Related papers: Type theoretical databases
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…
Typed operational semantics is a method developed by H. Goguen to prove meta-theoretic properties of type systems. This paper studies the metatheory of a type system with dependent record types, using the approach of typed operational…
The basics of set theory are usually copied, directly or indirectly, by computer scientists from introductions to mathematical texts. Often mathematicians are content with special cases when the general case is of no mathematical interest.…
A type analysable in one-based types in a simple theory is itself one-based.
Today, the practice of returning entities from a knowledge base in response to search queries has become widespread. One of the distinctive characteristics of entities is that they are typed, i.e., assigned to some hierarchically organized…
Inspired by the trend on unifying theories of programming, this paper shows how the algebraic treatment of standard data dependency theory equips relational data with functional types and an associated type system which is useful for type…
We define a general class of dependent type theories, encompassing Martin-L\"of's intuitionistic type theories and variants and extensions. The primary aim is pragmatic: to unify and organise their study, allowing results and constructions…
The SP theory of computing and cognition, described in previous publications, is an attractive model for intelligent databases because it provides a simple but versatile format for different kinds of knowledge, it has capabilities in…
The concept of $typed$ $topology$ is introduced. In a typed topological space, some open sets are assigned "types", and topological concepts such as closure, connectedness can be defined using types. A finite data set in $R^2$ is a…
We develop a representation theory of categories as a means to explore characteristic structures in algebra. Characteristic structures play a critical role in isomorphism testing of groups and algebras, and their construction and…
We present an approach for modeling the Semantic Web as a type system. By using a type system, we can use symbolic representation for representing linked data. Objects with only data properties and references to external resources are…
In this paper we formalize some foundation concepts and theorems of group theory in a variant of type theory called the Calculus of Constructions with Definitions. In this theory we introduce definition of a group, which is both general and…
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…
Algorithms of inference in a computer system oriented to input and semantic processing of text information are presented. Such inference is necessary for logical questions when the direct comparison of objects from a question and database…
A relevant thesis is that for the family of complete first order theories with NIP (i.e. without the independence property) there is a substantial theory, like the family of stable (and the family of simple) first order theories. We examine…
We present an approach to support partiality in type-level computation without compromising expressiveness or type safety. Existing frameworks for type-level computation either require totality or implicitly assume it. For example, type…
We develop semantics and syntax for bicategorical type theory. Bicategorical type theory features contexts, types, terms, and directed reductions between terms. This type theory is naturally interpreted in a class of structured…
We present the first definition of strictly associative and unital $\infty$-category. Our proposal takes the form of a type theory whose terms describe the operations of such structures, and whose definitional equality relation enforces…
We present a type theory with some proof-irrelevance built into the conversion rule. We argue that this feature is useful when type theory is used as the logical formalism underlying a theorem prover. We also show a close relation with the…
We begin a systematic development of structure theory for a first order theory, which is stable over a monadic predicate. We show that stability over a predicate implies quantifier free definability of types over stable sets, introduce an…