Related papers: An excursion into Dialectica and Differentiation
Defeasible reasoning is a simple but efficient approach to nonmonotonic reasoning that has recently attracted considerable interest and that has found various applications. Defeasible logic and its variants are an important family of…
During the process of teaching the concept of derivative, it is common and natural to refer to geometric interpretations, such as the use of the tangent line and the maximum and minimum points of a function, to illustrate the scope of the…
This paper discusses a Domain Specific Language (DSL) that has been developed to enable implementation of concepts of discrete mathematics. A library of data types and functions provides functionality which is frequently required by users.…
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…
Coinductive definitions, such as that of an infinite stream, may often be described by elegant logic programs, but ones for which SLD-refutation is of no value as SLD-derivations fall into infinite loops. Such definitions give rise to…
The goal of this paper is to extend classical logic with a generalized notion of inductive definition supporting positive and negative induction, to investigate the properties of this logic, its relationships to other logics in the area of…
Deep learning, despite its remarkable achievements, is still a young field. Like the early stages of many scientific disciplines, it is marked by the discovery of new phenomena, ad-hoc design decisions, and the lack of a uniform and…
Lenses are a well-established structure for modelling bidirectional transformations, such as the interactions between a database and a view of it. Lenses may be symmetric or asymmetric, and may be composed, forming the morphisms of a…
The generation of comprehensible explanations is an essential feature of modern artificial intelligence systems. In this work, we consider probabilistic logic programming, an extension of logic programming which can be useful to model…
In David Schmidt's PhD work he explored the use of denotational semantics as a programming language. It was part of an effort to not only treat formal semantics as specifications but also as interpreters and input to compiler generators.…
Lenses have a rich history and have recently received a great deal of attention from applied category theorists. We generalize the notion of lens by defining a category $\mathsf{Lens}_F$ for any category $\mathcal{C}$ and functor $F\colon…
This extended abstract gives a brief outline of the connections between the descriptions and variable concepts. Thus, the notion of a concept is extended to include both the syntax and semantics features. The evaluation map in use is…
Probing and enhancing large language models' reasoning capacity remains a crucial open question. Here we re-purpose the reverse dictionary task as a case study to probe LLMs' capacity for conceptual inference. We use in-context learning to…
The Dependent Object Types (DOT) calculus incorporates concepts from functional languages (e.g. modules) with traditional object-oriented features (e.g. objects, subtyping) to achieve greater expressivity (e.g. F-bounded polymorphism).…
In this paper we take a look at Automatic Differentiation through the eyes of Tensor and Operational Calculus. This work is best consumed as supplementary material for learning tensor and operational calculus by those already familiar with…
This paper proposes to use dialgebras to specify the semantics of interactive systems in a natural way. Dialgebras are a conservative extension of coalgebras. In this categorical model, from the point of view that we provide, the notions of…
We present semantic correctness proofs of Automatic Differentiation (AD). We consider a forward-mode AD method on a higher order language with algebraic data types, and we characterise it as the unique structure preserving macro given a…
Relational properties arise in many settings: relating two versions of a program that use different data representations, noninterference properties for security, etc. The main ingredient of relational verification, relating aligned pairs…
The identification of semantic relations between terms within texts is a fundamental task in Natural Language Processing which can support applications requiring a lightweight semantic interpretation model. Currently, semantic relation…
Category theory is the language of homological algebra, allowing us to state broadly applicable theorems and results without needing to specify the details for every instance of analogous objects. However, authors often stray from the realm…