Spatio-temporal logic is a variant of branching temporal logic where one of the so-called causal relations on spacetime plays the role of a time flow. Allowing only rational numbers as space and time co-ordinates, we prove that a first-order spatio-temporal theory over this flow is recursively enumerable if and only if the dimension of spacetime does not exceed 2. The situation is somewhat different compared to the case of real co-ordinates, because we establish that even dimension 2 does not permit (...) recursive enumerability in this case. The proof of the result on rational spacetime involves a more deeper portion of spacetime geometry than the corresponding, more evident result for the real co-ordinates. (shrink)

This paper argues that chance (risk or opportunity) discovery is challenging, from a reasoning point of view, because it represents a dilemma for inductive reasoning. Chance discovery shares many features with the grue paradox. Consequently, Bayesian approaches represent a potential solution. The Bayesian solution evaluates alternative models generated using a temporal logic planner to manage the chance. Surprise indices are used in monitoring the conformity of the real world and the assessed probabilities. Game theoretic approaches are proposed to deal with (...) multi-agent interaction in chance management. (shrink)

This paper presents an approach to artificial intelligence planning based on linear temporal logic (LTL). A simple and easy-to-use planning language is described, Planning Domain Description Language with control Knowledge (PDDL-K), which allows one to specify a planning problem together with heuristic information that can be of help for both pruning the search space and finding better quality plans. The semantics of the language is given in terms of a translation into a set of LTL formulae. Planning is then reduced (...) to “executing” the LTL encoding, i.e. to model search in LTL. The feasibility of the approach has been successfully tested by means of the system Pdk, an implementation of the proposed method. (shrink)

The situation calculus is one of the most established formalisms for reasoning about action and change. In this paper we will review the basics of Reiter’s version of the situation calculus, show how knowledge and time have been addressed in this framework, and point to some of the weaknesses of the situation calculus with respect to time. We then present a modal version of the situation calculus where these problems can be overcome with relative ease and without sacrificing the advantages (...) of the original. (shrink)

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)