Towards a Fuzzy Context Logic

A key step towards trustworthy, reliable and explainable, AI is bridging the gap between the quantitative domain of sensor-actuator systems and the qualitative domain of intelligent systems reasoning. Fuzzy logic is a well-known formalism suitable for aiming at this gap, featuring a quantitative mechanism that at the same time adheres to logical principles. Context logic is a two-layered logical language originally aimed at pervasive computing systems for reasoning about and within context, i.e., changing logical environments. Both logical languages are linguistically motivated. This chapter uncovers the close connection between the two logical languages presenting two new results. First, a proof is presented that context logic with a lattice semantics can be understood as an extension of fuzzy logic. Second, a fuzzification for context logic is proposed. The resulting language, which can be understood as a two-layered fuzzy logic or as a fuzzified context logic, expands both fields in a novel manner.