Negation in the Head of CP-logic Rules

CP-logic is a probabilistic extension of the logic FO(ID). Unlike ASP, both of these logics adhere to a Tarskian informal semantics, in which interpretations represent objective states-of-affairs. In other words, these logics lack the epistemic component of ASP, in which interpretations represent the beliefs or knowledge of a rational agent. Consequently, neither CP-logic nor FO(ID) have the need for two kinds of negations: there is only one negation, and its meaning is that of objective falsehood. Nevertheless, the formal semantics of this objective negation is mathematically more similar to ASP’s negation-as-failure than to its classical negation. The reason is that both CP-logic and FO(ID) have a constructive semantics in which all atoms start out as false, and may only become true as the result of a rule application. This paper investigates the possibility of adding the well-known ASP feature of allowing negation in the head of rules to CP-logic. Because CP-logic only has one kind of negation, it is of necessity this “negation-as-failure like” negation that will be allowed in the head. We investigate the intuitive meaning of such a construct and the benefits that arise from it.