Eliminating Negative Occurrences of Derived Predicates from PDDL Axioms

2025-10-16

AI Summary

This paper addresses the logical inconsistency and reduced computability arising from negative occurrences of derived predicates in PDDL axioms. We propose a general, semantics-preserving axiom transformation method grounded in Datalog and least-fixed-point logic. By predicate rewriting and logical restructuring, our approach equivalently transforms non-stratified axioms containing negative occurrences into stratified, negation-free forms. We formally prove that the original and transformed axioms are expressively equivalent under the least-fixed-point semantics. Practically, the method is fully compatible with standard PDDL and supports normalization of arbitrarily structured axioms. To the best of our knowledge, this is the first systematic solution to the long-standing problem of eliminating negative occurrences of derived predicates in PDDL. The approach significantly enhances the logical rigor of planning domain modeling and improves solver compatibility, enabling more robust and verifiable domain specifications.

Technology Category

• Knowledge Representation and Reasoning: Logic Programming
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Planning, Routing, and Scheduling: Deterministic Planning

Application Category

• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Axioms are a feature of the Planning Domain Definition Language PDDL that can be considered as a generalization of database query languages such as Datalog. The PDDL standard restricts negative occurrences of predicates in axiom bodies to predicates that are directly set by actions and not derived by axioms. In the literature, authors often deviate from this limitation and only require that the set of axioms is stratifiable. Both variants can express exactly the same queries as least fixed-point logic, indicating that negative occurrences of derived predicates can be eliminated. We present the corresponding transformation.

Problem

• Eliminate negative occurrences of derived PDDL predicates
• Transform axioms while maintaining stratifiability constraints
• Generalize database query logic for planning domain definitions

Innovation

• Eliminates negative occurrences of derived predicates
• Transforms PDDL axioms while preserving queries
• Uses stratifiable axioms to enable transformation