J. Harland, D. Pym, and M. Winiko. Programming in lygon: An overview. In Proceedings of the Fifth International Conference on Algebraic Methodology and Software Technology, Munich, pages 391405, July 1996.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....paired with the intuitionistic implication operator, depicted as = to load unlimited resources. It is beyond the scope of this paper to demonstrate the applications of all these operators. Many good examples can be found in the literature, particularly in the papers on Lygon and Lolli [5, 8]. 3 The I O Implementation Model The management of resources during proof search is a serious problem for the implementor. A naive implementation of the rules for the linear logic operators would lead to a level of backtracking, that would render the system useless. Consider, for example, the ....

James Harland, David Pym, and Michael Winiko#. Programming in Lygon: An overview. In Algebraic Methodology and Software Technology, 1996.

....is likely that the logic programming interpretation for CLF will draw heavily from it. However, in Forum proofs cannot be manipulated as rst class objects not even cut elimination is treated, let al..one an equational theory on proofs. The same is true of LinLog [And92] LO [AP91] ACL [KY93] Lygon [HPW96], and LLP [HWTK98] all of which treat logic programming over other fragments of classical or intuitionistic linear logic. Perrier describes how the basic idea of linear logic programming as concurrent computation can be improved by adopting proof nets [Gir87] rather than sequent calculus proofs ....

James Harland, David Pym, and Michael Winiko. Programming in Lygon: An overview. In M. Wirsing and M. Nivat, editors, Proceedings of the Fifth International Conference on Algebraic Methodology and Software Technology, pages 391-405, Munich, July 1996. Springer-Verlag LNCS 1101.

....that the logic programming interpretation for CLF will draw heavily from it. However, in Forum proofs cannot be manipulated as first class objects not even cut elimination is treated, let al..one an equational theory on proofs. The same is true of LinLog [And92] LO [AP91] ACL [KY93] Lygon [HPW96], and LLP [HWTK98] all of which treat logic programming over other fragments of classical or intuitionistic linear logic. Perrier describes how the basic idea of linear logic programming as concurrent computation can be improved by adopting proof nets [Gir87] rather than sequent calculus proofs ....

James Harland, David Pym, and Michael Winiko#. Programming in Lygon: An overview. In M. Wirsing and M. Nivat, editors, Proceedings of the Fifth International Conference on Algebraic Methodology and Software Technology, pages 391--405, Munich, July 1996. Springer-Verlag LNCS 1101.

....designed with bounded resources in mind. In particular, linear logic is not only a conservative extension of classical logic (so that classical reasoning, where appropriate, may be used) but also has been shown to be a natural way to model concurrency, database updates and state based transitions [11, 12, 15]. In particular, it has been shown that actions, such as those required by the classic blocks world scenario, can be modelled simply and naturally in linear logic [22, 23] Given also the existence of a number of logic programming languages based on linear logic (such as LO [4] Lolli [15] Forum ....

.... been shown that actions, such as those required by the classic blocks world scenario, can be modelled simply and naturally in linear logic [22, 23] Given also the existence of a number of logic programming languages based on linear logic (such as LO [4] Lolli [15] Forum [24] LLP [16] and Lygon [12]) it seems natural to explore the use of linear logic as a basis for BDI style agent systems. In [13] it was shown how a notion of forward chaining could be introduced into the standard sequent calculus for linear logic in order to provide such behaviour. In [14] the use of this framework as a ....

[Article contains additional citation context not shown here]

J. Harland, D. Pym and M. Winiko#, Programming in Lygon: An Overview, Proceedings of the Fifth International Conference on Algebraic Methodology and Software Technology 391-405, Munich, July, 1996.

....designed with bounded resources in mind. In particular, linear logic is not only a conservative extension of classical logic (so that classical reasoning, where appropriate, may be used) but also has been shown to be a natural way to model concurrency, database updates and statebased transitions [11, 12, 15]. In particular, it has been shown that actions, such as those required by the classic blocks world scenario, can be modelled simply and naturally in linear logic [22, 23] Given also the existence of a number of logic programming languages based on linear logic (such as LO [4] Lolli [15] Forum ....

.... been shown that actions, such as those required by the classic blocks world scenario, can be modelled simply and naturally in linear logic [22, 23] Given also the existence of a number of logic programming languages based on linear logic (such as LO [4] Lolli [15] Forum [24] LLP [16] and Lygon [12]) it seems natural to explore the use of linear logic as a basis for BDI style agent systems. In [13] it was shown how a notion of forward chaining could be introduced into the standard sequent calculus for linear logic in order to provide such behaviour. In [14] the use of this framework as a ....

[Article contains additional citation context not shown here]

J. Harland, D. Pym and M. Winikoff, Programming in Lygon: An Overview, Proceedings of the Fifth International Conference on Algebraic Methodology and Software Technology 391-405, Munich, July, 1996.

....(C ) 2. 2 The language and its interpretation Historically speaking, the rst proposal for a Linear Logic (LL) programming language was LO (Linear Objects) 3] which is a subset of LinLog [5] A list of other LL programming languages includes (and is not limited to) Forum [71] Lolli [39] Lygon [35] and ACL [58] Our subset of LL consists of LL synchronous connectives plus and ( The applicability of that LL fragment to AI planning is emphasised in [49] We use the following fragment for describing LL programs, where the symbols A and A c represent atomic formulae and x represents ....

....P G M, which basically means that a program is executed if at least G is achieved with a proof. The metavariable M, which may be 1 (contains no literals) as well, represents an arbitrary program context, which is not consumed during execution time. 2.2. 3 Global variables As it is stated in [35], one of the features of LL is that as formulae cannot be copied unless they commence with , variables, which appear outside the scope of a cannot be standardised apart, and hence variable names can persist across clauses. This is because in LL the universal quanti er does not distribute ....

[Article contains additional citation context not shown here]

J. Harland, D. Pym, M. Winiko, Programming in Lygon: An Overview. In Proceedings of the Fifth International Conference on Algebraic Methodology and Software Technology (AMAST), July 1996.

....us great hope for improvement. Finally, as the only part really relevant to LCC in this study was the expressibility, through its semantics, of safety properties in linear logic, we believe that our method can thus be used for other calculi based on linear logic, like LO [1] Lolli [7] or Lygon [6], where only a new parser should be needed (the properties are already expressed as linear logic formulae) Other coordination languages or rule based languages may also have a sound linear logic semantics, so there is still a lot of experimentation to do. ....

J. Harland, D. Pym, and M. Winiko. Programming in lygon: An overview. In Proceedings of the Fifth International Conference on Algebraic Methodology and Software Technology, Munich, pages 391-405, July 1996.

....we believe that our method can thus be used for other calculi based on linear logic and hope to extend concretely the prover in that direction in the future. The rst extension is that of handling the family of logic programming languages based on linear logic, like LO [1] Lolli [8] or Lygon [7], where only a new parser is needed (the properties are already expressed as linear logic formulae) Other coordination languages or rule based languages may also have a sound linear logic semantics, so there is still a lot of experimentation to do. ....

J. Harland, D. Pym, and M. Winiko. Programming in lygon: An overview. In Proceedings of the Fifth International Conference on Algebraic Methodology and Software Technology, Munich, pages 391-405, July 1996.

....figure for weakening from classical logic, is possible. Girard points out that we can mimic affine implication by using the linear constant 1 [9] Further, ensuring that a clause can be used at most once by writing C 1, the linear logic programming language, Lygon, can be used in affine mode [10]. These support approaching affine logic as a variant of linear logic. However, this approach ignores the effects of the structural rules on the underlying logic and its connectives. 7 Another approach is to investigate the impact of weakening on linear logic by looking at how it affects the ....

Harland, J., Pym, D., and Winikoff, M., "Programming in Lygon: an overview" April 1995, pp. 1--15 8

....even if the other conjuncts do not use all the linear resources. The # is seen to consume the leftovers. It is beyond the scope of this paper to demonstrate the applications of all these operators. Many good examples can be found in the literature, particularly in the papers on Lygon and Lolli [5, 6]. The proof theory of this fragment have also been discussed extensively in prior works [6] and is also beyond the scope of this paper. Of crucial importance is that there is a straightforward goal directed proof procedure (conceptually similar to the one used for Prolog) that is sound and ....

James Harland, David Pym, and Michael Winiko#. Programming in Lygon: An overview. In M. Wirsing and M. Nivat, editors, Algebraic Methodology and Software Technology, pages 391--405, Munich, Germany, 1996. Springer-Verlag LNCS 1101.

....clauses nondeterministically selected from the program. Besides the logic of Horn Clauses [31] and of hereditary Harrop formulas [28] several fragments of Girard s linear logic [15] have been isolated and proved to be ALPLs. Examples are LO [2] Lolli [18] and Forum [26] Furthermore, Lygon [17] has been proved to be the largest fragment of linear Preprint submitted to Elsevier Science 3 March 2000 logic enjoying uniform provability, in the sense stated in [30] All these languages adhere to the so called proofs as computations interpretation of linear logic, an interpretation in which ....

....clauses, hence allowing H to be a disjunction of atomic formulas. In order to provide constructs to control the rewriting process, in addition to and ) we allow and 8 to occur in goal formulas. We leave extensions of the fragment with other connectives (e.g. introducing in the goals as in [18,17]) for future works (see also discussion in Section 8) The appealing aspects of the resulting formalism is that it provides a clear way to study integration between rewrite based speci cation languages and logic programming languages. In fact, we can naturally integrate logic programming aspects ....

[Article contains additional citation context not shown here]

J. A. Harland, D. Pym, and M. Winiko. Programming in Lygon: An overview. In M. Wirsing and M. Nivat, editors, Algebraic Methodology and Software Technology, volume 1101 of Lecture Notes in Computer Science, pages 391-405, Munich, Germany, July 1996. Springer-Verlas.

.... the formulae p; p; q; q in a lazy manner, i.e. we first pass the entire collection to a chosen branch, which consumes the formulae needed, and passes on any excess to the next chosen branch (cf. 14] This strategy is the one most commonly used in linear logic programming languages such as Lygon [6, 14] and Lolli [7] Initially, we divide (p Omega q) Omega (p Omega q) into two copies of (p Omega q) and then one of these is further divided into p and q. Hence we arrive at the leaf p; p; q; q p, where it is clear that the formulae p; q; q are in excess, and are passed to the next branch, ....

J. Harland, D. Pym and M. Winikoff. Programming in Lygon: An Overview. Proc. AMAST'96, M. Wirsing and M. Nivat, editors, LNCS 1101, 391-405, July, 1996.

....and veri cation of linear logic programming languages. 1. INTRODUCTION In recent years a number of fragments of linear logic [16] have been proposed as a logical foundation for extensions of logic programming [28] Several new programming languages like LO [4] ACL [24] Lolli [20] and Lygon [17] have been proposed with the aim of enriching traditional logic programming languages like Prolog with a well founded notion of state and with aspects of concurrency. The oper email:bozzano disi.unige.it y email:martelli disi.unige.it ational semantics of this class of languages is given ....

....related to our work that we nd more promising. Linear Logic Programming. It would be interesting to extend the techniques we presented in this paper to larger fragments of linear logic. In particular, it would be interesting to de ne a bottom up evaluation for languages like Lolli[20] and Lygon[17], and to study techniques for rstorder formulation for all these languages. Veri cation. In [12] Delzanno and Podelski show that properties of concurrent systems expressed in temporal logic can be de ned in terms of xpoint semantics of logic programs. To give some ideas about this connection, ....

J. A. Harland, D. Pym, and M. Winiko. Programming in Lygon: An Overview. In Proc. of AMAST'96, LNCS 1101, pages 391-405, 1996.

....designed with bounded resources in mind. In particular, linear logic is not only a conservative extension of classical logic (so that classical reasoning, where appropriate, may be used) but also has been shown to be a natural way to model concurrency, database updates and statebased transitions [16, 20, 17]. It has also been shown that this logic has a natural notion of actions, such as those required by the classic blocks world scenario [29, 30] Given also the existence of a number of logic programming languages based on linear logic (such as LO [6] Lolli [20] Forum [31] LLP [21] and Lygon ....

.... 17] It has also been shown that this logic has a natural notion of actions, such as those required by the classic blocks world scenario [29, 30] Given also the existence of a number of logic programming languages based on linear logic (such as LO [6] Lolli [20] Forum [31] LLP [21] and Lygon [17]) it seems natural to explore the use of linear logic as a basis for BDI style agent systems. Some initial work in this direction was done by Abdullah Al Amin [3] however, that was limited to the use of a particular language (Lygon) and did not take reactive behaviour into account. In [18] it ....

[Article contains additional citation context not shown here]

J. Harland, D. Pym and M. Winiko, Programming in Lygon: An Overview, Proceedings of the Fifth International Conference on Algebraic Methodology and Software Technology 391-405, Munich, July, 1996.

....used exactly once. This property means that linear logic is a natural way to study state changes, and so provides a more direct way to model resource bounded applications than the traditional techniques. In particular, linear logic has been applied to concurrency problems [3, 4] database updates [5] and planning problems [6] Linear logic contains two forms of conjunction: one which is cumulative , i.e. for which p# p ## p, and one which is not, i.e. p N p p. Roughly speaking, the former is what allows linear logic to deal with resource issues, whilst the latter allows for these ....

J. Harland, D. Pym, and M. Winikoff. Programming in lygon: An overview. In Proceedings of the International Conference on Algebraic Methodology and Software Technology, pages 391--405. LNCS 1101, July 1996.

.... there are a number of different approaches to this issue[21, 12, 18, 19] which include restricting attention to a single conclusioned version, requiring don t care nondeterminism in the choice of goal formula (as in Forum[18] or allowing don t know nondeterminism in such choice (as in Lygon[21, 11]) It should also be noted that single conclusioned and multiple conclusioned systems for the same logic (such as LJ and LM for intuitionistic logic) can lead to different logic programming languages [9] Thus when seeking to extend such an analysis to a new logic, it is important to be able to ....

Harland J., Pym D., Winikoff M. Programming in Lygon: An Overview, Proceedings of the International Conference on Algebraic Methodology and Software Technology (AMAST) 391-405, M. Wirsing and M. Nivat (eds.), July, 1996. Published by Springer-Verlag as Lecture Notes in Computer Science 1101.

....and then the solution which has been found is broadcast to all other branches. Another branch is then selected and the process continues. Such strategies have properties similar to depth first search and are typically used in the implementation of linear logic programming languages such as Lygon [9, 23, 19] and Lolli [11] Eager strategies are those in which all branches are searched in parallel and one single set of equations is collected. This single set of equations is then solved once all equations have been found. Intermediate strategies solve a fixed number of branches worth of equations at ....

....This may be thought of as a pessimistic strategy, in that as only a minimal set of constraints is solved, if the derivation turns out to be unsuccessful, then a minimal amount of work has been done. This strategy is the one most commonly used in linear logic programming languages, such as Lygon [9, 23] and Lolli [11] and is analogous to depth first search. Eager distribution. The eager distribution is an strategy, in that an unbounded number of equations may be solved, and so all leaves must be closed before any attempt is made to solve the set of constraints. Hence a constraint solver ....

J. Harland, D. Pym and M. Winikoff, Programming in Lygon: An Overview, Proceedings of the International Conference on Algebraic Methodology and Software Technology (AMAST) 391-405, M. Wirsing and M. Nivat (eds.), July, 1996. Published by Springer-Verlag as Lecture Notes in Computer Science 1101.

....designed with bounded resources in mind. In particular, linear logic is not only a conservative extension of classical logic (so that classical reasoning, where appropriate, may be used) but also has been shown to be a natural way to model concurrency, database updates and state based transitions[12, 15, 13]. It has also been shown that this logic has a natural notion of actions, such as those required by the classic blocks world scenario[23, 24] Given also the existence of a number of logic programming languages based on linear logic (such as LO [4] Lolli [15] Forum [25] LLP [16] and Lygon ....

.... 13] It has also been shown that this logic has a natural notion of actions, such as those required by the classic blocks world scenario[23, 24] Given also the existence of a number of logic programming languages based on linear logic (such as LO [4] Lolli [15] Forum [25] LLP [16] and Lygon [13]) it seems natural to explore the use of linear logic as a basis for BDI style agent systems. Some initial work in this direction was done by Abdullah Al Amin [3] however, that was limited to the use of a particular language (Lygon) and did not take reactive behaviour into account. In [14] it ....

[Article contains additional citation context not shown here]

J. Harland, D. Pym and M. Winikoff, Programming in Lygon: An Overview, Proceedings of the Fifth International Conference on Algebraic Methodology and Software Technology 391-405, Munich, July, 1996.

....G#: P G# P A (#x.G # B in P , B# = A) This operational semantics has several desirable features. Most importantly, it is not very non deterministic, thereby reducing the need for backtracking to an acceptable level. More details of this model of computation can be found in [27, 35, 26, 17]. Proofs constructed according to this goal directed strategy are called uniform proofs [27, 35] Uniform proofs are not complete for all of BI (or indeed for all of intuitionistic logic) For example, consider the following, trivially provable, sequent: G # H # G # H. To see that there is ....

....a goal. We get a version of the resolution step for each of #x.G # A and # new x.G #A. In fact, there are also the cross cases, one in which # new is paired with # and one in which # is paired with #. The latter case is the one taken in linear logic and so in Lolli [18] and Lygon [17, 35]. The proof that uniform proofs are complete for hereditary Harrop sequents relies most naturally on a presentation of BI as a sequent calculus [34] in which the elimination rules are replaced by left rules which introduce connective to the left hand side of a sequent. Provided we restrict our ....

J. A. Harland, D. J. Pym, and M. Winiko, Programming in Lygon: an overview, Proceedings of AMAST '96 (Berlin) (M. Wirsing and M. Nivat, editors), Lecture Notes in Computer Science, no. 1101, Springer-Verlag, 1996, pp. 391--405.

....and then the solution which has been found is broadcast to all other branches. Another branch is then selected, and the process continues. Such strategies have properties similar to depth first search and are typically used in the implementation of linear logic programming languages such as Lygon [4, 17, 14] and Lolli [6] Eager strategies are those in which all branches are searched in parallel and one single set of equations is collected. This single set of equations is then solved once all equations have been found. Intermediate strategies solve a fixed number of branches worth of equations at ....

....may be thought of as a pessimistic strategy, in that as only a minimal set of constraints is solved, if the derivation turns out to be unsuccessful, then only a minimal amount of work has been done. This strategy is the one most commonly used in linear logic programming languages such as Lygon [4, 17] and Lolli [6] and is analogous to depth first search. Eager distribution. The eager distribution is an strategy, in that an unbounded number of equations may be solved, and so all leaves must be closed before any attempt is made to solve the set of constraints. Hence a constraint solver would ....

J. Harland, D. Pym and M. Winikoff, Programming in Lygon: An Overview, Proceedings of the International Conference on Algebraic Methodology and Software Technology (AMAST) 391-405, M. Wirsing and M. Nivat (eds.), July, 1996. Published by Springer-Verlag as Lecture Notes in Computer Science 1101.

....in 1987 [2] has such properties, and has been successfully applied to modelling updates, reasoning about the environment, and implementing concurrent behaviour. Linear logic is often described as resource sensitive, and has been the basis for a number of programming languages including Lygon [3], Lolli, Forum, ACL, LC, and LO. In this paper we investigate the advantages and disadvantages of developing agentoriented programs in Lygon, a programming language based on linear logic. In particular, we develop a bank deposit example which serves as an illustration of the advantages and ....

James Harland, David Pym, and Michael Winikoff. Programming in Lygon: An overview. In Martin Wirsing and Maurice Nivat, editors, Algebraic Methodology and Software Technology, LNCS 1101, pages 391--405. Springer, July 1996.

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J. Harland, D. Pym, and M. Winikoff. Programming in Lygon: An Overview. Proceedings of the Fifth International Conference on Algebraic Methodology and Software Technology 391-405, Munich, July, 1996.

....of higher order facilities [16] and negations and disjunctions in the heads of clauses [17] Secondly, this process can be applied to logics other than classical (or intuitionistic) logic. For example, a number of logic programming languages have been derived from linear logic including Lygon[11], Forum[15] LinLog [1] LO [2] Lolli [12] ACL [13] and LC [21] A popular proof search strategy is the notion of goal directed proof [16] which, roughly speaking, requires that the goal be decomposed before the program, and hence the computation uses the program as a context, and the goal as ....

J. Harland, D. Pym, and M. Winikoff. Programming in Lygon: An Overview. In M. Wirsing, editor, Lecture Notes in Computer Science, pages 391--405. Springer, July 1996.

No context found.

J. Harland, D. Pym, and M. Winiko. Programming in lygon: An overview. In Proceedings of the Fifth International Conference on Algebraic Methodology and Software Technology, Munich, pages 391405, July 1996.

No context found.

James Harland, David Pym, and Michael Winiko#. Programming in Lygon: An overview. In M. Wirsing and M. Nivat, editors, Algebraic Methodology and Software Technology, pages 391--405, Munich, Germany, 1996. Springer-Verlag LNCS 1101.

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