Link to this article: http://journals.cambridge.org/abstract_S0960129501003413How to cite this article: MAX KANOVICH and JACQUELINE VAUZEILLES (2001). The classical AI planning problems in the mirror of Horn linear logic: semantics, expressibility, complexity.We introduce Horn linear logic as a comprehensive logical system capable of handling the typical AI problem of making a plan of the actions to be performed by a robot so that he could get into a set of final situations, if he started with a certain initial situation. Contrary to undecidability of propositional Horn linear logic, the planning problem is proved to be decidable for a reasonably wide class of natural robot systems. The planning problem is proved to be EXPTIME-complete for the robot systems that allow actions with non-deterministic effects. Fixing a finite signature, that is a finite set of predicates and their finite domains, we get a polynomial time procedure of making plans for the robot system over this signature. The planning complexity is reduced to PSPACE for the robot systems with only pure deterministic actions. As honest numerical parameters in our algorithms we invoke the length of description of a planning task 'from W to Z' and the Kolmogorov descriptive complexity of Ax T , a set of possible actions. Downloaded: 05 Apr 2015 IP address: 132.174.254.155 M. Kanovich and J. Vauzeilles 690 fragment of it that could be used for specifying AI systems and their problems (cf., for instance, the connection method in Bibel (1986)). The aim of this research is to introduce a comprehensive logical system that automatically exploits peculiarities of the AI systems under consideration, and to show that such a logical system can indeed achieve a significant speedup over the traditional ones.The AI systems we consider have the following features.A robot is dealing with a finite number of objects. Each of the actions performed by the robot results in correlations newly established between the objects, with some old correlations being destroyed. The conditions enabling an action consist of the presence of certain old correlations.The typical AI problem is that of making a plan of the actions to be performed by the robot so that it could get into a set of final situations if it started with a certain initial situation
a b s t r a c tThe typical AI problem is that of making a plan of the actions to be performed by a controller so that it could get into a set of final situations, if it started with a certain initial situation.The plans, and related winning strategies, happen to be finite in the case of a finite number of states and a finite number of instant actions.The situation becomes much more complex when we deal with planning under temporal uncertainty caused by actions with delayed effects.Here we introduce a tree-based formalism to express plans, or winning strategies, in finite state systems in which actions may have quantitatively delayed effects. Since the delays are non-deterministic and continuous, we need an infinite branching to display all possible delays. Nevertheless, under reasonable assumptions, we show that infinite winning strategies which may arise in this context can be captured by finite plans.The above planning problem is specified in logical terms within a Horn fragment of affine logic. Among other things, the advantage of linear logic approach is that we can easily capture 'preemptive/anticipative' plans (in which a new action β may be taken at some moment within the running time of an action α being carried out, in order to be prepared before completion of action α).In this paper we propose a comprehensive and adequate logical model of strong planning under temporal uncertainty which addresses infinity concerns. In particular, we establish a direct correspondence between linear logic proofs and plans, or winning strategies, for the actions with quantitative delayed effects.
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