Isoinitial Models for Logic Programs: A Preliminary Study
Kung-Kiu Lau 
Dept. of Computer Science, University of Manchester 
Manchester M13 9PL, UK
kung-kiu@cs.man.ac.uk

Mario Ornaghi
Dip. di Scienze dell'Informazione, Universita' di Milano 
Via Comelico 39, 20135  Milano, Italy
ornaghi@dsi.unimi.it

Abstract:
The Herbrand model H of a definite logic program P is an initial model
among the class of all the models of P, interpreting P as an initial
theory. Such a theory proves (computes) only positive literals (atoms)
in P, so it does not deal with negation. In this paper, we introduce
isoinitial models of logic programs. We show that isoinitial semantics
deals with negation, and works in a uniform way for definite and
normal logic programs. Moreover, the lack of an isoinitial model
signals the absence of information. Thus it also provides a unifying
semantics for closed and open logic programs.