Linear Time Logic, Conditioned Models, and Planning with Incomplete Knowledge

Abstract

The “planning as satisfiability” paradigm, which reduces solving a planning problem P to the search of a model of a logical description of P, relies on the assumption that the agent has complete knowledge and control over the world. This work faces the problem of planning in the presence of incomplete information and/or exogenous events, still keeping inside the “planning as satisfiability” paradigm, in the context of linear time logic.

We give a logical characterization of a “conditioned model”, which represents a plan solving a given problem together with a set of “conditions” that guarantee its executability. During execution, conditions have to be checked by means of sensing actions. When a condition turns out to be false, a different “conditioned plan” must be considered. A whole conditional plan is represented by a set of conditioned models. The interest of splitting a conditional plan into significant sub-parts is due to the heavy computational complexity of conditional planning.

The paper presents an extension of the standard tableau calculus for linear time logic, allowing one to extract from a single open branch a conditioned model of the initial set of formulae, i.e. a partial description of a model and a set of conditions U guaranteeing its “executability”. As can be expected, if U is required to be minimal, the analysis of a single branch is not sufficient. We show how a global view on the whole tableau can be used to prune U from redundant conditions. In any case, if the calculus is to be used with the aim of producing the whole conditional plan off-line, a complete tableau must be built. On the other hand, a single conditioned model can be used when planning and execution (with sensing actions) are intermingled. In that case, the requirement for minimality can reasonably be relaxed.