Ste#en Holldobler and Josef Schneeberger. A new deductive approach to planning. New GenerationComputing,8:225--244, 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....a problem as challenging as addressing further aspects. In this paper, we present the Fluent Calculus as a specification language and system for robots which meets the requirement to address all of the aspects listed above in a uniform way. The calculus roots in the logic programming formalism of [21], which in [18] has been proved equivalent to approaches to the Frame Problem that appeal to non classical logics, namely, linearized versions of the connection method [3] and Gentzen s sequent calculus [37] resp. All three frameworks have been designed especially to address not only the ....

....state axioms [52, 65] An excellent overview of today s established action formalisms is provided by the set of reference articles published in [56] Our major achievements in this paper are the following. 1. We provide the Fluent Calculus, which roots in the logic programming formalism of [21], with a new, simpler algebraic foundation. In so doing, we overcome a limitation of the existing axiomatization, which does not permit domain specific equalities [65] 2. We present the programming language Flux (the Fluent Calculus Executor ) which implements the Fluent Calculus using ....

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Ste#en Holldobler and Josef Schneeberger. A new deductive approach to planning. New Generation Computing, 8:225--244, 1990.

....is due to our lack of omniscience. The formal account of the qualification problem presented in this paper addresses both finding explanations for unexpectedly observed disqualifications and accounting for miraculous disqualifications. We moreover sketch, on the basis of the fluent calculus [ Holldobler and Schneeberger, 1990; Thielscher, Throughout the paper, by (dis )qualified we mean physically (im )possible. The refinement that actions may be unqualified as to producing a certain e#ect will be discussed at the end, in Section 5. 1997 ] an action calculus which includes a proper treatment of abnormal ....

...., start ] being qualified according to (15) 4 FLUENT CALCULUS AND THE QUALIFICATION PROBLEM Finally, we briefly sketch a suitable action calculus which is capable of handling abnormal action disqualifications. Our encoding employs the representation technique underlying the fluent calculus [ Holldobler and Schneeberger, 1990; Thielscher, 1997 ] As opposed to the situation calculus [ McCarthy and Hayes, 1969; Reiter, 1991 ] the fluent calculus employs structured state terms, each of which consists in a collection of all fluent literals that are true in the state being represented. To this end, fluent literals are ....

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S. Holldobler and J. Schneeberger. A new deductive approach to planning. New Generation Computing, 8:225--244, 1990.

.... methods for reasoning about change are based on the ideas underlying the situation calculus [20, 21] Yet in recent years new deductive approaches have been developed which enable us to model situations, actions, and causality without the need to employ extra axioms due to the frame problem [1, 19, 14]. Instead of representing the atomic facts used to describe situations as fluents, these approaches take the facts as resources. Resources do not hold forever they are consumed and produced by actions. Consequently, resources which are not a#ected by an action remain as they are and need not be ....

....describe situations as fluents, these approaches take the facts as resources. Resources do not hold forever they are consumed and produced by actions. Consequently, resources which are not a#ected by an action remain as they are and need not be updated. In particular, the approach developed in [14] is based on logic programming with an associated equational theory. Although previous results illustrate the expressiveness of the equational logic programming approach (ELP, for short) This author was supported by HCM Project: Compulog Group Cooperation Group in Computational Logic under ....

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S. Holldobler and J. Schneeberger. A New Deductive Approach to Planning. New Generation Computing, 8:225--244, 1990.

.... following we provide a brief description of the fundamentals of the Fluent Calculus; for a complete introduction see [ Thielscher, 1999 ] or the electronically available, archived reference article [ Thielscher, 1998 ] The Fluent Calculus, which roots in the logic programming formalism of [ Holldobler and Schneeberger, 1990 ] is an order sorted second order language with equality, which includes the sorts action , sit , fluent , and state , with fluent being a sub sort of state . Fluents are reified propositions. That is to say, terms like, or see the online tutorial at http: pikas.inf. ....

Ste#en Holldobler and Josef Schneeberger. A new deductive approach to planning. New Generation Computing, 8:225--244, 1990.

....inferential aspect of the Frame Problem are addressed. This alternative access to the Fluent Calculus both clarifies its role in relation to the most popular axiomatization paradigm and should help to enhance its acceptance. 1 Introduction For a long time, the Fluent Calculus, introduced in [7] and so christened in [3] has been viewed exclusively as a close relative of approaches 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 a#nity of the Fluent Calculus ....

....in particular its axiomatization in the Fluent Calculus, furnishes a ready approach for elaborating the ideas developed in the present paper so as to deal with additional, indirect e#ects of actions. The version of the Fluent Calculus we arrived at in this paper di#ers considerably from its roots [7], e.g. in that it exploits the full expressive power of first order logic. In so doing it is much closer to the variant introduced in [14] but still novel is the notion of state update axioms. In particular the new function State(s) seems to lend more elegance to e#ect specifications and at the ....

S. Holldobler and J. Schneeberger. A new deductive approach to planning. New Generation Computing, 8:225--244, 1990.

....Reflections and Suggestions The fluent calculus, much like the situation calculus, provides a methodology for specifying and reasoning about states, actions and causality. It was originally set up as a first order logic program with equality using SLDE or SLDENF resolution as sole inference rule [11]. In the meantime, the fluent calculus has been revised as a predicate logic specification language using constraint handling rules for reasoning [12] Whereas the original version allowed for backward as well as forward reasoning, the revised version is a strictly forward reasoning approach. The ....

....an equation Z # =AC1 E ## and after performing an action A the plan P transforms Z into Z ## P re. The FC theory comprises AC1 axioms for the function # 2 and the definitions of action and causes predicates. For more details about the version of fluent calculus presented here see [11]. For the current extensions of the fluent calculus please refer to [12] 4.3 Logistics Example Let us consider the logistics example with cars, trucks and cities. Cars are delivered from one city to another on trucks. Cars may be loaded on trucks and unloaded from them. The trucks are driven ....

S.Holldobler, J.Schneeberger. A New Deductive Approach to Planning. New Generation Computing 8:225-244, 1990.

....algorithm will not terminate. In [2] we also investigated the detection of unsolvable planning problems using logic programming analysis and transformation techniques [1] In our approach, a logic program was written [2] implementing the equational logic programming approach to deductive planning [5, 6]. This logic program was first specialized with respect to a particular goal (defining an unsolvable planning problem) with partial evaluation [8] Second, the result of partial evaluation was approximated using a regular approximation tool [4] As failure is decidable in a regular approximation, ....

.... notions of a first order language, pre interpretation, interpretation and model as defined in [7] 2 Unsolvable Planning Problems Before we can define an unsolvable planning problem, we recall the logic program from [2] implementing the equational logic programming approach to deductive planning [5, 6]. The original approach employs a specific equational theory, called AC1 [6] to formalize situation descriptions, which, essentially, are multisets of resources that are available in the situation. In contrast, the following program represents situations by lists of resources, and the matching ....

S. Holldobler and J. Schneeberger. A New Deductive Approach to Planning. New generation Computing, 8:225--244, 1990.

....satisfy the constraints admit a unique successor state. We first illustrate the axiomatization by example. General correctness wrt. the notion of entailment in our high level language is proved in Section 6. Our axiomatization is based on a novel use of Fluent Calculus, which was introduced in [ Holldobler and Schneeberger, 1990 ] and so christened in [ Bornscheuer and Thielscher, 1997 ] While historically the Fluent Calculus arose from approaches to the Frame Problem using nonclassical, linear logics, in [ Thielscher, 1998c ] we argue that it can alternatively be viewed as a development of the Situation Calculus in ....

Steffen Holldobler and Josef Schneeberger. A new deductive approach to planning. New Generation Computing, 8:225--244, 1990.

....does the situation calculus. The approach then was called linear connection method or shortly LCM; for the logic we introduce here on the basis of LCM we propose the name transition logic or TL. The idea underlying LCM spawned a great number of studies based on this idea such as [Fro87, BdCFH89, HS90, GHS 92, BGH 92, BHS 93b, HT93, HT95, GHS96, Fro96, HT96, Thi96, EHT96, Thi97b, BT97, Thi97a, Bru97] to mention several of them. In TL certain facts may be treated as resources which may be consumed by actions. More specifically, a rule K ) L, called an action (or transition) rule ....

....not shown here for simplicity. In summary, crTL may be regarded as an approximate logical version of the STRIPS formalism. 5 In other words, TL inherits all advantages from STRIPS but as an additional feature it has also the expressiveness of classical logic. 6. 3 TL and the fluent calculus In [HS90] a classical calculus, in the meantime named fluent calculus (FC) has been introduced, which represents the manipulations of actions on the term level of classical logic. This is done in the tradition of representing the object level of a calculus logically at the meta level (see e.g. Kow79] ....

S. Holldobler and J. Schneeberger. A new deductive approach to planning. New Generation Computing, 8:225--244, 1990.

....in [4] Recently, M. Masseron et al. 20] applied the multiplicative fragment of linear logic [11] to planning and showed that in this framework planning problems can also be solved without frame axioms. A di#erent approach to deductive planning, which also avoids the frame axioms, was given in [15]. There, situations viz. collections of fluents are represented using a binary function i.e. essential properties describing situations. symbol , which is associative (A) commutative (C) and admits a unit element (1) For example, the situation in which two blocks a and b are on a ....

....work. Throughout the paper we use Prolog syntax. s(Z) q d s(g c (S) q q s(S) l q q s(g l (S) s(S) s(#) l Figure 1: A linear connection proof for the get lemonade example. 2 Deductive Planning In this section we briefly repeat W. Bibel s [3] S. Holldobler and J. Schneeberger s [15] as well as M. Masseron et al. approach [20] to deductive planning and show that these approaches are equivalent. We illustrate the three approaches with the help of a little example. Suppose a thirsty person named Bert wants to get some lemonade from a vending machine. The lemonade costs 75 ....

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S. Holldobler and J. Schneeberger. A new deductive approach to planning. New Generation Computing, 8:225--244, 1990.

....of resources. In a similar way, linear logic [12] can be used, which is a Gentzen style proof system without weakening and contraction rules. In the multiplicative fragment of the linear logic, literals and formulas cannot be copied or erased which also provides the idea of resources [22] In [16], classical logic along with an equational theory is used as a planning formalism. Facts describing a situation in the world are reified and represented as terms which are connected via a binary function symbol which is associative (A) commutative (C) and admits a unit element (1) viz. the ....

....i.e. it is consumed, whereas the fact loaded is added to the situation, i.e. it is produced. Finally, the goal causes(loaded alive, X) can be solved with computed answer substitution alive by applying (2) and performing an AC1 unification step. The three recent approaches [3, 22, 16] turned out to be equivalent for planning problems, where situations as well as the conditions and e#ects of actions are conjunctions of atomic facts [27, 13] This result does not only provide a standard semantics for fragments of the linear logic and the linear connection method, it also ....

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S. Holldobler and J. Schneeberger. A New Deductive Approach to Planning. New Generation Computing, 8:225--244, 1990.

....unaware of a formal semantics. In a separate paper, a formal transformation from PDDL into the fluent calculus is specified [16] The fluent calculus itself is a formal calculus for reasoning about situations, actions and causality which admits a well defined (standard) semantics as defined in [11] and [18] In this paper we consider in Section 2 a restricted fragment of the fluent calculus, which allows for the specification of planning problems as entailment problems in the spirit of [13] In Section 3 we formally define a transformation mapping these planning problems onto ....

....about situations, actions and causality. It is based on the idea to consider states as multi sets of fluents and to represent such states on the term level. The latter is done with the help of a binary function symbol ffi , which is associative, commutative and has a constant ; as unit element [11, 18] but is not idempotent. In this paper we consider a restricted version of the calculus specified in this section. Formally, the fluent calculus is an order sorted calculus with sorts action; sit , fluent; and state and ordering constraint fluent state . The set Sigma V of variables is the ....

S. Holldobler and J. Schneeberger. A new deductive approach to planning. New Generation Computing, 8:225--244, 1990.

....for planning essentially use such a frame. The goal of these approaches was to avoid the explicit statement of frame axioms or similar laws of inertia. They are in chronological order Bibel s linear connection method [2] Holldobler and Schneeberger s equational logic programming approach [19, 34], and Massaron, Tollu, and Vauzeilles s application of linear logic [14] to planning [25] At first glance, these approaches seem to be very different. Bibel imposes a syntactical condition called linearity on proofs for which no standard semantics exists so far. The linearity condition requires ....

....plan . These results are obtained by straightforward induction proofs on the length of the sequence of actions A . 3. 2 Conjunctive Equational Logic Programming In 1989 Josef Schneeberger and Steffen Holldobler developed a new approach to deductive planning based on equational Horn logic [19, 34]. Facts about a situation are encoded as terms connected by a binary function symbol ffi , which is associative, commutative, and admits a unit element ; 8X; Y; Z : X ffi (Y ffi Z) X ffi Y ) ffi Z 8X; Y : X ffi Y = Y ffi X 8X : X ffi ; X (AC1) These properties allow to write ffi in ....

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S. Holldobler and J. Schneeberger. A new deductive approach to planning. New Generation Computing, 8:225--244, 1990.

....logic [21] can be used, which is a Gentzen style proof system without weakening and contraction rules. In the multiplicative fragment of the linear logic, literals and formulas cannot be copied or erased, which also provides the idea of resources [37] In the equational logic programming approach [28], facts about a situation are represented as multisets of facts on the term level. An action ff with condition C and effect E is applicable in a situation S if C is contained in S , and if ff is applied in S then C is deleted from S and E is added. Thus, planning in the equational logic approach ....

....system. As argued in [23] multisets represent resources more adequately than sets and, moreover, it is more efficient to compute with multisets instead of sets. Furthermore, the concept of resources and multisets are more adequate solutions to the frame problem [29] The three recent approaches [7, 37, 28] are equivalent for planning problems where the condition and effect of actions are multisets of facts [48, 22] In [23] it is also shown that the equational logic approach can handle database transactions as well as objects and methods in much the same way as database transactions as well as ....

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S. Holldobler and J. Schneeberger. A New Deductive Approach to Planning. New Generation Computing, 8:225--244, 1990.

....a vastly increased search space and this is the reason why Kowalski advocates to use these axioms very carefully. However, in an equational logic programming language, where equational theories are included into the logic framework, the same planning problems can be solved without the frame axioms [21]. Formally, an equational logic program consists of an equational program EP and a logic program LP and is written hEP ; LPi. LP is a set of program clauses as usual ( 31] but the infix predicate symbol = may be used in the body of these clauses and will be interpreted as equality. EP is a ....

S. Holldobler and J. Schneeberger. A new deductive approach to planning. In Proceedings of the German Workshop on Artificial Intelligence, pages 63--73, 1989.

....with this axiom is to control its application in the process of answering a query like (Holds(on(a; b) w) i.e. the question of whether there is a state w such that block a is on block b. The desired plan is obtained as the binding for w. This is a typical kind of question in plan formation. In [Holldobler and Schneeberger, 1989], however, it was shown that the frame axiom(s) can be completely avoided if the world is specified by a multiset of assertions. For example, the world where two blocks a and b are on a table t and are clear (cl (x) can be specified by on(a,t) ffi on(b,t) ffi cl (a) ffi cl (b) 1) where ffi is ....

....this technique is inappropriate. Plotkin [Plotkin, 1972] proposed to build troublesome axioms into the unification procedure and, then, to use resolution equipped with such a generalized unification procedure. Gallier Raatz [Gallier and Raatz, 1986; Gallier and Raatz, 1989] and Holldobler [Holldobler, 1989] formally demonstrated that Plotkin s idea can be adapted to SLD resolution if a logic program is augmented with an unconditional (resp. conditional) equational theory. Before we review these results we need some technicalities. Terms, atoms, and clauses are defined as usual (see e.g. Lloyd, ....

[Article contains additional citation context not shown here]

Holldobler, S. and Schneeberger, J. (1989). A new deductive approach to planning. In Proceedings of the German Workshop on Artificial Intelligence, pages 63--73.

....the beginning of this paragraph This paper reports on an attempt to find answers for these and related questions in the context of the fluent calculus. The fluent calculus is a formal system for reasoning about situations, actions and causality which admits a well defined semantics as given in [11] and [20] In Section 2 a restricted fragment of the fluent calculus is considered, which allows for the specification of planning problems as entailment problems in the spirit of [14] In Section 3 a transformation is formally defined which maps these entailment problems onto satisfiability ....

....about situations, actions and causality. It is based on the idea to consider states as multi sets of fluents and to represent such states on the term level. The latter is done with the help of a binary function symbol ffi , which is associative, commutative and has a constant ; as unit element [11, 19, 20] but is not idempotent. In this paper we consider a restricted version of the calculus as specified in this section. Formally, the fluent calculus is an order sorted calculus with sorts action , sit , fluent; and state and ordering constraint fluent state . The set Sigma V of variables is the ....

S. Holldobler and J. Schneeberger. A new deductive approach to planning. New Generation Computing, 8:225--244, 1990.

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Ste#en Holldobler and Josef Schneeberger. A new deductive approach to planning. New GenerationComputing,8:225--244, 1990.

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S. Holldobler and J. Schneeberger. A new deductive approach to planning. New Generation Computing, 8:225--244, 1990.

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Ste#en Holldobler and Josef Schneeberger. A new deductive approach to planning. New GenerationComputing,8:225--244, 1990.

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S. Holldobler and J. Schneeberger. A New Deductive Approach to Planning. New Generation Computing, 8:225--244, 1990.

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S. Holldobler and J. Schneeberger. A new deductive approach to planning. New Gener. Comput., 8:225--244, 1990.

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S. Holldobler and J. Schneeberger. A New Deductive Approach to Planning. New Generation Computing, 8:225--244, 1990.

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S. Holldobler and J. Schneeberger. A New Deductive Approach to Planning. New Generation Computing, 8:225--244, 1990.

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S. Holldobler and J. Schneeberger. A New Deductive Approach to Planning. New Generation Computing, 8:225--244, 1990.

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