J-M. Andreoli and R. Pareschi. Logic programming with sequent systems: a linear logic approach. In Proc. of the Workshop on Extensions of Logic Programming, Lecture Notes in Artificial Intelligence 475, (Springer Verlag), Tubingen, Germany, 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....This flowering of developments has been backed by theoretical contributions concerning those aspects of Linear Logic which are essential to proof search. In particular, there have been several investigations of the crucial problem of permutations of inference figures during proof construction [3, 6, 31, 42, 25]. Other contributions have investigated in terms of proof search the complexity of different fragments of Linear Logic [36] In this paper, we contribute to the study of yet another aspect: the abstract interpretation of Linear Logic proofs. The practical outcome that we expect from this ....

J-M. Andreoli and R. Pareschi. Logic programming with sequent systems: a linear logic approach. In Proc. of the Workshop on Extensions of Logic Programming, Lecture Notes in Artificial Intelligence 475, (Springer Verlag), Tubingen, Germany, 1990.

....languages was inadequate. In each of these cases, a logic programming language based on linear logic proof search provided correct specifications. In a number of papers Andreoli and Pareschi develop a declarative treatment of object communication and concurrent object oriented computation [3, 4, 5]. As part of this work, Andreoli and Pareschi develop a concurrent specification language, LO [4] The work of Miller and Hodas [20] describes a linear logic programming language that refines the logics behind both Prolog and Prolog. A detailed analysis of this linear logic programming language ....

J.-M. Andreoli and R. Pareschi. Logic programming with sequent systems: a linear logic approach. In Proc. Workshop on Extensions of Logic Programming, Tuebingen. Lecture Notes in Artificial Intelligence, Springer-Verlag, Berlin, 1990.

....Computation, OBPDC 95, Tokyo, Japan, 1995, LNCS 1107, pp 148 167, Springer Verlag search methods for proving specications (and synthesizing programs) of distributed systems. A third complementary way is based on the proof search as computation paradigm and leads to works on logic programming [3], concurrent logic programming [5, 18, 20] in fragments of LL. As in the previous approach, proof construction is essential and we need to have eOEcient proof search methods for the logic we consider, for example based on specic proof schemas as uniform proofs in [14, 33] or canonical proofs [8, ....

....functional programming languages. Another approach is the one based on formulas as states and proofs as computations [22, 27] where the connections with Petri nets and Linear Logic have been investigated. It is also investigated in a rather dioeerent way in the context of logic programming [3]. Let us mention also works on linear logic programming [14] concurrent linear logic programming [18, 20] and object representation in Forum [7] that are based on proof search as computation programming paradigm. Our proposal focuses an the two latter approaches for modeling concurrent ....

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J.M. Andreoli and R. Pareschi. Logic programming with sequent systems: A linear logic approach. In Int. Workshop on Extensions of Logic Programming, LNCS 475, pages 130, T#bingen, Germany, December 1989.

....theories. The remarkable expressiveness of this computational paradigm is brought to light in a body of research accumulated over the past three years. In a number of papers Andreoli and Pareschi develop a declarative treatment of object communication and concurrent object oriented computation [8, 9, 11, 10]. A treatment of linear logic programming is given by Hodas and Miller [59] A role of linear logic in a declarative semantics of SLDNF resolution is considered by Cerrito [32] An approach that spans both the proof reduction and the proof search paradigms is proposed by Girard [51] Recent ....

J.-M. Andreoli and R. Pareschi. Logic programming with sequent systems: a linear logic approach. In Proc. Workshop on Extensions of Logic Programming, Tuebingen. Lecture Notes in Artificial Intelligence, Springer-Verlag, Berlin, 1990.

.... International Conference LPAR 92, Logic Programming and Automated Reasoning, LNAI 624, pp 42 53 (MLL) sequent calculus. From this point, it will be able to study from an automated deduction point of view the application of deduction in linear logic in different fields as programming logic [2, 12] or plans generation [14] In section 2, we give a concise presentation of linear logic and introduce in section 3 the concepts of logical structure and of proof net. In section 4, we focus on MLL and present the principle of automatic construction of proof nets. Section 5 includes an example to ....

....of view [14] If we consider the conjunctive planning using MLL with proper axioms, a plan corresponds to a proof net. Some extensions of the algorithm for the proper axioms treatment are possible. Considering logic programming, we can extend Prolog in the framework of MLL, in the same spirit as [2], but the expressivity gain is not obvious and moreover Omega sets some performance problems. But some works, like [12] emphasize the necessity to extend the work, for logic programming application, to additive and multiplicative linear logic (AMLL) and even to LL. To do this, we have two ....

J.M. Andreoli and R. Pareschi. Logic programming with sequent systems: A linear logic approach. In Int. Workshop on Extensions of Logic Programming, LNCS 475, pages 1--30, Tubingen, Germany, December 1989.

....in multiplicative linear logic (MLL) sequent calculus. Moreover proofs of correction, correctness and completeness are given. From this point it will be able to study from an automated deduction point of view the application of deduction in linear logic in different fields as programming logic [2, 13] or plans generation [15] In section 2, we give a concise presentation of linear logic and in section 3 we make precise the concepts of logical structure and of proof net. In section 4, we focus on multiplicative linear logic where the proof net notion is clearly defined and present the principle ....

....proper axioms, a plan corresponds to a proof net. The direct extension of the algorithm for the proper axioms treatment is possible but presents some difficulties because of the cuts on these axioms. Considering logic programming, we can extend Prolog in the framework of MLL, in the same spirit as [2], but the expressivity gain is not obvious and moreover Omega sets some performance problems. But some works, like [13] emphasize the necessity to extend the work, for logic programming application, to additive and multiplicative linear logic (AMLL) and even to complete linear logic (LL) Then if ....

J.M. Andreoli and R. Pareschi. Logic programming with sequent systems: A linear logic approach. In Int. Workshop on Extensions of Logic Programming, LNCS 475, pages 1--30, Tubingen, Germany, December 1989.

....we believe that the result of this paper, which is theoretical in nature, contributes to the understanding of the role of linear logic as an expressive and natural framework for describing control structure of logic programs. This logic programming perspective is based on [29] related work is in [19, 4, 5, 3]. Furthermore, our result addresses the issue of replacing copying and reuse by sharing as discussed below. A first indication that copying and reuse of hypotheses in intuitionistic logic might be replaceable by sharing is the contraction free formulation of intuitionistic logic, given by the ....

....the need for copying. The resulting iil proofs can then be embedded in imall. From the logic programming perspective given in [29] the main result of this paper addresses the issue of replacing copying and reuse in intuitionistic proofs by sharing. We believe that our results, together with [19, 4], contribute to the understanding of the role of linear logic as an expressive and natural framework for describing the control structure of logic programs. 2 Properties of iil In this section, we present a series of lemmas about iil that eventually establish the eliminability of cut and ....

J.-M. Andreoli and R. Pareschi. Logic programming with sequent systems: a linear logic approach. In Proc. Workshop on Extensions of Logic Programming, Tuebingen. Lecture Notes in Artificial Intelligence, Springer-Verlag, Berlin, 1990.

No context found.

J-M. Andreoli and R. Pareschi. Logic programming with sequent systems: a linear logic approach. In Proc. of the Workshop on Extensions of Logic Programming, Lecture Notes in Artificial Intelligence 475, (Springer Verlag), Tubingen, Germany, 1990.

....X 1 ; X r ; G (where X 1 ; X r are positive atoms and G is a goal) can be transformed into a proof where each occurrence of the Cut satisfies the following property: one of the premiss is a non logical axiom and the cut formula is necessarily G . This result is shown in [5] (in the framework of Classical logic, but it can be straightforwardly adapted to Linear logic) as a special case of a more general property: when Cut reduction is performed in a proof containing non logical axioms, all the Cuts cannot be eliminated, but they can be reduced so as to appear in ....

J-M. Andreoli and R. Pareschi. Logic programming with sequent systems: a linear logic approach. In Proc. of the Workshop on Extensions of Logic Programming, Lecture Notes in Artificial Intelligence 475, (Springer Verlag), Tubingen, Germany, 1990.

....extension in the logic underlying these languages, given by the introduction of a novel form of concurrent disjunction (denoted by the symbol ) will provide us with the capabilities of structuring such processes to support an organization like style of programming. We have shown elsewhere [4, 2, 3, 5] that this extension finds a rigorous proof theoretic counterpart in Linear Logic, a logic recently introduced to provide a theoretical basis for the study of concurrency [8] The programming language LO (for Linear Objects) which we have designed according to these principles, is therefore ....

....methods. They are built from atomic formulae, using four main connectives: and ( The first two connectives correspond, respectively, to concurrent forms of conjunction and disjunction. The other two correspond to two different, albeit strictly related, forms of implication. As shown in [4, 2, 3, 5], all these connectives can be reconstructed in terms of Linear Logic connectives [10, 9] in fact, is the additive conjunction of Linear Logic, is the multiplicative disjunction, is linear implication and ( is linear implication combined with the modality of course . We also use the ....

J-M. Andreoli and R. Pareschi. Logic programming with sequent systems: a linear logic approach. In Proc. of the Workshop on Extensions of Logic Programming, Lecture Notes in Artificial Intelligence 475, (Springer Verlag), Tubingen, Germany, 1990.

....any assumption on how the rules should be used for searching a proof of a given query (sequent) We want to hint here at some properties of the proof system behind LO which can be usefully exploited for defining an optimal strategy for searching LO proofs. These properties are formally shown in [6]. The important point which needs to be stressed is that the only proof rule which is going to be characterized by non determinism is (IV) Indeed, it is possible to show that a choice between proof rules (I) II) and (III) or between several applications of one of these rules on different ....

....primitives of Concurrent Constraint Logic Programming Languages [28] 4 Proof Theory We discuss here the relationship between LO and, respectively, Classical and Linear Logic. Proofs of the theorems in this section can be found in the Appendix. Further proof theoretic results can be found in [3, 4, 6]. 4.1 LO and Classical Logic 4.1.1 Properties of the Derivability Relation Let c be the derivability relation in Classical Logic. See [13] for various sequent systems for Classical Logic. The classical interpretation of a goal G is a classical formula written G c defined inductively by A ....

J-M. Andreoli and R. Pareschi. Logic programming with sequent systems: a linear logic approach. In Proc. of the Workshop on Extensions of Logic Programming, Lecture Notes in Artificial Intelligence 475, (Springer Verlag), Tubingen, Germany, 1990.

....any assumption on how the rules should be used for searching a proof of a given query (sequent) We want to hint here at some properties of the proof system behind LO which can be usefully exploited for defining an optimal strategy for searching LO proofs. These properties are formally shown in [2]. The important point which needs to be stressed is that the only proof rule which is going to be characterized by non determinism is (IV) Indeed, it is possible to show that a choice between proof rules (I) II) and (III) or between several applications of one of these rules on different ....

....makes possible in LO the kind of interactive sessions characterizing the use of object oriented languages like Smalltalk. 4 Proof Theory We discuss here the relationship of LO with Classical and Linear Logic. The theorems in this section are stated without proof. Complete proofs can be found in [2]. 4.1 LO and Classical Logic We denote with c the derivability relation in Classical Logic. See [8] for various sequent systems for Classical Logic. Let us consider the system LO 0 defined as follows: ffl The syntax of the formulae is the same as in LO except that the classical connective ....

J-M. Andreoli and R. Pareschi. Logic programming with sequent systems: a linear logic approach. In Proc. of the Workshop on Extensions of Logic Programming, Lecture Notes in Artificial Intelligence 475, (Springer Verlag), Tubingen, Germany, 1990.

No context found.

J.-M. Andreoli and R. Pareschi. Logic programming with sequent systems: a linear logic approach. In Proc. Workshop on Extensions of Logic Programming, Tuebingen. Lecture Notes in Artificial Intelligence, Springer-Verlag, Berlin, 1990.

No context found.

J.-M. Andreoli and R. Pareschi. Logic programming with sequent systems: A linear logic approach. In P. Schroder-Heister, editor, Proceedings of Workshop to Extensions of Logic Programming, Tubingen, 1989, pages 1--30. Springer-Verlag LNAI 475, 1991.

No context found.

J.-M. Andreoli and R. Pareschi. Logic programming with sequent systems: A linear logic approach. In P. Schroder-Heister, editor, Proceedings of Workshop to Extensions of Logic Programming, Tubingen, 1989, pages 1--30. Springer-Verlag LNAI 475, 1991.

No context found.

J.-M. Andreoli and R. Pareschi. Logic programming with sequent systems: A linear logic approach. In P. Schroder-Heister, editor, Proceedings of Workshop to Extensions of Logic Programming, Tubingen, 1989, pages 1--30. Springer-Verlag LNAI 475, 1991.

No context found.

J.-M. Andreoli and R. Pareschi. Logic programming with sequent systems: A linear logic approach. In P. Schroder-Heister, editor, Proceedings of Workshop to Extensions of Logic Programming, Tubingen, 1989, pages 1--30. Springer-Verlag LNAI 475, 1991.

No context found.

J.-M. Andreoli and R. Pareschi. Logic programming with sequent systems: A linear logic approach. In P. Schroder-Heister, editor, Proceedings of Workshop to Extensions of Logic Programming, Tubingen, 1989, pages 1--30. Springer-Verlag LNAI 475, 1991.

No context found.

J.-M. Andreoli and R. Pareschi. Logic programming with sequent systems: A linear logic approach. In P. Schroder-Heister, editor, Proceedings of Workshop to Extensions of Logic Programming, Tubingen, 1989, pages 1-30. Springer-Verlag LNAI 475, 1991.

No context found.

J.-M. Andreoli and R. Pareschi. Logic programming with sequent systems: A linear logic approach. In P. Schroder-Heister, editor, Proceedings of Workshop to Extensions of Logic Programming, Tubingen, 1989, pages 1-30. Springer-Verlag LNAI 475, 1991.

No context found.

J.-M. Andreoli and R. Pareschi. Logic programming with sequent systems: A linear logic approach. In P. Schroder-Heister, editor, Proceedings of Workshop to Extensions of Logic Programming, Tubingen, 1989, pages 1-30. Springer-Verlag LNAI 475, 1991.

No context found.

J.-M. Andreoli and R. Pareschi. Logic programming with sequent systems: A linear logic approach. In P. Schroder-Heister, editor, Proceedings of Workshop to Extensions of Logic Programming, Tubingen, 1989, pages 1-30. Springer-Verlag LNAI 475, 1991.

No context found.

J.-M. Andreoli and R. Pareschi. Logic programming with sequent systems: A linear logic approach. In P. Schroder-Heister, editor, Proceedings of Workshop to Extensions of Logic Programming, Tubingen, 1989, pages 1-30. Springer-Verlag LNAI 475, 1991.

No context found.

J.-M. Andreoli and R. Pareschi. Logic programming with sequent systems: A linear logic approach. In P. Schroder-Heister, editor, Proceedings of Workshop to Extensions of Logic Programming, Tubingen, 1989, pages 1-30. Springer-Verlag LNAI 475, 1991.

No context found.

J.M. Andreoli and R.Pareschi, 1990. Logic Programming with sequent systems : a linear logic approach, in em Proc. of the Workshop on Extensions of Logic Programming, Lecture Notes in Artificial Intelligence, Tubingen, Germany, Springer Verlag.

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