Related papers: Elaborating Inductive Definitions
We study one dimension in program evolution, namely the evolution of the datatype declarations in a program. To this end, a suite of basic transformation operators is designed. We cover structure-preserving refactorings, but also…
The last decade has seen huge progress in the development of advanced machine learning models; however, those models are powerless unless human users can interpret them. Here we show how the mind's construction of concepts and meaning can…
Current approaches for explaining deep learning systems applied to musical data provide results in a low-level feature space, e.g., by highlighting potentially relevant time-frequency bins in a spectrogram or time-pitch bins in a piano…
Recent models of intensional type theory have been constructed in algebraic weak factorization systems (AWFSs). AWFSs give rise to comprehension categories that feature non-trivial morphisms between types; these morphisms are not used in…
A type description is a succinct noun compound which helps human and machines to quickly grasp the informative and distinctive information of an entity. Entities in most knowledge graphs (KGs) still lack such descriptions, thus calling for…
Higher inductive types (HITs) in Homotopy Type Theory (HoTT) allow the definition of datatypes which have constructors for equalities over the defined type. HITs generalise quotient types and allow to define types which are not sets in the…
Conventional closed-world information extraction (IE) approaches rely on human ontologies to define the scope for extraction. As a result, such approaches fall short when applied to new domains. This calls for systems that can automatically…
A fertile field of research in theoretical computer science investigates the representation of general recursive functions in intensional type theories. Among the most successful approaches are: the use of wellfounded relations,…
This paper deals with an extended model of computations which uses the parameterized families of entities for data objects and reflects a preliminary outline of this problem. Some topics are selected out, briefly analyzed and arranged to…
Deep data types are those that are constructed from other data types, including, possibly, themselves. In this case, they are said to be truly nested. Deep induction is an extension of structural induction that traverses all of the…
This paper introduces an explanation framework designed to enhance the quality of rules in knowledge-based reasoning systems based on dataset-driven insights. The traditional method for rule induction from data typically requires…
The most common methods in explainable artificial intelligence are post-hoc techniques which identify the most relevant features used by pretrained opaque models. Some of the most advanced post hoc methods can generate explanations that…
We propose a computational modeling framework for inducing combinatory categorial grammars from arbitrary behavioral data. This framework provides the analyst fine-grained control over the assumptions that the induced grammar should conform…
Researchers have derived many theoretical models for specifying users' insights as they interact with a visualization system. These representations are essential for understanding the insight discovery process, such as when inferring user…
The specifics of data layout can be important for the efficiency of functional programs and interaction with external libraries. In this paper, we develop a type-theoretic approach to data layout that could be used as a typed intermediate…
This paper proposes a definition of what it means for one system description language to encode another one, thereby enabling an ordering of system description languages with respect to expressive power. I compare the proposed definition…
We consider the problem of defining the integers in Homotopy Type Theory (HoTT). We can define the type of integers as signed natural numbers (i.e., using a coproduct), but its induction principle is very inconvenient to work with, since it…
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…
To ensure decidability and consistency of its type theory, a proof assistant should only accept terminating recursive functions and productive corecursive functions. Most proof assistants enforce this through syntactic conditions, which can…
Metatheorems about type theories are often proven by interpreting the syntax into models constructed using categorical gluing. We propose to use only sconing (gluing along a global section functor) instead of general gluing. The sconing is…