A Multivalued logic model of planning

In this work a model for planning with multivalued fluents and graded actions, based on the infinite valued Lukasiewicz logic, is introduced. In AI planning there exist many real application domains in which the relevant properties cannot be expressed by a crisp boolean value, the actions can be applied with a graded level and the effects can depend on that level. In multivalued planning model proposed in this work, fluents can assume truth values in the interval [0, 1] and actions can be executed at different application degrees also varying in [0, 1]. The notions of planning problem and solution plan also reflect a multivalued approach. Multivalued fluents and graded actions allow to model many real situations where some features of the world cannot be modeled with boolean values and where actions can be executed with varying strength which produces graded effects as well. In the multivalued/fuzzy logics scenario we preferred to use a logic based on T-norms because of its well founded mathematical aspects. Among this class of logics we have chosen the Łukasiewicz logic be cause the semantics of its operators is more suitable for our framework. For these reasons we have excluded other well known logics as Product Logic, in which for instance the negation operator is not involutive. The proposed model can be seen as a generalization of the classical planning, since boolean and multivalued actions and fluents can be used in the same domain, and it is comparable with models allowing flexible actions and soft constraints. A correct/complete algorithm which solves bounded multivalued planning problems based on MIP compilation is also described and a prototype implementation is presented.