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Gradually typed languages allow statically typed and dynamically typed code to interact while maintaining benefits of both styles. The key to reasoning about these mixed programs is Siek-Vitousek-Cimini-Boyland's (dynamic) gradual…
A prominent challenge for modern language understanding systems is the ability to answer implicit reasoning questions, where the required reasoning steps for answering the question are not mentioned in the text explicitly. In this work, we…
This article contains a proposal to add coinduction to the computational apparatus of natural language understanding. This, we argue, will provide a basis for more realistic, computationally sound, and scalable models of natural language…
Algorithmic reasoning refers to the ability to understand the complex patterns behind the problem and decompose them into a sequence of reasoning steps towards the solution. Such nature of algorithmic reasoning makes it a challenge for…
This paper focuses on formally specifying and verifying the chain of formal semantics of the Esterel synchronous programming language using the Coq proof assistant. In particular, in addition to the standard logical (LBS) semantics,…
We classify programming languages according to evaluation order: each language fixes one evaluation order as the default, making it transparent to program in that evaluation order, and troublesome to program in the other. This paper…
Event-driven automation of reactive functionalities for complex event processing is an urgent need in today's distributed service-oriented architectures and Web-based event-driven environments. An important problem to be addressed is how to…
A linking theory explains how verbs' semantic arguments are mapped to their syntactic arguments---the inverse of the Semantic Role Labeling task from the shallow semantic parsing literature. In this paper, we develop the Computational…
The relationship between communicated language and intended meaning is often probabilistic and sensitive to context. Numerous strategies attempt to estimate such a mapping, often leveraging recursive Bayesian models of communication. In…
In this paper, an application of automated theorem proving techniques to computational semantics is considered. In order to compute the presuppositions of a natural language discourse, several inference tasks arise. Instead of treating…
Inconsistency handling is an important issue in knowledge management. Especially in ontology engineering, logical inconsistencies may occur during ontology construction. A natural way to reason with an inconsistent ontology is to utilize…
While Chain-of-Thought (CoT) prompting enhances the reasoning capabilities of large language models, the faithfulness of the generated rationales remains an open problem for model interpretability. We propose a novel theoretical lens for…
We extend the simply-typed guarded $\lambda$-calculus with discrete probabilities and endow it with a program logic for reasoning about relational properties of guarded probabilistic computations. This provides a framework for programming…
We present an elaboration of inductive definitions down to a universe of datatypes. The universe of datatypes is an internal presentation of strictly positive families within type theory. By elaborating an inductive definition -- a…
Program verification is to develop the program's proof system, and to prove the proof system soundness with respect to a trusted operational semantics of the program. However, many practical program verifiers are not based on operational…
We present guarded interaction trees -- a structure and a fully formalized framework for representing higher-order computations with higher-order effects in Coq, inspired by domain theory and the recently proposed interaction trees. We also…
We phrase parsing with context-free expressions as a type inhabitation problem where values are parse trees and types are context-free expressions. We first show how containment among context-free and regular expressions can be reduced to a…
Language models (LMs) are said to be exhibiting reasoning, but what does this entail? We assess definitions of reasoning and how key papers in the field of natural language processing (NLP) use the notion and argue that the definitions…
Chain-of-Thought reasoning significantly improves the performance of large language models on complex tasks, but incurs high inference latency due to long generation traces. Step-level speculative reasoning aims to mitigate this cost, yet…
A $\lambda$-calculus is introduced in which all programs can be evaluated in probabilistic polynomial time and in which there is sufficient structure to represent sequential cryptographic constructions and adversaries for them, even when…