ON NEW CUMULATIVE VARIANTS OF DEFAULT LOGIC: CHARACTERIZATION AND ALGORITHMS OF EXTENSIONS
Ming Zhang · Chinese Journal of Computers · 1998
Recently, Giordano and Martelli have proposed two new variants ofRelier's default logic (DL): commitment to assumptions default logic (CADL) andquasi-default logic (QDL). The first variant is cumulative and commits toassumptions, like Brewka's cumulative default logic (CDL), but is not semimonotonic.The other one is also cumulative, but does not commit to assumptions, and hence isvery closed to Relier's DL. Unfortunately, Giordano and Martelli have only givenquasi-inductive characterizations of extensions for the two variants. Clearly, it isnot straightforward to derive characterizations, by which algorithms for computingextensions and solving reasoning tasks in CADL and QDL can be gotten easily.This paper establishes a relation between CADL and CDL extensions by applyingthe notion of joint compatibility of a default set. Based on the relation, a newcharacterization is gotten immediately and algorithms for reasoning tasks in CADL arepresented with a sightly difference that the credulous reasoning in CADL is harderthan one in CDL since the membership problem of △= (D,W) is no longer reducedinto one of △R= (DCA[R], WCA[R]). A relation between sets of generatingdefaults for DL extension and ones for QDL extensions is also established. Farther, afinite characterization of QDL extensions is derived by introducing the notion ofQcompatibility, and algorithms and complexity for main reasoning tasks in QDL arealso gotten.