Expressive power and complexity of disjunctive datalog under the stable model semantics

Abstract

DATALOG¬ is a well-known logical query language, whose expressive power and data complexity under the stable model semantics has been recently determined. In this paper we consider the extension of DATALOG¬ to disjunctive DATALOG¬ (DDL¬), which allows disjunction in the head of program clauses, under the stable model semantics. We investigate and determine the expressiveness and the data complexity of DDL¬, as well as the expression complexity. The main findings of this paper are that disjunctive datalog captures precisely the class of all ∑ 2 p -recognizable queries under the brave version of reasoning, and symmetrically the class of all Π 2 p -recognizable queries under the cautious version; the data complexity is ∑ 2 p -completeness in the brave version, and Π 2 p -complete in the cautious version, while the expression complexity is NEXPTIMENP-complete in the brave version and co-NEXPTIMENPcomplete in the cautious version.