A Many-Valued Temporal Logic and Reasoning Framework for Decision Making

Temporality and uncertainty are important features of real world systems where the state of a system evolves over time and the transition through states depends on uncertain conditions. Examples of such application areas where these concepts matter are smart home systems, disaster management, and robot control etc. Solving problems in such areas usually requires the use of formal mechanisms such as logic systems, statistical methods and other reasoning and decision-making methods. In this chapter, we extend a previously proposed temporal reasoning framework to enable the management of uncertainty based on a many-valued logic. We prove that this new many-valued temporal propositional logic system is sound and complete. We also provide extended reasoning algorithms that can now handle both temporality and uncertainty in an integrated way. We illustrate the framework through a simple but realistic scenario in a smart home application.