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1, page 8, above) over the set of values. In the Blocksworld domain, for example, each block is in each world state in exactly one place (on the table or on one of the other blocks) and has exactly one “thing” on top of it (either nothing, or one of the other blocks). b)} are exactly-one invariants. b), making the invariant explicit. We make use of the state variable representation in the construction of pattern database heuristics, in chapter 4. Models for Planning with Time Planning problems including various temporal aspects have been addressed by several AI planning systems: actions with explicit duration, goals with deadlines and external events (events not under the control of the planner, but occurring at known times) were introduced by Vere (1983) and by Allen & Koomen (1983); the IxTeT planning system (Laborie & Ghallab 1995) combined durative actions with a model of resources, allowing finer control of concurrency and more; the planning model of the Zeno system (Penberthy & Weld 1994) described the world by continuous variables and actions causing continuous change to those variables; to name just a few.
Hierarchical Task Decomposition Models Hierarchical task decomposition models (or hierarchical task network (HTN) models, as they are usually called) were introduced early in the development of planning systems (the NOAH planning system, by Sacerdoti (1975) and the NONLIN system, by Tate (1977), are usually named as the original sources). The first (and until quite recently, only) planning systems to be used in applications (the SIPE system (Wilkins 1990) and the O-Plan system (Tate, Drabble, & Kirby 1994)) were based on HTN models, so clearly such models have some merit (Wilkins & desJardins 29 (2000) argue this point), but, like logical background theories, HTN models were not considered in the later more formal works on planning (presumably due to the somewhat “procedural” flavour of such models).
This combinatorial blow-up is due to the fact that goals (and action preconditions) are conjunctions of atomic facts that need to be achieved simultaneously. g. Gaschnig, 1979; Pearl, 1984). This chapter describes the hm (m = 1, 2, . ) family of admissible heuristics, based on a particular relaxation which is to assume that the cost of any set (conjunction) of more than m goals equals the cost of the most costly subset of size m (it is popular to describe this relaxation as “ignoring delete effects”, but this is accurate only for the special case m = 1).