Possibilistic Temporal Reasoning based on Fuzzy Temporal Constraints

In this paper we propose a propositional temporal language based on fuzzy temporal constraints which turns out to be expressive enough for domains –like many coming from medicine– where knowledge is of propositional nature and an explicit handling of time, imprecision and uncertainty are required. The language is provided with a natural possibilistic semantics to account for the uncertainty issued by the fuzziness of temporal constraints. We also present an inference system based on specific rules dealing with the temporal constraints and a general fuzzy modus ponens rule whereby behaviour is shown to be sound. The analysis of the different choices as fuzzy operators leads us to identify the well-known Lukasiewicz implication as very appropriate to define the notion of possibilistic entailment, an essential element of our inference system.