A simple logic of trust based on propositional assignments

Cristiano Castelfranchi and Rino Falcone introduced an influential cognitive theory of social trust that is based on the concepts of belief, goal, ability, willingness and opportunity. In this paper we propose a simple logic of belief and action that allows to express these concepts. While our logic of belief is standard, our logic of action has a very simple kind actions: actions setting the truth value of a propositional variable to either true or false. We call such actions propositional assignments and argue that our logic provides a framework that is simple but expressive enough to account for Castelfranchi and Falcone’s concept. We prove its completeness and give a decision procedure.