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Existing refinement calculi provide frameworks for the stepwise development of imperative programs from specifications. This paper presents a refinement calculus for deriving logic programs. The calculus contains a wide-spectrum logic…
Large language models (LLMs) have demonstrated remarkable potential across a broad range of applications. However, producing reliable text that faithfully represents data remains a challenge. While prior work has shown that task-specific…
Regular expressions and automata models with capture variables are core tools in rule-based information extraction. These formalisms, also called regular document spanners, use regular languages in order to locate the data that a user wants…
We define a new subclass of nondeterministic finite automata for prefix-closed languages called Flanked Finite Automata (FFA). We show that this class enjoys good complexity properties while preserving the succinctness of nondeterministic…
In order to address complex systems, apply pattern recongnition on their evolution could play an key role to understand their dynamics. Global patterns are required to detect emergent concepts and trends, some of them with qualitative…
In mathematics, LaTeX is the de facto standard to prepare documents, e.g., scientific publications. While some formulae are still developed using pen and paper, more complicated mathematical expressions used more and more often with…
State of the art research for date-time entity extraction from text is task agnostic. Consequently, while the methods proposed in literature perform well for generic date-time extraction from texts, they don't fare as well on task specific…
The sequent calculus is a formalism for proving validity of statements formulated in First-Order Logic. It is routinely used in computer science modules on mathematical logic. Formal proofs in the sequent calculus are finite trees obtained…
Formally verified compilers and formally verified static analyzers are a solution to the problem that certain industries face when they have to demonstrate to authorities that the object code they run truly corresponds to its source code…
Semantic legal metadata provides information that helps with understanding and interpreting legal provisions. Such metadata is therefore important for the systematic analysis of legal requirements. However, manually enhancing a large legal…
We present the first formalization and metatheory of language soundness for a user-schedulable language, the widely used array processing language Halide. User-schedulable languages strike a balance between abstraction and control in…
Interactive proof assistants make it possible for ordinary mathematicians to write definitions and theorems in a formal proof language, like a programming language, so that a computer can parse them and check them against the rules of a…
We explore different ways of implementing temporal constraints expressed in an extension of Answer Set Programming (ASP) with language constructs from dynamic logic. Foremost, we investigate how automata can be used for enforcing such…
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…
The requirements engineering process is a crucial stage of the software development life cycle. It involves various stakeholders from different professional backgrounds, particularly in the requirements elicitation phase. Each stakeholder…
Legal texts often contain computational legal clauses--provisions whose understanding requires complex logic. While frontier Large Reasoning Models (LRMs) can describe such clauses, building production-ready systems is limited by reasoning…
According to the United States Internal Revenue Service, ``the average American spends $\$270$ and 13 hours filing their taxes''. Even beyond the U.S., tax filing requires complex reasoning, combining application of overlapping rules with…
The logic of definitions is a family of logics for encoding and reasoning about judgments, which are atomic predicates specified by inference rules. A definition associates an atomic predicate with a logical formula, which may itself depend…
This paper presents a language, Alda, that supports all of logic rules, sets, functions, updates, and objects as seamlessly integrated built-ins. The key idea is to support predicates in rules as set-valued variables that can be used and…
The goal of this lecture is to show how modern theorem provers---in this case, the Coq proof assistant---can be used to mechanize the specification of programming languages and their semantics, and to reason over individual programs and…