Related papers: Les types de donn\'ees syntaxiques du syst\`eme F
The definition is a common form of human expert knowledge, a building block of formal science and mathematics, a foundation for database theory and is supported in various forms in many knowledge representation and formal specification…
Sentences containing definite descriptions, expressions of the form `The $F$', can be formalised using a binary quantifier $\iota$ that forms a formula out of two predicates, where $\iota x[F, G]$ is read as `The $F$ is $G$'. This is an…
In the present paper we introduce positive flows and processes, which generalize the ordinary dynamical systems and stochastic processes. We develop a branch of theory of positive operators based on the concepts of phase and positive…
We present gradual type theory, a logic and type theory for call-by-name gradual typing. We define the central constructions of gradual typing (the dynamic type, type casts and type error) in a novel way, by universal properties relative to…
Streams, or infinite sequences, are infinite objects of a very simple type, yet they have a rich theory partly due to their ubiquity in mathematics and computer science. Stream differential equations are a coinductive method for specifying…
We develop a system which must be able to perform the same inferences that a human reader of an accident report can do and more particularly to determine the apparent causes of the accident. We describe the general framework in which we are…
State of the art optimisation passes for dependently typed languages can help erase the redundant information typical of invariant-rich data structures and programs. These automated processes do not dramatically change the structure of the…
A numeral system is a sequence of an infinite different closed normal $\lambda$-terms which has closed $\lambda$-terms for successor and zero test. A numeral system is said adequate iff it has a closed $\lambda$-term for predecessor. A…
We prove a theorem stating that any semantics can be encoded as a compositional semantics, which means that, essentially, the standard definition of compositionality is formally vacuous. We then show that when compositional semantics is…
Hybrid probabilistic logic programs can represent several scenarios thanks to the expressivity of Logic Programming extended with facts representing discrete and continuous distributions. The semantics for this type of programs is crucial…
In this paper, we consider the relationship between phase-type distributions and positive systems through practical examples. Phase-type distributions, commonly used in modelling dynamic systems, represent the temporal evolution of a set of…
Type systems certify program properties in a compositional way. From a bigger program one can abstract out a part and certify the properties of the resulting abstract program by just using the type of the part that was abstracted away.…
A definable set $X$ in the first-order language of rings defines a family of random vectors: for each finite field $\mathbb{F}_q$, let the distribution be supported and uniform on the $\mathbb{F}_q$-rational points of $X$. We employ results…
This paper describes the design principles of methodology of knowledge-oriented information systems based on ontological approach. Such systems implement technology subject-oriented extraction of knowledge from the set of natural language…
A new class of Semantic Numeration Systems, namely, positive rational Semantic Numeration Systems is introduced. For cardinal semantic operators, differences in the formation of carry (common carry) and remainders are defined. The…
The Resource Description Framework (RDF) is a Semantic Web standard that provides a data language, simply called RDF, as well as a lightweight ontology language, called RDF Schema. We investigate embeddings of RDF in logic and show how…
It is widely recognized that the proliferation of annotation schemes runs counter to the need to re-use language resources, and that standards for linguistic annotation are becoming increasingly mandatory. To answer this need, we have…
Type-and-effect systems incorporate information about the computational effects, e.g., state mutation, probabilistic choice, or I/O, a program phrase may invoke alongside its return value. A semantics for type-and-effect systems involves a…
We develop the usage of certain type theories as specification languages for algebraic theories and inductive types. We observe that the expressive power of dependent type theories proves useful in the specification of more complicated…
We investigate completeness and parametricity for a general class of realizability semantics for System F defined in terms of closure operators over sets of $\lambda$-terms. This class includes most semantics used for normalization…