The classical AI planning problems in the mirror of Horn linear logic: semantics, expressibility, complexity

Abstract

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

Collaborative Planning with Confidentiality

“…We also demonstrate the logical foundation of our approach in a variant of linear logic [13,16,17,26]. While this is not necessary in determining the complexity of the planning problem, it relates our approach to a number of similar formalisms which have had success in the past.…”

“…We define a state of the environment to be a set of facts. To illustrate the definitions we use an example common from the literature: the blocks world [26,34,40].…”

“…While this is not necessary in determining the complexity of the planning problem, it relates our approach to a number of similar formalisms which have had success in the past. On the one hand, there is a wide literature on viewing the classical planning problem in logical settings [6,10,26,34,36,40]. On the other hand, multiset rewriting formalisms have proved useful in the analysis of security protocols [7,12] as well as in the field of computation and concurrency [27][28][29][30][31]38].…”

LinGraph: a graph-based automated planner for concurrent task planning based on linear logic

“…Intuitionistic linear logic was previously shown to be a suitable representational language for planning problems [30,31,33,38]. Our work relies on these results, but proposes a new, graph-based algorithm for constructing proofs in a suitable fragment of intuitionistic linear logic that reduces the search space by eliminating irrelevantly permuted uses of identical resources within the planning problem.…”

“…The use of linear logic for planning problems involves using simultaneous conjunction, linear implication and disjunction to respectively represent state, actions and nondeterministic effects [8,42], with Horn fragments to address undecidability problems [33]. Certain inherent strengths of linear logic, such as its native support for concurrency have also been explored in the context of planning problems [31].…”