concerns the development of metatheory for extensible languages. It uses as its starting point a view that programming languages tailored to specific application domains are to be constructed by composing components from an open…
We present a semi-automated framework to construct and reason about programs in a deeply-embedded while-language. The while-language we consider is a simple computation model that can simulate (and be simulated by) Turing Machines with a…
Critiques are important for enhancing the performance of Large Language Models (LLMs), enabling both self-improvement and constructive feedback for others by identifying flaws and suggesting improvements. However, evaluating the critique…
This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…
Large Language Models tend to struggle when dealing with specialized domains. While all aspects of evaluation hold importance, factuality is the most critical one. Similarly, reliable fact-checking tools and data sources are essential for…
While Large Language Models (LLMs) are fundamentally next-token prediction systems, their practical applications extend far beyond this basic function. From natural language processing and text generation to conversational assistants and…
Scientific feasibility assessment asks whether a claim is consistent with established knowledge and whether experimental evidence could support or refute it. We frame feasibility assessment as a diagnostic reasoning task in which, given a…
Artificial intelligence assisted mathematical proof has become a highly focused area nowadays. One key problem in this field is to generate formal mathematical proofs from natural language proofs. Due to historical reasons, the formal proof…