On the Role of Negation in Choice Logic Programs

We introduce choice logic programs as negation-free datalog programs that allow rules to have exclusive-only (possibly empty) disjunctions in the head. Such programs naturally model decision problems where, depending on a context, agents must make a decision, i.e. an exclusive choice out of several alternatives. It is shown that such a choice mechanism is in a sense equivalent with negation as supported in semi-negative datalog programs. We also discuss an application where strategic games can be naturally formulated as choice programs: it turns out that the stable models of such programs capture exactly the set of Nash equilibria. We then consider the effect of choice on “negative information” that may be implicitly derived from a program. Based on an intuitive notion of unfounded set for choice programs, we show that several results from (seminegative) disjunctive programs can be strengthened; characterizing the position of choice programs as an intermediate between simple positive programs and programs that allow for the explicit use of negation in the body of a rule. Supported by the FWO. yAll correspondence to this author.