G. Groe, S. Holldobler, and J. Schneeberger. Linear deductive planning. Journal of Logic and Computation, 6(2):233-262, 1996.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... the execution of p in s leads to the ful llment of g should be a logical consequence of an appropriate axiomatization of situations, actions and causality (see [12, 13] This problem was extensively studied for simple plans consisting of sequences or partial orderings of primitive actions (e.g. [1, 14, 4]) However less attention was given to complex plans including conditional and recursive actions as well as non deterministic choice operators (see Section 7) This article is organized as follows. First, we demonstrate the need for complex plans by a simple example, the omelette baking problem, ....

....Recently, White translated Golog into an extended linear logic [18] While the transformation seems to be quite straightforward, the variant of linear logic used by White is non standard. On the other hand, there is a close relation between the uent calculus and linear logic as formally shown in [4]. Since the uent calculus admits a standard and well understood semantics it seems to be preferable to the corresponding fragments of linear logic. 8 Open Problems and Future Research We intend to use the planning language presented in this article to program autonomous robots. In order to do ....

G. Groe, S. Holldobler, and J. Schneeberger. Linear deductive planning. Journal of Logic and Computation, 6(2):233-262, 1996.

....the equational logic approach is standard first order logic with equality, and the approach based on linear logic is a Gentzen like proof system without weakening and contraction. One of the tempting features of these approaches is that they do not require to state frame axioms explicitly. In [GHS92] it was shown that the approaches are essentially equivalent. They are all built on the key idea that facts describing situations are resources which can be consumed and produced. More precisely, a situation is a multiset of facts. The facts are consumed when the conditions of actions are to be ....

....a positive literal occurring in C j . Since only the clause f:st(P )g contains no positive literals it is the bottom element with respect to OE. The clauses representing the elements of the set of goal situations contain no negative literals and therefore are top elements with respect to OE. In [GHS92] it is proven that this partial ordering OE can be extended to a total ordering OE C for the clauses contained in linear connection proofs. Thus, the clauses of the matrices representing subproofs of a globally linear connection proof are ordered totally by OE C . 9 :st(P ) I 1 1 st(P 0 ) ....

G. Groe, S. Holldobler, and J. Schneeberger. On linear deductive planning. Technical Report AIDA--92--08, FG Intellektik, FB Informatik, TH Darmstadt, 1992.

....method , is in general suitable for conjunctive planning problems, where situations as well as conditions and effects of actions are conjunctions of facts. Moreover, it turned out to be equivalent to a subset of Linear Logic [11] namely, the multiplicative fragment [23] a result established in [30, 13]. The latter observation initiated the analysis whether and how the expressiveness of the linear connection method can be enhanced to disjunctive planning problems, where uncertainty in form of non deterministic actions is handled. These are actions which are known to have several outcomes, all of ....

Große, G., Holldobler, S., Josef Schneeberger, J.: Linear deductive planning. Journal of Logic and Computation, 1996.

....on which quarter we spend. Recently three new deductive approaches to planning were proposed which formalize this idea of resources. They are based on the linear connection method [2] an equational Horn logic [10] and on the multiplicative fragment of the linear logic[12] 2 It turned out [6, 18] that for conjunctive planning problems 1 e.g. picking up a will not effect the fact that b is on the table 2 In this context the concept of linearity refers to the property of these logical calculi to use linear (i.e. non these three approaches are essential equivalent. In the following ....

G. Große, S. Holldobler, and J. Schneeberger. Linear deductive planning. Technical Report AIDA-92-08, FG Intellektik, FB Informatik, TH Darmstadt, August 1992.

....take the facts as resources . Resources do not hold forever they are consumed and produced by actions. Consequently, resources which are not affected by an action remain as they are and need not be updated. All three approaches turned out to be equivalent for a certain class of planning problems [19]. In particular, the approach developed in [26] is based on logic programming with an associated equational theory. Since its first formalization, this method has been extended into various directions, e.g. to handle objects [20] specificity [28] concurrent [3] as well as non deterministic ....

G. Große, S. Holldobler, and J. Schneeberger. Linear Deductive Planning. Journal of Logic and Computation, 1995. (To appear).

....actions, etc. Thielscher, 1994; Bornscheuer and Thielscher, 1994 ] Moreover, this method is provably equivalent to a modification of the Connection Method designed for planning problems [ Bibel, 1986 ] and to an approach to planning based on Linear Logic [ Masseron et al. 1990 ] see [ Gro e et al. 1995 ] The rest of this paper is organized as follows. In Section 2, we introduce the formal notion of a causal relationship. Based on this concept, we define postprocessing steps used to compute ramifications according to underlying domain constraints. In Section 3, we present an algorithm to ....

.... the unit clause ramify(S ffi f ; E ffi e; S ffi f; E ffi e ffi f) holds ( C ; S ffi f) 10) In words, if the situation at hand contains the fluent literal f and entails C , and if in addition e has occurred the necessity of this sophistication, as regards our program (7) has been shown in [Gro e et al. 1995]. We neglect this difference here which is justified by results presented in [Thielscher, 1994] 5 Regarding the fifth clause in (8) note that a subgoal :holds ( F ; S ) has an SLDENF refutation iff the affirmative query holds ( F ; S ) finitely fails, i.e. is not refutable. as effect ....

G. Große, S. Holldobler, and J. Schneeberger. Linear Deductive Planning. J. of Logic and Computation, 1995.

.... sequel we will present the equational logic approach based on [12] as it has turned out that this approach admits a standard semantics and is equivalent to the linear connection method developed in [2] and the linear logic approach developed in [15] both of which do not have a standard semantics [8]. 3.1 Representing Fluents and Situations As a first step towards an equational logic approach to planning we have to choose an appropriate representation for fluents and situations. As already mentioned we like to represents fluents by resources and, consequently, situations are represented by ....

G. Große, S. Holldobler, and J. Schneeberger. Linear deductive planning. Journal of Logic and Computation, 1996. (to appear).

....are axiomatized by rewrite rules, the difficulties associated with the frame problem disappear [63] In addition, the conservative mappings of Horn logic with equality and of linear logic studied in Sections 4.2 and 4. 3, respectively, directly show how other logics of change recently proposed [48, 38, 39, 65, 66] can be subsumed as special cases. Added benefits include the straightforward support for concurrent change and the logical support for object oriented representation. The paper begins with a summary of the theory of general logics [70] that provides the conceptual basis for our discussion of ....

....saying what changes an action makes, without having to explicitly list all the things it doesn t change as well [ That is the frame problem. Recently, some new logics of action and change have been proposed, among which we can point out the approach of Holldobler and Schneeberger [48, 38, 39], based on Horn logic with equations, and the approach of Masseron, Tollu, and Vauzeilles [65, 66] based on linear logic. The main interest of these formalisms is that they need not explicitly state frame axioms, because they treat facts as resources which are produced and consumed. Having proved ....

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G. Große, S. Holldobler, and J. Schneeberger, Linear deductive planning, Journal of Logic and Computation 6(2), 1996, pages 233--262.

....approaches where atomic facts about situations are regarded as resources that can be produced and consumed in the course of time. This method has recently been shown to be equivalent to two other resource oriented formalisms, presented in [2, 23] for a certain class of planning problems [9]. Moreover, since its first formalization, the basic ELP framework has been extended into various directions, e.g. to handle objects [11] and specificity [13] non deterministic actions [3, 22] and ramifications [23] Based on the ELP approach, a logic program associated with the equational ....

G. Große, S. Holldobler, and J. Schneeberger. Linear Deductive Planning. Journal of Logic and Computation, 1995. (To appear).

....to the Frame Problem [12] which appeal to non classical logics, namely, linearized versions of, respectively, the connection method [1, 2] and Gentzen s sequent calculus [11] The affinity of the Fluent Calculus and these two formalisms has been emphasized by several formal comparison results. In [5], for example, the three approaches have been proved to deliver equivalent solutions to a resource sensitive variant of Strips planning [4] Yet the Fluent Calculus possesses a feature by which it stands out against the two other frameworks: It stays entirely within classical logic. In this ....

G. Große, S. Holldobler, and J. Schneeberger. Linear Deductive Planning. J. of Logic and Computation, 6(2):233--262, 1996.

....for regular formulas. Any regular OE 2 F ffi is provable iff there is an instance and ground instance such that the resulting formula is also provable. ut Let us demonstrate the applicability of the DLE for planning tasks by a simple example. We borrow the getting a drink example from [13]. We have five 50 Pfennig coins and want to get two cokes for one Mark from an automaton that only accepts one Mark coins. Assuming that there is an action to exchange two 50 Pfennig coins in a one Mark coin, the resulting planning problem (which could be rewritten as a regular formula) reads as: ....

G. Große, S. H olldobler, J. Schneeberger. Linear deductive planning. Journal of Logic and Computation, 6: 233-262, 1996.

....need to state frame axioms explicitly. There are three deductive approaches to planning proposed to formalize this idea of resources. One based on the linear connection method [2] one on equational Horn logic [16] and one on the multiplicative fragment of the linear logic [23] 4 It turned out [13, 37] that for conjunctive planning problems these three approaches are essentially equivalent. In the following we will examine the resource oriented planning approach based on equational logic [15] more closely. Originally, this approach was restricted to conjunctive planning problems, i.e. problems ....

G. Große, S. Holldobler, and J. Schneeberger. Linear deductive planning. Technical Report AIDA-92-08, FG Intellektik, FB Informatik, TH Darmstadt, August 1992.

....the action is executed. Unfortunately, neither Bibel s nor Girard s approach admits a standard semantics. However, the equational logic approach to deductive planning of Holldobler and Schneeberger does [13] and, moreover, is provably equivalent to Bibel s approach and fragments of linear logic [9]. Although in the meantime the original approach has been extended in various ways [14, 4] it always dealt with total order planning. In this paper we present a new approach which combines resource based reasoning and partial order least commitment planning in a constraint equational logic ....

....are consumed as conditions whenever an action is applied and produced as effects whenever the action is executed. In [13] an equational logic approach to total order planning is presented which is based on resources and, in contrast to [1] and [7] preserves a standard model. Moreover, as shown in [9] the equational logic is equivalent to [1] as well as to the multiplicative fragment of linear logic [7] and implements the law of inertia without additional axioms elegantly and efficiently [12, 31] In a resource based approach the world W , the goal G as well as the conditions C and effects ....

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G. Große, S. Holldobler, and J. Schneeberger. Linear deductive planning. Journal of Logic and Computation, 6(2):233--262, 1996.

....are quite different at first glance. 2] requires that in a connection proof each literal is connected at most once, 14] is standard first order logic with equality, and [18] is a Gentzen like proof system without weakening and contraction rule. Surprisingly, the three approaches are equivalent [10, 9] for conjunctive planning problems. They are all built on the key idea that facts describing situations are resources which can be consumed and produced. More precisely, a situation is a multiset of facts. The facts are consumed when the conditions of an action are to be satisfied and are produced ....

....program determined by A iff an equivalent plan p 0 is computed by a globally linear connection proof of hI; A; Gi . Proof (sketch: To prove the theorem we first show that a globally linear connection proof can be transformed into an SLDE refutation using essentially the techniques presented in [9]. The only difference being that after application of a rule representing an action with several alternative effects, 10) has to be applied to split the alternatives. Conversely, the proof is obtained by induction on the length of the SLDE refutation. 6 Disjunction in Linear Logic In the last ....

G. Große, S. Holldobler, and J. Schneeberger. Linear deductive planning. Technical Report AIDA-92-08, FG Intellektik, FB Informatik, TH Darmstadt, August 1992.

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