Explorer Logics for Action

Logics of action, for reasoning about the effects of state change, and logics of belief, accounting for belief revision and update, have much in common. Furthermore, we may undertake an action because we hold a particular belief, and revise our beliefs in the light of observed consequences of an action. So studies of these two aspects are inevitably intertwined. However, we argue, a clear separation of the two is helpful in understanding their interactions. We give a semantic presentation of such a separation, introducing a semantic setting that supports one logic for describing the effects of actions, which are modeled as changing the values of particular atomic properties, or fluents, and another for expressing more complex facts or beliefs about the world. We use a simple state-logic, to account for state change, and show how it can be integrated with a variety of domain-logics, of fact or belief, for reasoning about the world. Stateand domain-logics are linked, syntactically and semantically; but separate. The state-logic, our logic for action, is quantified propositional logic. Bounded existential propositional quantification is used to specify which literals may be established by a given action. This provides a logically transparent account of the treatment of updates introduced in [1], which itself provided a treatment of the frame problem extending the uses in event calculi of the forget operator, occlude and release predicates, all published in 1994 [2–4]. Our, purely classical, logical setting can be seen as a recasting of the state-transition model of action, underlying STRIPS [5] and ADL [6]. Our treatment, like ADL, caters for actions with conditional effects, which can handle ramifications unrepresentable in classic STRIPS; it also includes concurrent actions, non-deterministic effects, and domain axioms or integrity constraints, which are not present in ADL. We introduce an operator, novel in this context, that computes fixpoints of certain monotone actions, to handle the problem of nested ramification. We exploit non-determinacy to provide a decomposition of actions, as compositions of simpler fundamental operations on states. These decompositions provide a basis for the static analysis of interference, which is applied in our treatment of iteration, re-ordering and concurrent composition of actions. Our setting combines operational and inferential aspects. Domain logics are inferential, and can vary, from classical to exotic. The state logic provides an operational calculus of actions that retains the clarity and simplicity of propositional reasoning, which underlies STRIPS’ enduring appeal. It also has practical benefits: applications can exploit propositional reasoning tools, such as BDD packages and SAT solvers to provide a direct route to efficient implementations [7]. keyword action, transition system, logic, semantics, frame problem, representation