Planning in Answer Set Programming Using Ordered Task Decomposition

Abstract

In this paper we investigate a formalism for solving planning problems based on ordered task decomposition using Answer Set Programming (ASP). Our planning methodology is an adaptation of Hierarchical Task Network (HTN) planning, an approach that has led to some very efficient planners. The ASP paradigm evolved out of the stable semantics for logic programs in recent years and is strongly related to nonmonotonic logics. It also led to various very efficient implementations (Smodels, DLV ). While all previous approaches for using ASP for planning rely on action-based planning, we consider for the first time a formulation of HTN planning as described in the SHOP planning system and define a systematic translation method from SHOP 's representation of the planning problem into logic programs with negation. We show that our translation is sound and complete: answer sets of the logic program obtained by our translation correspond exactly to the solutions of the planning problem. Our approach does not rely on a particular system for computing answer sets and serves several purposes. (1) It constitutes a means to evaluate ASP systems by using well-established benchmarks from the planning community. (2) It makes the more expressive HTN planning available in ASP. (3) When our approach is implemented on ASP solvers, its time requirement appears to grow no faster than roughly proportional to that of a dedicated HTN planning system (SHOP ). (4) It outperforms the transformation of an STRIPS-style planning problem into ASP proposed in [Son et al., 2001]. The particular relevance of that transformation method to our work is that, in their work, [Son et al., 2001] proposed to use a form of control knowledge to speed up the classical planning process. In this paper, we show that HTN control knowledge provides more time-efficient transformations compared to the control strategies presented in [Son et al., 2001].

The DLV system for knowledge representation and reasoning

“…Our experimental results are complemented by other efforts on benchmarking ASP systems recently reported in the literature [Dix et al 2002;Koch and Leone 1999;Lin and Zhao 2002;Nicolas et al 2002;Simons et al 2002;Eiter et al 1998a;Janhunen et al 2003]. In general, these confirm our claim that DLV handles deductive database applications and P 2 -complete problems more efficiently than the other systems, while the situation is less clear on NP-complete problems where the results depend, to a larger extent, on the encodings adopted.…”

Model checking multi-agent systems with logic based Petri nets

“…The main ideas introduced in this paper are (1) to introduce a new kind of Petri net, the simple logic Petri net, (2) to use these nets for specifying (AgentSpeak-) agents, and (3) to transform these nets into logic programs and use ASP engines [1,5,7,8] for solving the model-checking task-the detection of deadlocks in SLPN's.…”

“…-We introduce (Section 3 the class SLPN of Valid Simple Logic Petri nets [Definition 6] and their semantics [Definitions [6][7][8]). -We show their relation to Answer Set Programming, by providing a transformation from SLPN into logic programs with negation and showing that this transformation is sound and complete (Theorem 1).…”

An introduction to fuzzy answer set programming

“…[12,16,20,23]. The idea behind the answer set semantics, a generalization of the stable model semantics [14], is both intuitive and elegant.…”