Standard formulations of intuitionistic logic, whether by logicians or by category theorists,
generally do not take into account partially defined elements.(For a recent reference see …

The term" fuzzy logic," as it is understood in this book, stands for all aspects of representing
and manipulating knowledge based on the rejection of the most fundamental principle of …

This paper presents a type theory in which it is possible to directly manipulate $ n $-
dimensional cubes (points, lines, squares, cubes, etc.) based on an interpretation of …

Without wishing to enter into the argument over" constructive" set theories we present
Heyting-valued models for intuitionistic Zermelo-Frankel style set theories in § 2 and apply …

This book is about some recent work in a subject usually considered part of" logic" and the"
foundations of mathematics", but also having close connec tions with philosophy and …

Categories, Types and Structures. Page 1 HAL Id: hal-03316030 https://ens.hal.science/hal-03316030
Submitted on 10 Aug 2021 HAL is a multi-disciplinary open access archive for the deposit and …

Mathematics and logic have been central topics of concern since the dawn of philosophy.
Since logic is the study of correct reasoning, it is a fundamental branch of epistemology and …

There are basically two ways to view intuitionistic logic: as a philosophical‐foundational
issue in mathematics; or as a technical discipline within mathematical logic. Considering first …

Topos theory has led to unexpected connections between classical and constructive
mathematics. This text explores Lawvere and Tierney's concept of topos theory, a …

One of the most important constructions in topos theory ia that of the category Shv (A) of
sheaves on a locale (= complete Heyting algebra) A. Normally, the objects of this category …