Related papers: An Algorithmic Structuration of a Type System for …
Homotopy type theory is an interpretation of Martin-L\"of's constructive type theory into abstract homotopy theory. There results a link between constructive mathematics and algebraic topology, providing topological semantics for…
Data analysis and data mining are concerned with unsupervised pattern finding and structure determination in data sets. The data sets themselves are explicitly linked as a form of representation to an observational or otherwise empirical…
Python's typing system has evolved pragmatically into a powerful but theoretically fragmented system, with scattered specifications. This paper proposes a formalization to address this fragmentation. The central contribution is a formal…
The depth-bounded fragment of the pi-calculus is an expressive class of systems enjoying decidability of some important verification problems. Unfortunately membership of the fragment is undecidable. We propose a novel type system,…
We introduce type annotations as a flexible typing mechanism for graph systems and discuss their advantages with respect to classical typing based on graph morphisms. In this approach the type system is incorporated with the graph and…
We propose a mathematical framework for a unification of the distributional theory of meaning in terms of vector space models, and a compositional theory for grammatical types, for which we rely on the algebra of Pregroups, introduced by…
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).…
This document develops general concepts useful for extracting knowledge embedded in large graphs or datasets that have pair-wise relationships, such as cause-effect-type relations. Almost no underlying assumptions are made, other than that…
The article suggests a description of a system of tables with a set of special lists absorbing a semantics of data and reflects a fullness of data. It shows how their parallel processing can be constructed based on the descriptions. The…
A datatype defining rewrite system (DDRS) is an algebraic (equational) specification intended to specify a datatype. When interpreting the equations from left-to-right, a DDRS defines a term rewriting system that must be ground-complete.…
The introduction of first-class type classes in the Coq system calls for re-examination of the basic interfaces used for mathematical formalization in type theory. We present a new set of type classes for mathematics and take full advantage…
The main objective of this paper is to show that the notion of type which was developed within the frames of logic and model theory has deep ties with geometric properties of algebras. These ties go back and forth from universal algebraic…
This thesis investigates how the sub-structure of words can be accounted for in probabilistic models of language. Such models play an important role in natural language processing tasks such as translation or speech recognition, but often…
FAIR Digital Objects support research data management aligned with the FAIR principles. To be machine-actionable, they must support operations that interact with their contents. This can be achieved by associating operations with FAIR-DO…
Higher-order logic HOL offers a very simple syntax and semantics for representing and reasoning about typed data structures. But its type system lacks advanced features where types may depend on terms. Dependent type theory offers such a…
We propose to use orthologic as the basis for designing type systems supporting intersection, union, and negation types in the presence of subtyping assumptions. We show how to extend orthologic to support monotonic and antimonotonic…
Algebraic datatypes, and among them lists and trees, have attracted a lot of interest in automated reasoning and Satisfiability Modulo Theories (SMT). Since its latest stable version, the SMT-LIB standard defines a theory of algebraic…
The problem of entity-typing has been studied predominantly in supervised learning fashion, mostly with task-specific annotations (for coarse types) and sometimes with distant supervision (for fine types). While such approaches have strong…
Infinite types and formulas are known to have really curious and unsound behaviors. For instance, they allow to type {\Omega}, the auto- autoapplication and they thus do not ensure any form of normalization/productivity. Moreover, in most…
Data modeling is a process of developing a model to design and develop a data system that supports an organization s various business processes. A conceptual data model represents a technology-independent specification of structure of data…