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Eliminating Negative Occurrences of Derived Predicates from PDDL Axioms

Claudia Grundke, Gabriele Röger

TL;DR

This paper tackles the challenge of negative occurrences of derived predicates in PDDL axioms by introducing a transformation that compiles these negations away. The core method uses stage axioms to expose and control the fixed-point computation within each stratified stratum, enabling replacement of negative derived-predicate occurrences with positively defined, ordering-based predicates. The key contributions include a formal general-elimination framework, an illustrative example with path and acyclic predicates, and a rigorous space-use analysis showing the blow-up is polynomial in the input size $Q$. The approach potentially benefits planning techniques that rely on relaxed reachability or heuristic relaxation, though grounding could be a practical bottleneck; the authors also propose empirical evaluation to assess feasibility in real-world planners.

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.

Eliminating Negative Occurrences of Derived Predicates from PDDL Axioms

TL;DR

This paper tackles the challenge of negative occurrences of derived predicates in PDDL axioms by introducing a transformation that compiles these negations away. The core method uses stage axioms to expose and control the fixed-point computation within each stratified stratum, enabling replacement of negative derived-predicate occurrences with positively defined, ordering-based predicates. The key contributions include a formal general-elimination framework, an illustrative example with path and acyclic predicates, and a rigorous space-use analysis showing the blow-up is polynomial in the input size . The approach potentially benefits planning techniques that rely on relaxed reachability or heuristic relaxation, though grounding could be a practical bottleneck; the authors also propose empirical evaluation to assess feasibility in real-world planners.

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.
Paper Structure (8 sections, 2 theorems, 11 equations, 3 algorithms)

This paper contains 8 sections, 2 theorems, 11 equations, 3 algorithms.

Table of Contents

  1. Introduction
  2. Background
  3. Elimination of Negative Occurrences
  4. General Elimination
  5. Example
  6. Blow-up
  7. Conclusion and Future Work
  8. Proof of Theorem \ref{['thm:stagelemma']} (Continuation)

Key Result

theorem thmcountertheorem

The relations $\prec^{i,j}$, $\preceq^{i,j}$, $\nprec^{i,j}$, $\npreceq^{i,j}$ and $\triangleleft^{i,j}$ can be defined by a stratified axiom program with a single stratum.

Theorems & Definitions (5)

  • definition thmcounterdefinition: Stratified Axiom Program
  • theorem thmcountertheorem
  • proof : Proof sketch
  • theorem thmcountertheorem
  • proof