In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

The stable model (SM) semantics lacks the properties of existence, relevance and cumulativity. If we prospectively consider the class of conservative extensions of the SM semantics (i.e., semantics that for each normal logic program P retrieve a superset of the set of stable models of P), one may wander how do the semantics of this class behave in what concerns the aforementioned properties. That is the type of issue dealt with in this paper. We define a large class of conservative extensions of the SM semantics, dubbed affix stable model semantics (ASM), and study the above referred properties into two non-disjoint subfamilies of the class ASM, here dubbed ASMh and ASMm. From this study a number of results stem which facilitate the assessment of semantics in the class ASMh ASMm with respect to the properties of existence, relevance and cumulativity, whilst unveiling relations among these properties. As a result of the approach taken in our work, light is shed on the characterization of the SM semantics, as we show that 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. We also characterize the relevance failure of SM semantics in a more clear way than usually stated in the literature.
Properties of Stable Model Semantics Extensions