Update-programms can update programs

Abstract

In the recent literature the issue of program change via updating rules (also known as revision rules) has been reduced to the issue of obtaining a new set of models, by means of the update rules, from each of the models of an initial program. Any program whose models are exactly the new set of models will count as an update of the original program. Following the classical approaches to theory updating, it is of course essential to start by specifying precisely how a program's models are to change, before even attempting to specify program change. But to stop there is to go only halfway.

Another limitation of existing approaches to logic program updating concerns their not dealing with 3-valuedness, i.e. with partial models. The limitation is twofold: on the one hand, only programs under 2-valued semantics are approachable; on the other, when there are contradictory update rules, in lieu of leaving undefined the effects of the contradictory rules and keeping those of the others, no update is possible at all. In this paper, we generalize the notion of justified update to partial (or 3-valued) interpretations and expound a correct transformation on normal programs which, from an initial program, produces another program whose models enact the required change in the initial program's models, as specified by the update rules. Forthwith, we generalize our approach to logic programs as well as update programs extended with explicit negation.