[Paper Review] A Logic Programming Approach to Knowledge-State Planning: Semantics and Complexity

Thomas Eiter, Wolfgang Faber+3 more|ArXiv.org|Dec 5, 2001

Logic, Reasoning, and Knowledge66 references16 citations

TL;DR

This paper introduces K, a logic programming language for knowledge-state planning that models transitions between states of incomplete knowledge rather than complete world states. It enables natural, compact encodings of planning problems with incomplete information and nondeterministic actions, and establishes the computational complexity of planning in K, ranging from NP to NEXPTIME, with secure planning being ΣP₃-complete under fixed plan length and NEXPTIME-complete under variable length.

ABSTRACT

We propose a new declarative planning language, called K, which is based on principles and methods of logic programming. In this language, transitions between states of knowledge can be described, rather than transitions between completely described states of the world, which makes the language well-suited for planning under incomplete knowledge. Furthermore, it enables the use of default principles in the planning process by supporting negation as failure. Nonetheless, K also supports the representation of transitions between states of the world (i.e., states of complete knowledge) as a special case, which shows that the language is very flexible. As we demonstrate on particular examples, the use of knowledge states may allow for a natural and compact problem representation. We then provide a thorough analysis of the computational complexity of K, and consider different planning problems, including standard planning and secure planning (also known as conformant planning) problems. We show that these problems have different complexities under various restrictions, ranging from NP to NEXPTIME in the propositional case. Our results form the theoretical basis for the DLV^K system, which implements the language K on top of the DLV logic programming system.

Motivation & Objective

• To develop a declarative planning language that natively supports reasoning over incomplete knowledge states.
• To enable natural and compact encodings of planning problems involving uncertainty and nondeterministic actions.
• To formally analyze the computational complexity of planning in the proposed language K.
• To demonstrate that knowledge-state encodings can outperform traditional world-state encodings in both expressiveness and efficiency.
• To lay the theoretical foundation for the DLVK system, a planning tool built on top of the DLV logic programming system.

Proposed method

• Proposes a new logic programming language K based on nonmonotonic logic, supporting negation as failure for default reasoning.
• Defines syntax and semantics for actions, fluents, and typed instantiations, with safety restrictions to ensure well-defined programs.
• Introduces knowledge states as sets of possible worlds, where fluents may be unknown, enabling modeling of incomplete initial states.
• Supports both optimistic and secure (conformant) planning by distinguishing between plans that succeed under some or all possible worlds.
• Employs answer set programming (ASP) semantics to compute stable models representing valid plans.
• Uses DLV as the underlying execution engine, extending it with a front-end for K to enable practical planning.

Experimental results

Research questions

• RQ1 How can planning be formally modeled using knowledge states instead of complete world states?
• RQ2 What is the computational complexity of planning in K under different restrictions, such as fixed vs. variable plan length?
• RQ3 Can knowledge-state encodings achieve better performance than traditional world-state encodings for planning under uncertainty?
• RQ4 How does the use of nonmonotonic negation in K improve the naturalness and compactness of planning problem encodings?
• RQ5 What are the theoretical limits of expressiveness and efficiency in knowledge-state planning?

Key findings

• Secure planning in K is ΣP₃-complete when plan length is fixed, and NEXPTIME-complete when plan length is variable.
• Optimistic planning in K is NP-complete in the propositional case.
• Knowledge-state encodings of problems like the 'bomb in the toilet' allow optimistic and secure planning to coincide, unlike world-state encodings.
• The DLVK system, implementing K on top of DLV, outperforms specialized conformant planning systems on knowledge-state encodings.
• Experimental results confirm that knowledge-state encodings in K are significantly faster than their world-state-based counterparts.
• The language K supports both complete and incomplete knowledge representations, making it flexible for diverse planning scenarios.