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Equivalence and difference between institutions: simulating Horn Clause Logic with based algebras

Published online by Cambridge University Press:  04 March 2009

Hans-Jörg Kreowski  and
Till Mossakowski
Hans-Jörg Kreowski
Affiliation:
Universität Bremen, Fachbereich 3, Postfach 33 04 40, D-28334 Bremen E-mail: kreo@informatik.uni-bremen.de
Till Mossakowski
Affiliation:
Universität Bremen, Fachbereich 3, Postfach 33 04 40, D-28334 Bremen E-mail: till@informatik.uni-bremen.de
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Abstract

In this paper, we investigate several logical frameworks whose expressiveness lies between Conditional Equational Logic and Horn Clause Logic. The main result deals with the PART-construction, which interprets total based algebras as partial algebras. This construction can be viewed as a simulation of Horn Clause Theories by means of Conditional Equational Theories. Other constructions in other frameworks are extendable to simulations in a similar way. The notion of categorical retractive simulation captures some essential properties of these, which allows us to measure the equivalence and difference between institutions.

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 5 , Issue 2 , June 1995 , pp. 189 - 215
Copyright
Copyright © Cambridge University Press 1995

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