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Large language models (LLMs) have transformed natural language processing, but their reliable deployment requires effective uncertainty quantification (UQ). Existing UQ methods are often heuristic and lack a probabilistic interpretation.…
We introduce a novel quantum programming language featuring higher-order programs and quantum controlflow which ensures that all qubit transformations are unitary. Our language boasts a type system guaranteeingboth unitarity and…
A term calculus for the proofs in multiplicative-additive linear logic is introduced and motivated as a programming language for channel based concurrency. The term calculus is proved complete for a semantics in linearly distributive…
We investigate program equivalence for linear higher-order(sequential) languages endowed with primitives for computational effects. More specifically, we study operationally-based notions of program equivalence for a linear…
We present a linearity theorem for a proof language of intuitionistic multiplicative additive linear logic, incorporating addition and scalar multiplication. The proofs in this language are linear in the algebraic sense. This work is part…
Logical relations constitute a key method for reasoning about contextual equivalence of programs in higher-order languages. They are usually developed on a per-case basis, with a new theory required for each variation of the language or of…
In this paper we are concerned with understanding the nature of program metrics for calculi with higher-order types, seen as natural generalizations of program equivalences. Some of the metrics we are interested in are well-known, such as…
Embeddings from Visual-Language Models are increasingly utilized to represent semantics in robotic maps, offering an open-vocabulary scene understanding that surpasses traditional, limited labels. Embeddings enable on-demand querying by…
This paper presents an equational theory for the QRAM model of quantum computation, formulated as an embedded language inside of homotopy type theory. The embedded language approach is highly expressive, and reflects the style of…
Program equivalence in linear contexts, where programs are used or executed exactly once, is an important issue in programming languages. However, existing techniques like those based on bisimulations and logical relations only target at…
The equivalence test is a main part in any classification problem. It helps to prove bounds for the main parameters of the considered combinatorial structures and to study their properties. In this paper, we present algorithms for…
Substructural logics naturally support a quantitative interpretation of formulas, as they are seen as consumable resources. Distances are the quantitative counterpart of equivalence relations: they measure how much two objects are similar,…
Important variables of processes are often categorical, i.e. names or labels representing, e.g. categories of inputs, or types of reactors or a sequence of steps. In this work, we use Natural Language Processing Models to derive embeddings…
Classification is a machine learning method used in many practical applications: text mining, handwritten character recognition, face recognition, pattern classification, scene labeling, computer vision, natural langage processing. A…
We construct a machine which takes as input a locally small symmetric closed complete multicategory $\mathsf V$. And its output is again a locally small symmetric closed complete multicategory $\mathsf V\text-\mathcal{C}at$, the…
The exponential modalities of linear logic have been used by various authors to model infinite-dimensional quantum systems. This paper explains how these modalities can also give rise to the complementarity principle of quantum mechanics.…
We present a logical separability analysis for a functional quantum computation language. This logic is inspired by previous works on logical analysis of aliasing for imperative functional programs. Both analyses share similarities notably…
Classical computation, grounded in formal, logical systems, has been the engine of technological progress for decades, excelling at problems that can be described with unambiguous rules. This paradigm, however, leaves a vast ocean of human…
Following the classical approach of Birkhoff, we suggest an enriched version of enriched universal algebra. Given a suitable base of enrichment $\mathcal V$, we define a language $\mathbb L$ to be a collection of $(X,Y)$-ary function…
Logic programming under the answer-set semantics nowadays deals with numerous different notions of program equivalence. This is due to the fact that equivalence for substitution (known as strong equivalence) and ordinary equivalence are…