Planning with effectively propositional logic
We present a fragment of predicate logic which allows the use of equality and quantification but whose models are limited to finite Herbrand interpretations. Formulae in this logic can be thought as syntactic sugar on top of the Bernays-Schonfinkel fragment and can, therefore, still be effectively grounded into a propositional representation. We motivate the study of this logic by showing that practical problems from the area of planning can be naturally and succinctly represented using the added syntactic features. Moreover, from a theoretical point of view, we show that this logic allows, when compared to the propositional approach, not only more compact encodings but also exponentially shorter refutation proofs.
We give an On log n time algorithm to preemptively schedule n equal-length jobs with release times on two identical, parallel machines so as to minimize the mean flow time. The complexity of the general problem of minimizing the mean weighted flow time is also reviewed, both for nonpreemptive and preemptive scheduling.