Related papers: A Linear Algebra Approach to Linear Metatheory
The so-called light logics have been introduced as logical systems enjoying quite remarkable normalization properties. Designing a type assignment system for pure lambda calculus from these logics, however, is problematic. In this paper we…
We revisit the Vectorial Lambda Calculus, a typed version of Lineal. Vectorial (as well as Lineal) has been originally designed for quantum computing, as an extension to System F where linear combinations of lambda terms are also terms and…
We propose a categorial grammar based on classical multiplicative linear logic. This can be seen as an extension of abstract categorial grammars (ACG) and is at least as expressive. However, constituents of {\it linear logic grammars (LLG)}…
In this paper, we define a realizability semantics for the simply typed $\lambda\mu$-calculus. We show that if a term is typable, then it inhabits the interpretation of its type. This result serves to give characterizations of the…
Linear Discriminant Analysis (LDA) is a fundamental method for classification. Its simple linear structure facilitates interpretation, and it is naturally suited to multi-class settings. LDA is also closely connected to several classical…
We give a new characterization of elementary and deterministic polynomial time computation in linear logic through the proofs-as-programs correspondence. Girard's seminal results, concerning elementary and light linear logic, achieve 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 ---…
The theory of Lambda-rings, in the sense of Grothendieck's Riemann-Roch theory, is an enrichment of the theory of commutative rings. In the same way, we can enrich usual algebraic geometry over the ring Z of integers to produce…
Generalized metrics, arising from Lawvere's view of metric spaces as enriched categories, have been widely applied in denotational semantics as a way to measure to which extent two programs behave in a similar, although non equivalent, way.…
On the topic of probabilistic rewriting, there are several works studying both termination and confluence of different systems. While working with a lambda calculus modelling quantum computation, we found a system with probabilistic…
We present semi-supervised models with data augmentation (SMDA), a semi-supervised text classification system to classify interactive affective responses. SMDA utilizes recent transformer-based models to encode each sentence and employs…
Despite deep learning models running well-defined mathematical functions, we lack a formal mathematical framework for describing model architectures. Ad-hoc notation, diagrams, and pseudocode poorly handle nonlinear broadcasting and the…
Nominal abstract syntax is an approach to representing names and binding pioneered by Gabbay and Pitts. So far nominal techniques have mostly been studied using classical logic or model theory, not type theory. Nominal extensions to simple,…
Active learning in semi-supervised classification involves introducing additional labels for unlabelled data to improve the accuracy of the underlying classifier. A challenge is to identify which points to label to best improve performance…
In recent years, the interest in using proof assistants to formalise and reason about mathematics and programming languages has grown. Type-logical grammars, being closely related to type theories and systems used in functional programming,…
This paper introduces context algebras and demonstrates their application to combining logical and vector-based representations of meaning. Other approaches to this problem attempt to reproduce aspects of logical semantics within new…
Graph simulation (using graph schemata or data guides) has been successfully proposed as a technique for adding structure to semistructured data. Design patterns for description (such as meta-classes and homomorphisms between schema…
We give a semantics for the lambda-calculus based on a topological duality theorem in nominal sets. A novel interpretation of lambda is given in terms of adjoints, and lambda-terms are interpreted absolutely as sets (no valuation is…
Generalization problems in languages with binders involve computing the most common structure between expressions while respecting bound variable renaming and freshness constraints. These problems often lack a least general solution.…
While deep learning is a powerful tool for natural language processing (NLP) problems, successful solutions to these problems rely heavily on large amounts of annotated samples. However, manually annotating data is expensive and…