Published in Volume XV, 2005, pages 124-136

**Authors:** Victor FELEA

### Abstract

For a general logic program, a totally ordered set of logic values is considered

and an undefined value denoted $u$. Partial interpretations are also defined.

An interpretation $I$ is considered as a vector of sets from Herbrand base of

the program $P$. A program $P$ may contain the constants defined for every logic value.

A pseudo-negation denoted $rceil$ is defined. This pseudo-negation differs from

a negation because the property of idempotence for the pseudo-negation is not satisfied.

The negation from the clauses bodies of a program $P$ is interpreted via the

pseudo-negation. For the partial multi-valued interpretation $I$, the notion of model

of $P$ is defined. A partial ordering is defined between multi-valued interpretations.

An operator between interpretations is defined for a program P. Using this operator,

a pseudo-stable semantics for the program P is introduced. The pseudo-stable models

that satisfy a certain property are minimal elements of the set of all models for a

program P having that property.

### Bibtex

@article{sacscuza:felea2005oppmflp, title={On Partial Pseudo-Stable Models For Logic Programs.}, author={Victor FELEA}, journal={Scientific Annals of Computer Science}, volume={15}, organization={``A.I. Cuza'' University, Iasi, Romania}, year={2005}, pages={124--136}, publisher={``A.I. Cuza'' University Press} }