Related papers: Strong normalization through idempotent intersecti…
We provide characterization of the strong termination property of the CCV (complete call-by-value) lambda-mu calculus introduced in the first part of this series of the paper. The calculus is complete with respect to the standard…
We provide a generalization of the normal mode decomposition for non-symmetric or locality constrained situations. This allows for instance to locally decouple a bipartitioned collection of arbitrarily correlated oscillators up to…
We study a conservative extension of classical propositional logic distinguishing between four modes of statement: a proposition may be affirmed or denied, and it may be strong or classical. Proofs of strong propositions must be…
This thesis embarks on a comprehensive exploration of formal computational models that underlie typed programming languages. We focus on programming calculi, both functional (sequential) and concurrent, as they provide a compelling rigorous…
We propose StyleCap, a method to generate natural language descriptions of speaking styles appearing in speech. Although most of conventional techniques for para-/non-linguistic information recognition focus on the category classification…
We study the strong normalization of a new Curry-Howard correspondence for HA + EM1, constructive Heyting Arithmetic with the excluded middle on Sigma01-formulas. The proof-term language of HA + EM1 consists in the lambda calculus plus an…
Inductive and coinductive types are commonly construed as ontological (Church-style) types, denoting canonical data-sets such as natural numbers, lists, and streams. For various purposes, notably the study of programs in the context of…
This paper introduces a new term rewriting system that is similar to the embedded read-back mechanism for interaction nets presented in our previous work, but is easier to follow than in the original setting and thus to analyze its…
We present a proof-theoretic analysis of the logic NL$\lambda$ (Barker \& Shan 2014, Barker 2019). We notably introduce a novel calculus of proof nets and prove it is sound and complete with respect to the sequent calculus for the logic. We…
Intersection and union types denote conjunctions and disjunctions of properties. Using bidirectional typechecking, intersection types are relatively straightforward, but union types present challenges. For union types, we can case-analyze a…
We study methods to obtain the consistency of forcing axioms, and particularly higher forcing axioms. We first force over a model with a supercompact cardinal $\theta>\kappa$ to get the consistency of the forcing axiom for $\kappa$-strongly…
Neural language models (LMs) are typically trained using only lexical features, such as surface forms of words. In this paper, we argue this deprives the LM of crucial syntactic signals that can be detected at high confidence using existing…
There are different ways to define similarity for grouping similar texts into clusters, as the concept of similarity may depend on the purpose of the task. For instance, in topic extraction similar texts mean those within the same semantic…
Let $\pi : X\to \Lambda$ be a flat family of smooth complex projective varieties parameterized by a smooth quasi-projective variety $\Lambda$, and let $f: X\to X$ be a family of automorphisms with positive topological entropy. Suppose…
Large language models (LLMs) have achieved notable success in code generation. However, they still frequently produce uncompilable output because their next-token inference procedure does not model formal aspects of code. Although…
In a recent paper, a realizability technique has been used to give a semantics of a quantum lambda calculus. Such a technique gives rise to an infinite number of valid typing rules, without giving preference to any subset of those. In this…
The modal logic S4 can be used via a Curry-Howard style correspondence to obtain a lambda-calculus. Modal (boxed) types are intuitively interpreted as `closed syntax of the calculus'. This lambda-calculus is called modal type theory ---…
We present Dependent Lambek Calculus, a domain-specific dependent type theory for verified parsing and formal grammar theory. In $\textrm{Lambek}^D$, linear types are used as a syntax for formal grammars,and parsers can be written as linear…
We present an algorithm to decide the intruder deduction problem (IDP) for a class of locally stable theories enriched with normal forms. Our result relies on a new and efficient algorithm to solve a restricted case of higher-order…
Humans can reason compositionally when presented with new tasks. Previous research shows that appropriate prompting techniques enable large language models (LLMs) to solve artificial compositional generalization tasks such as SCAN. In this…