Related papers: Categorical semantics of a simple differential pro…
This paper is a short empirical study of the performance of centrality and classification based iterative term set expansion methods for distributional semantic models. Iterative term set expansion is an interactive process using…
Prioritized default reasoning has illustrated its rich expressiveness and flexibility in knowledge representation and reasoning. However, many important aspects of prioritized default reasoning have yet to be thoroughly explored. In this…
Emerging computational paradigms, such as probabilistic and hybrid programming, introduce new primitive operations that often need to be combined with classic programming constructs. However, it still remains a challenge to provide a…
Two distinct research approaches have been proposed for assigning a purely extensional semantics to higher-order logic programming. The former approach uses classical domain theoretic tools while the latter builds on a fixed-point…
Probabilistic modeling is iterative. A scientist posits a simple model, fits it to her data, refines it according to her analysis, and repeats. However, fitting complex models to large data is a bottleneck in this process. Deriving…
In this paper we show that reversible analysis of logic languages by abstract interpretation can be performed without loss of precision by systematically refining abstract domains. The idea is to include semantic structures into abstract…
There is no known way of giving a domain-theoretic semantics to higher-order probabilistic languages, in such a way that the involved domains are continuous or quasi-continuous - the latter is required to do any serious mathematics. We…
We define a monoidal semantics for algebraic theories. The basis for the definition is provided by the analysis of the structural rules in the term calculus of algebraic languages. Models are described both explicitly, in a form that…
The ramification method in Implicit Computational Complexity has been associated with functional programming, but adapting it to generic imperative programming is highly desirable, given the wider algorithmic applicability of imperative…
A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…
Ambiguity is shown in the context of the differential calculus of several variables and with the help of the language of category theory, a way to solve it in its most general form is offered. It is also shown that this new definition is…
Many theories of semantic interpretation use lambda-term manipulation to compositionally compute the meaning of a sentence. These theories are usually implemented in a language such as Prolog that can simulate lambda-term operations with…
This paper presents preliminary work on a general system for integrating dependent types into substructural type systems such as linear logic and linear type theory. Prior work on this front has generally managed to deliver type systems…
Deep neural networks suffer from the major limitation of catastrophic forgetting old tasks when learning new ones. In this paper we focus on class incremental continual learning in semantic segmentation, where new categories are made…
Programs written in dynamic languages make heavy use of features --- run-time type tests, value-indexed dictionaries, polymorphism, and higher-order functions --- that are beyond the reach of type systems that employ either purely syntactic…
In categorical compositional semantics of natural language one studies functors from a category of grammatical derivations (such as a Lambek pregroup) to a semantic category (such as real vector spaces). We compositionally build…
Many software analysis methods have come to rely on machine learning approaches. Code segmentation - the process of decomposing source code into meaningful blocks - can augment these methods by featurizing code, reducing noise, and limiting…
We introduce the notions of a $\mathbf{D}$-standard abelian category and a $\mathbf{K}$-standard additive category. We prove that for a finite dimensional algebra $A$, its module category is $\mathbf{D}$-standard if and only if any derived…
Reverse differentiation is an essential operation for automatic differentiation. Cartesian reverse differential categories axiomatize reverse differentiation in a categorical framework, where one of the primary axioms is the reverse chain…
We generalise the distribution semantics underpinning probabilistic logic programming by distilling its essential concept, the separation of a free random component and a deterministic part. This abstracts the core ideas beyond logic…