A dynamic domain consists of a set of legal states and a transition function that maps states to states. AI formalisms for specifying dynamic domains have so far focused on describing the effects of actions, that is, the transition functions. In this paper we propose a notion of characteristic set of position systems for the purpose of describing legal states. A position system for a type of objects is a set of properties that are mutually exclusive, and that in each (...) state, every object of the type must satisfy exactly one of these properties called its position under the position system. A set of position systems, one for each type of objects in the domain, is characteristic if there is a one-to-one mapping between legal states and sets of objects’ positions under these position systems. These position systems are useful for reasoning about these dynamic systems including planning. In particular, we show that once we have characteristic sets of position systems for a dynamic domain, planning can be done by writing rules about when to move objects from one position to another. (shrink)

There are various contexts in which it is not pertinent to generate and attend to all the classical consequences of a given premiss—or to trace all the premisses which classically entail a given consequence. Such contexts may involve limited resources of an agent or inferential engine, contextual relevance or irrelevance of certain consequences or premisses, modelling everyday human reasoning, the search for plausible abduced hypotheses or potential causes, etc. In this paper we propose and explicate one formal framework for a (...) whole spectrum of consequence relations, flexible enough to be tailored for choices from a variety of contexts. We do so by investigating semantic constraints on classical entailment which give rise to a family of infra-classical logics with appealing properties. More specifically, our infra-classical reasoning demands (beyond ${\alpha\models\beta}$ ) that Mod(β) does not run wild, but lies within the scope (whatever that may mean in some specific context) of Mod(α), and which can be described by a sentence ${\bullet\alpha}$ with ${\beta\models\bullet\alpha}$ . Besides being infra-classical, the resulting logic is also non-monotonic and allows for non-trivial reasoning in the presence of inconsistencies. (shrink)