A Logic for Reasoning about Actions and Explicit Observations

We propose a formalism for reasoning about actions based on multi-modal logic which allows for expressing observations as first-class objects. We introduce a new modal operator, namely [o | α], which allows us to capture the notion of perceiving an observation given that an action has taken place. Formulae of the type [o | α]φ mean ‘after perceiving observation o, given α was performed, necessarily φ’. In this paper, we focus on the challenges concerning sensing with explicit observations, and acting with nondeterministic effects. We present the syntax and semantics, and a correct and decidable tableau calculus for the logic.