Parametrized Gradual Semantics Dealing with Varied Degrees of Compensation

Abstract

Compensation is a strategy that a semantics may follow when it faces dilemmas between quality and quantity of attackers. It allows several weak attacks to compensate one strong attack. It is based on compensation degree, which is a tuple that indicates (i) to what extent an attack is weak and (ii) the number of weak attacks needed to compensate a strong one. Existing principles on compensation do not specify the parameters, thus it is unclear whether semantics satisfying them compensate at only one degree or several degrees, and which ones. This paper proposes a parameterised family of gradual semantics, which unifies multiple semantics that share some principles but differ in their strategy regarding solving dilemmas. Indeed, we show that the two semantics taking the extreme values of the parameter favour respectively quantity and quality, while all the remaining ones compensate at some degree. We define three classes of compensation degrees and show that the novel family is able to compensate at all of them while none of the existing gradual semantics does.