Rintanen, J.: Constructing Conditional Plans by a Theorem-Prover. Journal of Artificial Intelligence 10 (1999) 323--352  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... and POMDPs can be found in Boutilier, Dean and Hanks [7] Instead we will focus on why this Disjunction Probability Non Observable CGP [31] CMBP [9, 1] C PLAN [13, 8] Fragplan [16] Buridan [17] UDTPOP [23] PartiallyObservable SENSp [12] Cassandra [25] PUCCINI [14] SGP [34] QBF Plan [27] GPT [6] MBP [2] C Buridan [10] DTPOP [23] C MAXPLAN [19] ZANDER [19] Mahinur [22] POMDP [7] Fully Observable WARPLAN C [33] CNLP [24] JIC [11] Plinth [15] Weaver [4] PGP [3] MDP [7] Table 1: A classification of planners that deal with uncertainty. Planers in the top row are often ....

Rintanen, J. 1999. Constructing Conditional Plans by a Theorem Prover, Journal of Artificial Intelligence Research 10,

.... are often referred toascontingency planners Disjunction Probability CGP [34] Non CMBP [11, 1] Buridan[19] Observable C PLAN [10, 15] UDTPOP [26] Fragplan [18] SENSp[14] C Buridan [12] Cassandra[28] DTPOP [26] Partially PUCCINI [16] C MAXPLAN [21] Observable SGP [37] ZANDER [21] QBF Plan [30] Mahinur [25] GPT [7] POMDP [8] MBP [2] JIC [13] Fully WARPLAN C [36] Plinth [17] Observable CNLP [27] Weave r [ 5 ] PGP [4] MDP [8] We do not discuss this work in detail here. A survey of some of this work can be found in Blythe [6] A more detailed survey of work on MDPsandPOMDPs can be ....

J. Rintanen. Constructing conditional plans by a theorem prover. Journal of AI Research, 10:323--352, 1999.

....reducible to each other. A natural reduction from QBF to K is described in [12] In the last few years extensive effort was carried out into the development of highly optimized QBF solvers [17, 5] One motivation for this effort is the hope of using QBF solvers as generic search engines [25], much in the same way that SAT solvers are being used as generic search engines. This suggests that another approach to K satisfiability is to find a natural reduction of K to QBF, and then apply a highly optimized QBF solver. We describe now such a reduction. A similar approach is suggested in ....

J. Rintanen. Constructing conditional plans by a theorem-prover. J. of A. I. Res., 10:323--352, 1999.

....planning) like . On the other hand, the systems CNLP and CASSANDRA deal with conditional planning (where the sequence of actions to be executed depends on dynamic conditions) More recent works propose the use of automated reasoning techniques for planning under incomplete knowledge. In [41] a technique for encoding conditional planning problems in terms of 2 QBF formulas is proposed. The work in [11] proposes a technique based on regression for solving secure planning problems in the framework of the Situation Calculus, and presents a Prolog implementation of such a technique. In ....

Rintanen, J., 1999. Constructing Conditional Plans by a Theorem-Prover. Journal of Artificial Intelligence Research 10, 323--352.

.... classical propositional logic (see e.g. 20] for such an application in Artificial Intelligence) Besides the implementation of different nonmonotonic reasoning tasks as realized by the system QUIP, successful applications based on reductions to QBFs have also been applied to conditional planning [31] . There are several reasons why we are interested in a reformulation of the approach of [7] using QBFs. First, it provides a straightforward implementation of the general framework by appeal to extant QBF solvers. Second, in the original approach several steps were expressed at the metalevel. In ....

J. Rintanen. Constructing Conditional Plans by a Theorem Prover. Journal of Artificial Intelligence Research, 10:323--352, 1999.

....reason about effects of actions, including sensing actions; and FLUX [26] implemented in constraint logic programming, is capable of generating and verifying conditional plans. A conditional planner based on a QBF theorem prover, that does not allow sensing actions, was also recently developed [21]. Conformant planning [3, 6, 2, 23] is another approach to deal with incomplete information. In conformant planning, a solution is a sequence of actions that achieves the goal from every possible initial state. Recent experimental result shows [3] that conformant planning based on model checking ....

J. Rintanen. Constructing conditional plans by a theorem prover. Journal of Artificial Intelligence Research, 10:323--352, 2000.

.... an explanation can be computed using a nested backtracking procedure (modeling nested subroutine calls) or using flat backtracking calling a subroutine for 2 tasks (e.g. calls to DLV) A further possible perspective are translations to QBF solvers, which proved valuable in other applications [33]. We can compute an partial explanation similarly. Computing a best one amounts to an optimization problem, which can be solved by binary search over the range [0,1] of , and thus in polynomial time with a 3 oracle. A substantially faster algorithm seems unlikely to exist. 4 DERIVATION OF ....

J. Rintanen. Constructing conditional plans by a theoremprover. J. Artif. Intell. Res., 10:323--352, 1999.

.... classical propositional logic (see e.g. 22] for such an application in Artificial Intelligence) Besides the implementation of different nonmonotonic reasoning tasks as realised by the system QUIP, successful applications based on reductions to QBFs have also been applied to conditional planning [36]. In order to conduct some experimental evaluation of our translations, we tested their implementation in the system QUIP based on a class of benchmark problems using different underlying QBF solvers. More specifically, we used the solvers ssolve [15] QuBe [18] and semprop [25] on randomly ....

....natural generalisation of a similar method successfully applied to problems in NP. In general, the use of QBFs for knowledge representation purposes has been advocated in the literature [5, 37] and, besides the current framework, reductions of other reasoning tasks to QBFs have been discussed in [36, 11]. We reported some experiments using the implementation of our encodings for autoepistemic logic. Due to the absence of available solvers for modal nonmonotonic logics, we focused here on a comparison of different QBF solvers, constituting core engines for the system QUIP. Finally, a particular ....

J. Rintanen. Constructing Conditional Plans by a Theorem Prover. Journal of Artificial Intelligence Research, 10:323--352, 1999.

....the current state is fully observable or only partially observable during plan execution. The paper considers the complexity of each of these classes of planning problems. This is not a new line of research; among the papers with results on planning complexity published in the last decade are [3, 1, 6, 10, 11, 4, 8, 14, 2, 5]. The work presented here is unusual in employing a single framework to study the complexity of such a wide range of polynomial length planning problems. In fact, one contribution of the paper is a uni ed representation in secondorder propositional logic of the decision problems associated with ....

....can be inferred that block B 1 cannot be moved to the location of block B 2 (unless block B 2 is moved somewhere else) It also follows that blocks B 1 and B 2 cannot be moved concurrently to the same location. A number of results reported here are similar to (although distinct from) results in [10, 14, 2, 5]. In each case this will be noted when the result is encountered in the text. A more comprehensive survey of planning complexity results is beyond the scope of this paper. Due to space restrictions, proofs are omitted. 2 Preliminaries 2.1 Action Representation Framework Begin with a set A of ....

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Jussi Rintanen. Constructing conditional plans by a theorem prover. Journal of Arti cial Intelligence Research, 10:323-352, 1999.

.... satis ability (SAT) solvers for quanti ed Boolean logic (QBL) Applications include program veri cation using bounded model checking [3] and bounded model construction [1] hardware applications including testing and equivalence checking [17] and arti cial intelligence tasks like planning [14]. Solvers for (unquanti ed) Boolean logic have reached a state of maturity; there are many success stories where SAT solvers such as [11, 19, 22] have been successfully applied to industrial scale problems. However, the picture for QBL is rather di erent. Despite the growing body of research on ....

....one of the quanti ers, quanti ed variables have small scopes on average. In contrast, poorly structured formulae with large average weight have many quanti ers with large scopes. The two domains we consider are system veri cation using bounded model construction [1] and conditional planning [14]. For the rst domain, we show that problems are always well structured. In the second domain, the degree of structure varies considerably. The corresponding e ectiveness of our decision procedure also varies in relationship to this structure. 3.1 Bounded Model Construction Bounded model ....

[Article contains additional citation context not shown here]

Jussi Rintanen. Constructing conditional plans by a theorem-prover. Journal of Arti cial Intelligence Research, 10, 1999.

.... satisfiability (SAT) solvers for quantified Boolean logic (QBL) Applications include program verification using bounded model checking [3] and bounded model construction [1] hardware applications including testing and equivalence checking [17] and artificial intelligence tasks like planning [14]. Solvers for (unquantified) Boolean logic have reached a state of maturity; there are many success stories where SAT solvers such as [11, 19, 22] have been successfully applied to industrial scale problems. However, the picture for QBL is rather di#erent. Despite the growing body of research on ....

....one of the quantifiers, quantified variables have small scopes on average. In contrast, poorly structured formulae with large average weight have many quantifiers with large scopes. The two domains we consider are system verification using bounded model construction [1] and conditional planning [14]. For the first domain, we show that problems are always well structured. In the second domain, the degree of structure varies considerably. The corresponding e#ectiveness of our decision procedure also varies in relationship to this structure. 3.1 Bounded Model Construction Bounded model ....

[Article contains additional citation context not shown here]

Jussi Rintanen. Constructing conditional plans by a theorem-prover. Journal of Artificial Intelligence Research, 10, 1999.

....fully observable or only partially observable during plan execution. The paper considers the complexity of each of these classes of planning problems. This is certainly not a new line of research. Many papers with results on planning complexity have been published in the last decade, among them [3, 1, 6, 10, 11, 4, 8, 14, 2, 5]. In general terms, the work presented here is unusual in employing a single framework to study the complexity of such a wide range of polynomial length planning problems. In fact, one of the contributions of the paper is the development of a uni ed representation in second order propositional ....

....can be inferred that block B 1 cannot be moved to the location of block B 2 (unless block B 2 is moved somewhere else) It also follows that blocks B 1 and B 2 cannot be moved concurrently to the same location. A number of results reported here are similar to (although distinct from) results in [10, 14, 2, 5]. In each case this will be noted when the result is encountered in the text. A more comprehensive survey of planning complexity results is beyond the scope of this paper. Due to space restrictions, proofs are omitted. 2 Preliminaries 2.1 Action Representation Framework For the analysis in ....

[Article contains additional citation context not shown here]

Jussi Rintanen. Constructing conditional plans by a theorem prover. Journal of Arti cial Intelligence Research, 10:323-352, 1999.

....for a journal or another conference, nor will it be submitted for such during ECP s review period. 1 Introduction Research in planning is more and more focusing on the problem of planning in nondeterministic domains and with incomplete information, see for instance [PC96; KBSD97; WAS98; CRT98; Rin99a; BG00] A crucial assumption, upon which the search mechanism and the structure of the generated plans depend, is how information is available at run time. For instance, the approaches in [KBSD97; CRT98] construct conditional plans under the assumption of full observability, i.e. the state of ....

....approach both in terms of efficiency and in the quality of the returned plans. A comparison against other conditional planners follows from the experimental evaluation in [BCRT01] where the DFS algorithm outperforms the SGP and GPT conditional planners. Another interesting system is QBFPLAN [Rin99a] that extends the SAT based approach to planning to the case of nondeterministic domains. The planning problem is reduced to a QBF satisfiability problem, that is then given in input to an efficient solver [Rin99b] QBFPLAN relies on a symbolic representation, but the approach seems to be ....

J. Rintanen. Constructing conditional plans by a theorem-prover. Journal of Artificial Intellegence Research, 10:323-- 352, 1999.

....states: plans must satisfy conditions on their whole execution paths, i.e. on the sequences of states resulting from execution. For these reasons, recent research in planning is addressing either the problem of planning for reachability goals in non deterministic domains (see for instance [16, 19, 7, 17, 3]) or the problem of planning for goals that can express temporal properties in deterministic domains (see for instance [10, 1] Very few works in planning relax both the restrictions on deterministic domains and on reachability goals, see, e.g. 12, 15] These works show that planning for ....

....the one we propose. The issue of temporally extended goals is certainly not new. However, most of the works in this direction restrict to deterministic domains, see for instance [10, 1] Most of the planners able to deal with non deterministic domains, do not deal with temporally extended goals [7, 17, 3]. In this paper we focus on the case of full observability. An extension of the work to the case of planning for extended goals under partial observability is one of the main objectives for future research. ....

J. Rintanen. Constructing conditional plans by a theorem-prover. Journal of Artificial Intellegence Research, 10:323--352, 1999.

....solutions. This process can be quite consuming, and checking the reached convergence is not obvious. Compared to mbp, gpt can not be forced to return an acyclic policy (or even checking for its existence) and is unable to distinguish between cyclic and acyclic solutions. 7.1. 3 QbfPlan QbfPlan [ Rintanen, 1999a ] is a generalization of the satplan approach [ Kautz et al. 1996 ] to the case of planning in nondeterministic domains. In QbfPlan, the planning problem is reformulated in qbf, rather than in propositional logic. The problem is then solved by an ecient qbf solver [ Rintanen, 1999b ] QbfPlan is ....

....the symbolic operations. In gure 12 we depict the behavior of the strong algorithm for increasing size of the bowls and increasing number of rotten eggs. Search times are plotted in logarithmic scale. 7.3. 2 Chain of Rooms We consider now the CHAIN(n) domain from the QbfPlan distribution [ Rintanen, 1999a ] There is a sequence of rooms connected by two doors. For each pair of rooms, only one of the doors is open, while the other is closed. The goal is to go from room 0 to room n. Table 3 lists the results for the CHAIN I (CHAIN Inertial) problems, where the status of the doors is xed (i.e. they ....

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J. Rintanen. Constructing conditional plans by a theorem-prover. Journal of Articial Intellegence Research, 10:323-352, 1999.

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Rintanen, J.: Constructing Conditional Plans by a Theorem-Prover. Journal of Artificial Intelligence 10 (1999) 323--352

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J. Rintanen. Constructing conditional plans by a theorem prover. Journal of Artificial Intelligence Research, 10:323--352, 1999.

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Jussi Rintanen, Constructing conditional plans by a theorem prover, Journal of Arti cial Intelligence Research, 10, 1999, pp. 323-352.

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J. Rintanen. Constructing conditional plans by a theorem-prover. Journal of Artificial Intelligence Research, 10:323--352, 1999.

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J. Rintanen. Constructing conditional plans by a theorem prover. Journal of Artificial Intelligence Research (JAIR), 10:323--352, 1999.

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J. Rintanen. Constructing conditional plans by a theorem-prover. JAIR, 10:323--352, 1999.

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J. Rintanen. Constructing conditional plans by a theorem-prover. Journal of Arti cial Intellingence Research, 10, 1999.

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J. Rintanen. Constructing conditional plans by a theoremprover. J. Artif. Intell. Res., 10:323--352, 1999.

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J. Rintanen. Constructing conditional plans by a theorem prover. Journal of AI Research, 10:323--352, 1999.

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Rintanen, J.: 1999a, `Constructing Conditional Plans by a Theorem Prover'. Journal of Artificial Intelligence Research 10, 323--352.

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