Fuzzy type theory with partial functions

Fuzzy Type Theory, Descriptions, and Partial Functions

This paper studies the possibility to deal with partial functions in fuzzy type theory. Among various ways how to represent them we chose introduction of a special value “undefined” laying outside the corresponding domain. In FTT, we can quite naturally utilize the description operator by extending its action also to subnormal fuzzy sets.

Partial Functions in Operational Type Theory (DRAFT)

An Operational Type Theory (OPTT) is developed based on a theory of operational joinability of untyped terms. The theory accomodates functions which might diverge or abort on some inputs. To preserve logical soundness, OPTT distinguishes proofs from programs, and formulas from types. OPTT incorporates proof irrelevance, thus facilitating the combination of internal and external verification.

Partial Recursive Functions in Martin-Löf Type Theory

In this article we revisit the approach by Bove and Capretta for formulating partial recursive functions in Martin-Löf Type Theory by indexed inductive-recursive definitions. We will show that all inductiverecursive definitions used there can be replaced by inductive definitions. However, this encoding results in an additional technical overhead. In order to obtain directly executable partial r...

On fuzzy type theory

a new type-ii fuzzy logic based controller for non-linear dynamical systems with application to 3-psp parallel robot

abstract type-ii fuzzy logic has shown its superiority over traditional fuzzy logic when dealing with uncertainty. type-ii fuzzy logic controllers are however newer and more promising approaches that have been recently applied to various fields due to their significant contribution especially when the noise (as an important instance of uncertainty) emerges. during the design of type- i fuz...

A Data Type of Partial Recursive Functions in Martin-Löf Type Theory

In this article we investigate how to represent partial-recursive functions in Martin-Löf’s type theory. Our representation will be based on the approach by Bove and Capretta, which makes use of indexed inductive-recursive definitions (IIRD). We will show how to restrict the IIRD used so that we obtain directly executable partial recursive functions, Then we introduce a data type of partial rec...