Affiliations: [a] Dept. of Mathematics and Computer Science, Lehman College (CUNY), Bronx, NY 10468, USA | [b] Depts. of Computer Science, Philosophy, Mathematics, Graduate Center (CUNY), 33 West 42nd Street, NYC, NY 10036, USA, E-mail: mlflc@cunyvrn.cuny.edu | [c] Dept. of Mathematics and Comp. Inf Science, Mercy College, 555 Broadway, Dobbs Ferry, NY 10522, USA
Note: [1] This is an expanded version of [10].
Note: [*] Research partly supported by NSF Grant CCR-8702307 and PSC-CUNY Grant 6-67295.
Abstract: We investigate the relationship between three-valued Kripke/Kleene semantics and stratified semantics for stratifiable logic programs. We first show these are compatible, in the sense that if the three-valued semantics assigns a classical truth value, the stratified approach will assign the same value. Next, the familiar fixed point semantics for pure Horn clause programs gives both smallest and biggest fixed points fundamental roles. We show how to extend this idea to the family of stratifiable logic programs, producing a semantics we call weak stratified. Finally, we show weak stratified semantics coincides exactly with the three-valued approach on stratifiable programs, though the three-valued version is generally applicable, and does not require stratification assumptions.
