J. A. Harland and D. J. Pym. The Uniform Proof-theoretical Foundation of Linear Logic Programming (Extended Abstract). In Vijay A. Saraswat and Kazunori Ueda, editors, Proceedings of the International Logic Programming Symposium, pages 304-318. The MIT Press, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... in uniform proof formulations of intuitionistic logic [21] At the same time, with the advent of linear logic [9] new logic programming languages have emerged that support notions of resources and resource management, and rely on related no2 tions of uniform provability for both intuitionistic [10, 13] and classical linear logic [20, 23] In de ning the language L, our goal is to isolate a higher order extension of Horn Clauses that (i) provides support for representing objects, i.e. complex data structures comprising data and methods (formulas) while at the same time (ii) allowing methods ....

J. A. Harland and D. J. Pym. The Uniform Proof-theoretical Foundation of Linear Logic Programming (Extended Abstract). In Vijay A. Saraswat and Kazunori Ueda, editors, Proceedings of the International Logic Programming Symposium, pages 304-318. The MIT Press, 1991.

....of formulas since they cannot arbitrarily be duplicated unless they are prefixed by the modality (on the left) and (on the right) and thus each occurrence of the same formula does count in a derivation. 2 According to recent works in the field of Logic Programming [39] and LL Programming [26, 36, 24] it is possible to interpret sequents as descriptions of instant configurations of a computation whose complete behavior is captured by a proof of the sequent itself. Under this perspective the left hand side of a sequent is viewed as a set of program clauses (by choosing only particular classes ....

....connectives assume a more refined operational meaning which allows one to use them as programming constructs inside an ideal interpreter for the considered logic language. This metaphor, proofs as computations, has been investigated from many different point of views in LL as shown by the works in [3, 2, 24, 27, 29, 18]. The reader can refer to [1, 37] to have an extensive bibliography and survey on the topic. We will focus on a particular presentation of LL proof theory based on previous work on Logic Programming and non standard logics [39] 2.2 Forum: Higher Order Linear Logic Forum [36] can be considered ....

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J.A. Harland and D. J. Pym. The Uniform Proof-Theoretical Foundation of Linear Logic Programming (Extended Abstract). In Proceedings of the International Logic Programming Symposium, pages 304--318. The MIT Press, 1991.

.... the permutability of their rules [9, 33, 51] Proof search paradigms, based on the interpretation of formulas as programs and proofs as computations, have been investigated with a particular attention to the impact of LL in the definition of Logic Programming languages as shown, for instance, in [9, 39, 42, 60]. 1.1 Proofs as computations in LL: an overview The proofs as computations paradigm has been investigated from many different point of views. The common denominator of these approaches can be found in the methodology followed to analyze the underlying logic system. Here we can distinguish three ....

....of a proof is due here to: choice of clauses ( on the left) splitting of context due to the use of Omega (on the right) or Gammaffi (left) and higher order unifications. Other approaches reveal the same trade off between expressivity and complexity of the proof search procedure. Lygon [39], for example, is focused on the definition of a resolution rule for LL. However, the structure of the considered formulas is quite complex allowing occurrences of . ....

J.A. Harland and D. J. Pym. The Uniform Proof-Theoretical Foundation of Linear Logic Programming (Extended Abstract). In Proceedings of the International Logic Programming Symposium, pages 304--318. The MIT Press, 1991.

....a simple presentation of the underlying logic. Thus, the set of rules of E hhf has been reduced, by using permutability of Forum rules, to a set of search rules, i.e. right introduction rules, and a single left rule generalizing the usual notion of resolution, see also the language Lygon [9]. Applications of such a language have been inspired by seminal works on design of Linear Logicbased programming languages, like LO [3] and ACL [12] For the sake of this presentation, it is enought to recall the operational behaviour of the connectives used for the description of the language, ....

J. A. Harland and D. J. Pym. The Uniform Proof-theoretical Foundation of Linear Logic Programming (Extended Abstract). In Proocedings of the International Logic Programming Symposium, San Diego, pages 304--318. The MIT Press, 1991.

....choice of the proper clause to be executed. Some recent works on extensions of logic programming languages have isolated fragments of Girard s Linear Logic and proved them to be ALPLs, e.g. LO [1] Lolli [6] Forum [10] Other approaches rely on a different formulation of uniformity, e.g. Lygon [5], which, due to the richness of the considered fragment, loses some intuitiveness in the interpretation of its programs. Forum is a presentation of full Higher Order Linear Logic in terms of an Abstract Logic Programming Language, thus, it seems a good compromise between expressiveness of ....

J. A. Harland and D. J. Pym. The Uniform Proof-theoretical Foundation of Linear Logic Programming (Extended Abstract). In Proocedings of the International Logic Programming Symposium, San Diego, pages 304--318. The MIT Press, 1991.

....choice of the proper clause to be executed. Some recent works on extensions of logic programming languages have isolated fragments of Girard s Linear Logic and proved them to be ALPLs, e.g. LO [1] Lolli [6] Forum [9] Other approaches rely on a different formulation of uniformity, e.g. Lygon [5], which, due to the richness of the considered fragment, loses some intuitiveness in the interpretation of its programs. Forum is a presentation of full Higher Order Linear Logic in terms of an Abstract Logic Programming Language, thus, it seems a good compromise between expressiveness of ....

J. A. Harland and D. J. Pym. The Uniform Proof-theoretical Foundation of Linear Logic Programming (Extended Abstract). In Proocedings of the International Logic Programming Symposium, San Diego, pages 304--318. The MIT Press, 1991.

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