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In regions that practice common law, relevant historical cases are essential references for sentencing. To help legal practitioners find previous judgement easier, this paper aims to label each court judgement by some tags. These tags are…
We study model checking algorithms for infinite families of finite-state labeled transition systems against temporal properties written in CTL*. Such families arise, for example, as models of highly configurable systems or software product…
We show how categorial deduction can be implemented in higher-order (linear) logic programming, thereby realising parsing as deduction for the associative and non-associative Lambek calculi. This provides a method of solution to the parsing…
As language models (LMs) deliver increasing performance on a range of NLP tasks, probing classifiers have become an indispensable technique in the effort to better understand their inner workings. A typical setup involves (1) defining an…
We discuss an extension of the standard logical rules (functional application and abstraction) in Categorial Grammar (CG), in order to deal with some specific cases of polysemy. We borrow from Generative Lexicon theory which proposes the…
We present a labelled sequent calculus for Boolean BI, a classical variant of O'Hearn and Pym's logic of Bunched Implication. The calculus is simple, sound, complete, and enjoys cut-elimination. We show that all the structural rules in our…
Argumentation theory is a powerful paradigm that formalizes a type of commonsense reasoning that aims to simulate the human ability to resolve a specific problem in an intelligent manner. A classical argumentation process takes into account…
The paper describes a parser for Categorial Grammar which provides fully word by word incremental interpretation. The parser does not require fragments of sentences to form constituents, and thereby avoids problems of spurious ambiguity.…
This book can be seen either as a text on theorem proving that uses techniques from general algebra, or else as a text on general algebra illustrated and made concrete by practical exercises in theorem proving. The book considers several…
Graded Type Theory provides a mechanism to track and reason about resource usage in type systems. In this paper, we develop GraD, a novel version of such a graded dependent type system that includes functions, tensor products, additive…
The categorical compositional distributional model of natural language provides a conceptually motivated procedure to compute the meaning of sentences, given grammatical structure and the meanings of its words. This approach has…
We present a compositional semantics for various types of polar questions and wh-questions within the framework of Combinatory Categorial Grammar (CCG). To assess the explanatory power of our proposed analysis, we introduce a…
These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…
Comparative constructions play an important role in natural language inference. However, attempts to study semantic representations and logical inferences for comparatives from the computational perspective are not well developed, due to…
The goal of this paper is to design a causal inference method accounting for complex interactions between causal factors. The proposed method relies on a category theoretical reformulation of the definitions of dependent variables,…
Separation logics are a family of extensions of Hoare logic for reasoning about programs that mutate memory. These logics are "abstract" because they are independent of any particular concrete memory model. Their assertion languages, called…
Long-context understanding has emerged as a critical capability for large language models (LLMs). However, evaluating this ability remains challenging. We present SCALAR, a benchmark designed to assess citation-grounded long-context…
Natural Language Processing technology has advanced vastly in the past decade. Text processing has been successfully applied to a wide variety of domains. In this paper, we propose a novel framework, Text Based Classification(TBC), that…
Many combinatorial proofs rely on induction. When these proofs are formulated in traditional language, they can be bulky and unmanageable. Coalgebras provide a language which can reduce reduce many inductive proofs in graded poset theory to…
The lambda calculus with constructors is an extension of the lambda calculus with variadic constructors. It decomposes the pattern-matching a la ML into a case analysis on constants and a commutation rule between case and application…