Abstract
AbstractWe present a general approach to planning with incomplete information in Answer Set Programming (ASP). More precisely, we consider the problems of conformant and conditional planning with sensing actions and assumptions. We represent planning problems using a simple formalism where logic programs describe the transition function between states, the initial states and the goal states. For solving planning problems, we use Quantified Answer Set Programming (QASP), an extension of ASP with existential and universal quantifiers over atoms that is analogous to Quantified Boolean Formulas (QBFs). We define the language of quantified logic programs and use it to represent the solutions different variants of conformant and conditional planning. On the practical side, we present a translation-based QASP solver that converts quantified logic programs into QBFs and then executes a QBF solver, and we evaluate experimentally the approach on conformant and conditional planning benchmarks.
Highlights
We propose a general and uniform framework for planning in Answer Set Programming (ASP; Lifschitz 2002)
To match this level of complexity, we introduce a quantified extension of ASP, called Quantified Answer Set Programming (QASP), in analogy to Quantified Boolean Formulas (QBFs)
The core of this framework consists of a general yet simplified fragment of logic programs that aims at representing transition systems, similar to action languages (Gelfond and Lifschitz 1998) and temporal logic programs (Cabalar et al . 2018), We extend the basic setting of ASP with quantifiers and define quantified logic programs, in analogy to QBFs
Summary
We propose a general and uniform framework for planning in Answer Set Programming (ASP; Lifschitz 2002). Consider an initial situation where the robot is in the first room, only the first room is clean, and no room is occupied In this case, the classical planning problem is to find a plan that, applied to the initial situation, achieves the goal. There are four possible initial situations, depending on the state of cleanliness of the two rooms In this case, the conformant planning problem is to find a plan that, applied to all possible initial situations, achieves the goal. While bounded classical and conformant planning are still expressible since their corresponding decision problems are still at the first and second level of the polynomial hierarchy, bounded conditional planning is Pspace-complete (Turner 2002) To match this level of complexity, we introduce a quantified extension of ASP, called Quantified Answer Set Programming (QASP), in analogy to Quantified Boolean Formulas (QBFs). We empirically evaluate our solver on conformant and conditional planning benchmarks
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