37 research outputs found
Note on paraconsistency and reasoning about fractions
We apply a paraconsistent logic to reason about fractions.Comment: 6 page
Straight-line instruction sequence completeness for total calculation on cancellation meadows
A combination of program algebra with the theory of meadows is designed
leading to a theory of computation in algebraic structures which use in
addition to a zero test and copying instructions the instruction set . It is proven that total functions on cancellation
meadows can be computed by straight-line programs using at most 5 auxiliary
variables. A similar result is obtained for signed meadows.Comment: 24 page
The structure of finite meadows
A meadow is a commutative ring with a total inverse operator satisfying
0^{-1}=0. We show that the class of finite meadows is the closure of the class
of Galois fields under finite products. As a corollary, we obtain a unique
representation of minimal finite meadows in terms of finite prime fields.Comment: 12 page
A process algebra based framework for promise theory
We present a process algebra based approach to formalize the interactions of
computing devices such as the representation of policies and the resolution of
conflicts. As an example we specify how promises may be used in coming to an
agreement regarding a simple though practical transportation problem.Comment: 9 pages, 4 figure
Equations for formally real meadows
We consider the signatures of meadows
and of signed meadows. We give two complete
axiomatizations of the equational theories of the real numbers with respect to
these signatures. In the first case, we extend the axiomatization of
zero-totalized fields by a single axiom scheme expressing formal realness; the
second axiomatization presupposes an ordering. We apply these completeness
results in order to obtain complete axiomatizations of the complex numbers.Comment: 24 pages, 14 tables, revised, new Theorem 3.
Universality of Univariate Mixed Fractions in Divisive Meadows
Univariate fractions can be transformed to mixed fractions in the equational
theory of meadows of characteristic zero.Comment: 12 page
Some properties of finite meadows
The aim of this note is to describe the structure of finite meadows. We will
show that the class of finite meadows is the closure of the class of finite
fields under finite products. As a corollary, we obtain a unique representation
of minimal meadows in terms of prime fields.Comment: 8 pages, 1 tabl
The initial meadows
A \emph{meadow} is a commutative ring with an inverse operator satisfying
. We determine the initial algebra of the meadows of characteristic 0
and show that its word problem is decidable.Comment: 11 page