M. Masseron, C. Tollu, and J. Vauzeilles. Generating plans in linear logic. In Foundations of Software Technology and Theoretical Computer Science, volume 472 of Lecture Notes in Computer Science, pages 63--75. Springer-Verlag, 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....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 representational but also the inferential aspect of the Frame Problem [4] These approaches have thus been characterized as attempts to reconcile the expressive power of logical reasoning with the classical ....

Marcel Masseron, Christophe Tollu, and Jacqueline Vauzielles. Generating plans in linear logic I. Actions as proofs. Journal of Theoretical Computer Science, 113:349--370, 1993.

.... 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 ....

M. Masseron, C. Tollu, and J. Vauzielles. Generating Plans in Linear Logic I. Actions as Proofs. Theoretical Computer Science, 113:349--370, 1993.

....which each literal is used at most once. Unfortunately, Bibel was unable to give a semantics for the linear connection method and as R. Kowalski states if Bibel s system really works, then it deserves an explanation and it deserves a semantics (see Discussion 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. ....

....the results from [16] or [14] One should observe that the pre as well as the postcondition of an action are just collections of fluents which can intuitively be understood as conjunctions of fluents. A more precise interpretation will be given in Section 4. This restriction holds also for [20]. W. Bibel allows a more general form, but all examples given in [3, 5] are restricted in precisely the same way. The purpose of this paper is as follows. 1. We proved that the equational logic programming approach to deductive planning is equivalent to a the linear connection method and the ....

[Article contains additional citation context not shown here]

M. Masseron, C. Tollu, and J. Vauzielles. Generating plans in linear logic. In Proceedings of the 10th FST-TCS. Springer, LNCS 472, 1990.

.... 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 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 ....

M. Masseron, C. Tollu, and J. Vauzielles. Generating plans in linear logic I. Actions as proofs. J. of Theoretical Computer Science, 113:349--370, 1993.

....the concept 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) ....

....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 ....

M. Masseron, C. Tollu, and J. Vauzielles. Generating Plans in Linear Logic. In Foundations of Software Technology and Theoretical Computer Science, 63--75. Springer, Volume 472 of LNCS, 1990.

....fact that the resource skill formalism deals with constraints and services as the composition of skills. Furthermore, we developed plan merging algorithms for which our plan representation is very suited. Another planning logic that is very close to ours is the one developed by Masseron et al. [20]. One important di erence is the fact that in their formalism it is possible to include nondeterministic actions, i.e. actions with an outcome that is uncertain albeit limited to a set of given outcomes. On the other hand, our formalism can handle constraints, whereas the planning logic of ....

M. Masseron. Generating plans in linear logic. Theoretical Computer Science, 113(2):349-370, 1993.

....usual sequent calculus. 1 Introduction Linear logic [12] has become known as a very expressive formalism for reasoning about action and change. During its rather rapid development linear logic has found applications in logic programming [14, 19] modeling concurrent computation [11] planning [18], and other areas. Its expressiveness, however, results in a high complexity. Propositional linear logic is undecidable. The multiplicative fragment (MLL) is already NP complete [16] The complexity of the multiplicative exponential fragment (MELL) is still unknown. Consequently, proof search in ....

M. Masseron, C. Tollu, J. Vauzeilles. Generating plans in linear logic. In Foundations of Software Technology and Theoretical Computer Science, LNCS, Springer,1991.

....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 that each literal is engaged in at most one connection. For example, the proof in Figure 1 ....

....Furthermore, the equational logic formalization of deductive planning meets the first and second requirement stated by McCarthy and repeated in the introduction. 3.3 Conjunctive Linear Logic In 1990 M. Masseron, C. Tollu, and J. Vauzeilles applied Girard s linear logic to planning problems [25]. They essentially used only the multiplicative fragment of linear logic, which we briefly repeat in the following. Formulas in this fragment are either ground atoms or of the form t , where s and t are formulas. If not stated otherwise, s; t; denote formulas and Gamma; Delta; ....

[Article contains additional citation context not shown here]

M. Masseron, C. Tollu, and J. Vauzielles. Generating plans in linear logic. In Foundations of Software Technology and Theoretical Computer Science, pages 63--75. Springer, LNCS 472, 1990.

....the concept of resources. In a similar way, linear 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 ....

....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 ....

M. Masseron, C. Tollu, and J. Vauzielles. Generating Plans in Linear Logic. In Foundations of Software Technology and Theoretical Computer Science, volume 472 of LNCS, pages 63-- 75. Springer, 1990.

....of resources. Second, in a similar way linear logic [5] 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 [11]. Third, in the equational logic programming approach [8] facts about a situation are represented as multisets of facts on the term level. An action ff with (the multiset of) conditions C and (the multiset of) effects E is applicable in a situation S if C is contained in S ; and if ff is applied ....

....are used instead of sets and that planning is performed in a purely deductive system. As argued in [7] multisets represent resources more adequately than sets and, moreover, it is more efficient to compute with multisets instead of sets. These three so called resource oriented approaches [2, 11, 8] are equivalent for planning problems where the conditions and effects of actions are multisets of facts [6] This result does not only provide a standard semantics for fragments of the linear logic and the linear connection method, it also suggests that resources can be treated i.e. the ....

M. Masseron, C. Tollu, and J. Vauzielles. Generating plans in linear logic. In Foundations of Software Technology and Theoretical Computer Science, pages 63--75. Springer, LNCS 472, 1990.

....subsequent discussion that the problem of representing situations, actions, and goals in first order logic is related to the weakening and contraction rules in Gentzen style systems. Jean Yves Girard [9] has developed linear logic as a logic which abandons these structural rules. M. Masseron et al. [21] have applied linear logic to planning. In this framework the actions add , wait, and heat of the iron and sulfur example are formalized as proper axioms as follows. 1 1 Figure 8 shows a linear proof of the sequent using the proper axioms for the actions add , wait, and heat . 1 S 1 ....

....of the sequent using the proper axioms for the actions add , wait, and heat . 1 S 1 1 Fe; S ; 1 FeS 1:l Fe; FeS Omega :l 1; Fe FeS cut Fe FeS cut Fig. 8. A linear proof of the sequent Fe FeS . For the formal definitions of 1 : l , Omega : l , r and cut see [21] or [9] If we compare the proofs shown in Figures 4 and 8, then it becomes apparent that the SLDE refutation proof of Figure 4 can be transformed into the linear proof of Figure 8 and vice versa. This was rigorously proved in [11, 30] Together with Theorem 1 we find that the linear connection ....

M. Masseron, C. Tollu, and J. Vauzielles. Generating plans in linear logic. In Foundations of Software Technology and Theoretical Computer Science, pages 63--75. Springer, LNCS 472, 1990.

....as a re nement of classical as well as of intuitionistic logic. It subsumes these logics because both of them can be embedded into linear logic. Mainly, linear logic has become known as a very expressive logic of action and change. It has found applications in logic programming [14,20] planing [19], modeling concurrent computation [11] and other areas. Its expressiveness, however results in a high complexity. Validity is undecidable for propositional linear logic. The multiplicative fragment is already NP complete [16] The complexity of the multiplicative exponential fragment (MELL) is ....

M. Masseron, C. Tollu, J. Vauzeilles. Generating plans in linear logic. In Foundations of Software Technology and Theoretical Computer Science, LNCS, Springer,1991.

....resource schemes that match certain constraints. In this algorithm the representation of the skills and the constraints on the skills play a far more important role. The resource skill formalism as described in Section 2 has a strong resemblance to the planning logic developed by Masseron et al. [13]. One important di erence is the fact that in their formalism it is possible to include nondeterministic actions, i.e. actions with an outcome that is uncertain albeit limited to a set of given outcomes. It is not clear how this planning logic can be used to implement e cient plan merging ....

M. Masseron. Generating plans in linear logic. Theoretical Computer Science, 113(2):349370, 1993.

....automatic software synthesis, but it is not enough for planning actions in an environment where resources are limited. In this paper we propose a subset of linear logic operators enough for describing robot actions in a resource sensitive world. Although linear logic has been used for planning [21, 16, 15, 5] and a lot of problems has been solved, there are still many unanswered questions like which linear logic operators are needed to adequately represent the planning domain, which algorithms to use for proving linear logic formulas and from pragmatic point of view is it overall reasonable to use ....

....been used by Jacopin [16] as a classical AI planning kernel. As only the multiplicative conjunction is used in formulas there, the framework has a little use if concerned more serious planning and solving real world problems. The multiplicative conjunction operator ( has been used also in [21], where a demonstration of robot planning system has been given. The usage of , and additive disjunctions ( operator, which importance to AI planning is emphasized [5] is also brie y discussed there but not demonstrated. From the complete set of linear logic operators we are using , ....

M. Masseron, C. Tollu, J. Vauzeilles. Generating plans in linear logic. In: Proceedings of 10th Conference on Foundations of Software Technology and Theoretical Computer Science, Banglore, India, 17-19 December, 1990, Springer-Verlag, Vol. 472 of Lecture Notes in Computer Science, pp. 63-75, 1990.

....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 representational but also the inferential aspect of the Frame Problem [4] These approaches have thus been characterized as attempts to reconcile the expressive power of logical reasoning with the classical ....

Marcel Masseron, Christophe Tollu, and Jacqueline Vauzielles. Generating plans in linear logic I. Actions as proofs. Journal of Theoretical Computer Science, 113:349-370, 1993.

....about actions can be formalized as entailment problems in a suitable logic. There is a variety of proposals for reasoning about actions, notably the situation [19, 16] the uent [11, 31] and the event calculus [13, 27] approaches based on the linear connection method [1, 2] linear logic [8, 17], transaction logic [3] temporal action logics [4] action languages [7] the features and uent approach [26] etc. We opt for the uent calculus because it is a logic with standard semantics and a sound and complete calculus, and many of the problems in reasoning about actions like the frame ....

M. Masseron, C. Tollu, and J. Vauzielles. Generating plans in linear logic. In Foundations of Software Technology and Theoretical Computer Science, pages 63{

.... fundamental Frame Problem [39] Our calculus roots in the logic programming formalism of [20] which in [16] 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 [34], resp. All three frameworks have been designed especially to address not only the representational but also the inferential aspect of the Frame Problem [4] On the other hand, with the full expressive power of rst order logic, the Fluent Calculus as presented in [60] can be viewed as a ....

Marcel Masseron, Christophe Tollu, and Jacqueline Vauzielles. Generating plans in linear logic I. Actions as proofs. Journal of Theoretical Computer Science, 113:349-370, 1993.

....the usual sequent calculus. 1 Introduction Linear logic [12] has become known as a very expressive formalism for reasoning about action and change. During its rather rapid development linear logic has found applications in logic programming [14,19] modeling concurrent computation [11] planning [18], and other areas. Its expressiveness, however, results in a high complexity. Propositional linear logic is undecidable. The multiplicative fragment (MLL) is already NP complete [16] The complexity of the multiplicative exponential fragment (MELL) is still unknown. Consequently, proof search in ....

M. Masseron, C. Tollu, J. Vauzeilles. Generating plans in linear logic. In Foundations of Software Technology and Theoretical Computer Science, LNCS, Springer,1991.

....the situation calculus. Under a given interpretation properties do or do not hold, but they may not change their truth value during the reasoning process. Since several years alternative approaches are developed whose main characterization is the feature that fluents are represented as resources [2, 9, 19, 15]. Resources can be consumed and produced. They are consumed whenever the conditions of an action are to be satisfied and they are produced by the effects whenever an action is applied. In the sequel we will present the fluent calculus based on [15] as it has turned out that this approach admits a ....

....produced by the effects whenever an action is applied. In the sequel we will present the fluent calculus based on [15] 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 [19], both of which do not have a standard semantics [10] 4 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 ....

M. Masseron, C. Tollu, and J. Vauzielles. Generating plans in linear logic. In Foundations of Software Technology and Theoretical Computer Science, pages 63--75. Springer, LNCS 472, 1990.

.... goals in Intellectics, i.e. Arti cial Intelligence 1 and Cognitive Science (e.g. 18] There are a variety of proposals available this days, notably the situation [19, 15] uent [11, 24] and event calculus [14, 22] approaches based on the linear connection method [1, 2] linear logic [7, 17], transaction logic [3] temporal action logics [5] action languages [6] the features and uent approach [21] etc. The most prominent problem addressed in these approaches is the problem of whether a certain goal can be reached by executing a certain sequence of actions in a certain situation. ....

M. Masseron, C. Tollu, and J. Vauzeilles. Generating plans in linear logic. In Foundations of Software Technology and Theoretical Computer Science, volume 472 of Lecture Notes in Computer Science, pages 63-75. Springer Verlag, 1990. 15

No context found.

M. Masseron, C. Tollu, and J. Vauzeilles. Generating plans in linear logic. In Foundations of Software Technology and Theoretical Computer Science, volume 472 of Lecture Notes in Computer Science, pages 63--75. Springer-Verlag, 1990.

No context found.

M. Masseron, C. Tollu, and J. Vauzeille. Generating plans in linear logic. Theoretical Computer Science, 113:349--370, 1993.

No context found.

M. Masseron, C. Tollu, and J. Vauzielles. Generating Plans in Linear Logic. In Foundations of Software Technology and Theoretical Computer Science, vol. 472 of LNCS, p. 63--75. Springer, 1990.

No context found.

M. Masseron, C. Tollu, and J. Vauzielles. Generating Plans in Linear Logic. In Foundations of Software Technology and Theoretical Computer Science, volume 472 of LNCS, pages 63--75. Springer-Verlag, 1990.

No context found.

M. Masseron, C. Tollu, and J. Vauzielles. Generating Plans in Linear Logic. In Foundations of Software Technology and Theoretical Computer Science, 63--75. Springer, volume 472 of LNCS, 1990.

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