A Logic for Reasoning about Actions and Explicit Observations Gavin Rens 1,2 , Ivan Varzinczak 1 , Thomas Meyer 1,2 , and Alexander Ferrein 3 1 KRR, CSIR Meraka, Pretoria, South Africa 2 School of Computer Science, University of KwaZulu-Natal, South Africa {grens,ivarzinczak,tmeyer}@meraka.org.za 3 Robotics and Agents Research Lab, University of Cape Town, South Africa alexander.ferrein@uct.ac.za Abstract. 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. 1 Introduction and Motivation Imagine a robot that is in need of an oil refill. There is an open can of oil on the floor within reach of its gripper. If there is nothing else in the robot’s gripper, it can grab the can (or miss it, or knock it over) and it can drink the oil by lifting the can to its ‘mouth’ and pouring the contents in (or miss its mouth and spill). The robot may also want to confirm whether there is anything left in the oil-can by weighing its contents with its arm. And once holding the can, the robot may wish to replace it on the floor. The domain is (partially) formalized as follows. The robot has the set of (intended) actions A = {grab, drink, weigh, replace} with expected meanings. The robot can perceive observations only from the set Ω = {obsNil , obsHeavy , obsMedium , obsLight }. Intuitively, when the robot performs a weigh action, it will perceive either obsHeavy , obsMedium or obsLight ; for other actions, it will ‘perceive’ obsNil , no perception. The robot experiences its world (domain) via three Boolean features: P = {full , drank, holding} meaning respectively that the the oil-can is full, that the robot has drunk the oil and that it is currently holding something in its gripper. This formalization seems more intuitive than lumping all observations in with propositions, for instance, by making P = {full , drank, holding, obsnil , heavy , medium, light }. It is the norm in dynamic logics (and some other agent oriented logics) to deal with observations as elements of knowledge, as propositions; and perception is normally coded as action, that is, observations-as-propositions evaluate to ‘true’ J. Li (Ed.): AI 2010, LNAI 6464, pp. 395–404, 2010. Springer-Verlag Berlin Heidelberg 2010