Planning with Spatio-Temporal Search Control Knowledge

Knowledge based approaches developed for AI planning can convert an intractable planning problem to a tractable one. Current techniques often use temporal logics to express Search Control Knowledge (SCK) in logic based planning. However, traditional temporal logics are limited in expressiveness since they are unable to express spatial constraints which are as important as temporal ones in many planning domains. To this end, we propose a two-dimensional (spatial and temporal) logic namely PPTL<inline-formula><tex-math notation="LaTeX">$^{\mathrm{SL}}$ </tex-math><alternatives><inline-graphic xlink:href="lu-ieq1-2810144.gif"/></alternatives></inline-formula> by temporalizing separation logic with PPTL (Propositional Projection Temporal Logic) which is well-suited to specify SCK involving both spatial and temporal constraints in planning. We prove that PPTL<inline-formula> <tex-math notation="LaTeX">$^{\mathrm{SL}}$</tex-math><alternatives><inline-graphic xlink:href="lu-ieq2-2810144.gif"/> </alternatives></inline-formula> is decidable essentially via an equisatisfiable translation from PPTL<inline-formula> <tex-math notation="LaTeX">$^{\mathrm{SL}}$</tex-math><alternatives><inline-graphic xlink:href="lu-ieq3-2810144.gif"/> </alternatives></inline-formula> to its restricted form. Moreover, we implement a tool, <italic>S-TSolver</italic>, which effectively computes plans under the guidance of the spatio-temporal SCK expressed by PPTL<inline-formula> <tex-math notation="LaTeX">$^{\mathrm{SL}}$</tex-math><alternatives><inline-graphic xlink:href="lu-ieq4-2810144.gif"/> </alternatives></inline-formula> formulas. The effectiveness of the tool is evaluated on selected benchmark domains from the International Planning Competition.

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