Properties of Conservative Extensions to Stable Model Semantics: a Structural Approach

The stable model (SM ) semantics lacks the properties of existence, relevance and cumulativity. It is thus reasonable to look for conservative extensions of this semantics (i.e., semantics that for each normal logic program P retrieve a superset of the set of stable models of P ) that may enjoy some or all of the above properties. In this work we define a large class of conservative extensions of the SM , dubbed affix stable model semantics, ASM , and study the above referred properties into two non-disjoint subfamilies, ASM and ASM, of the class ASM . Among the results obtained, the following should be emphasized: (1) We present a refined definition of cumulativity for semantics of the set ASM ∪ ASM, that turns into an easier job the dismissal of this property by resorting to counter examples; (2) We divide the sets of rules of normal logic programs into layers and use the decomposition of models into that layered structure to define three new (structural) properties, defectivity, excessiveness and irregularity, which allow to state a number of relations between the properties of existence, relevance and cumulativity for semantics of the ASM ∪ ASM class; (3) As a consequence of our work, we show that for the SM semantics case, the properties of (lack of) existence and (lack of) cautious monotony are equivalent, which opposes statements on this issue that may be found in the literature.