In this chapter, we present a propositional calculus for several intervalvalued fuzzy logics, i.e., logics having intervals as truth values. More precisely, the truth values are preferably subintervals of the unit interval. The idea behind it is that such an interval can model imprecise information. To compute the truth values of ‘p implies q’ and ‘p and q’, given the truth values of p and q, w...

In this paper we show that Shannon’s General Purpose Analog Computer (GPAC) is equivalent to a particular class of recursive functions over the reals with the flavour of Kleene’s classical recursive function theory. We first consider the GPAC and several of its extensions to show that all these models have drawbacks and we introduce an alternative continuous-time model of computation that solve...

Recursive analysis is a model of analog computation which is based on type 2 Turing machines. Various classes of functions computable in recursive analysis have recently been characterized in a machine independent and algebraical context. In particular nice connections between the class of computable functions (and some of its sub and supclasses) over the reals and algebraically defined (suband...

This work presents a unified theory of recursive program schemes, context-free grammars, grammars on arbitrary algebraic structures and, in fact, recursive definitions of all kind by means of regular systems. The equivalences of regular systems associated with either all their solutions or their least solutions (in all domains of appropriate type satisfying a set of algebraic laws expressed by ...

circuits are used for formalizing regular hardware structures which can ] be expressed by means of primitive recursion. In general, . . . . . . . regular circuit structures lead to regular signal structures. If for example, a structure is described, that con~ ~ sists of n combinational circuits connected in parallel, then it would be appropriate to use the type list for : grouping together the ...