A Logical Semantics for PDDL+

Abstract

PDDL+ is an extension of PDDL2.1 which incorporates fully-featured autonomous processes and allows for better modelling of mixed discrete-continuous domains. Unlike PDDL2.1, PDDL+ lacks a logical semantics, relying instead on state-transitional semantics enriched with hybrid automata semantics for the continuous states. This complex semantics makes analysis and comparisons to other action formalisms difficult. In this paper, we propose a natural extension of Reiter’s situation calculus theories inspired by hybrid automata. The kinship between PDDL+ and hybrid automata allows us to develop a direct mapping between PDDL+ and situation calculus, thereby supplying PDDL+ with a logical semantics and the situation calculus with a modern way of representing autonomous processes. We outline the potential benefits of the mapping by suggesting a new approach to effective planning in PDDL+.

Heuristic Planning for Continuous Systems in Hybrid Temporal Situation Calculus

“…Batusov and Soutchanski provide a translation [3] from PDDL+ to Hybrid Temporal Situation Calculus (HTSC ) and show that HTSC is more expressive than PDDL+ due to its ability to capture complex temporal effects and since it is based on First-Order-Logic. We provide a translation of an excerpt of the car domain from PDDL+.…”

“…Depending on what the context is, the change affecting temporalF luentN ame is different. Batusov and Soutchanski [3] propose constructing for every possible context, the final equation that describes how temporalF luentN ame changes, which is quite computationally expensive since there are exponentially many contexts. Instead of constructing a flow equation for every possible context, we compute the total effect as the sum of all flows that have an effect on F .…”

“…Domains written in PDDL+ are translated automatically to Hybrid Temporal Situation Calculus with our PDDLPlusToHTSC translator using the formulation provided by Batusov et. al [3]. This translation can then be converted to Prolog code with minor manual modifications.…”

A Practical Approach to Discretised PDDL+ Problems by Translation to Numeric Planning

“…Previous usages of this kind of temporal model can be traced back to TLPlan (Bacchus &Ady, 2001) andOptop (McDermott, 2003). Batusov and Soutchanski (2019) recently propose an alternative logical semantic of pddl+ which extends Situation Calculus (SC), i.e., a logical formalism to represent dynamic domains, giving it a continuous component inspired by the HA interpretation. The target formalism of this mapping is an extension of a particular case of SC, namely Basic Action Theory (Reiter, 2001), which is a convenient representation for addressing reasoning problems.…”