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Focusing the inverse method for linear logic
 Proceedings of CSL 2005
, 2005
"... 1.1 Quantification and the subformula property.................. 3 1.2 Ground forward sequent calculus......................... 5 1.3 Lifting to free variables............................... 10 ..."
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Cited by 51 (15 self)
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1.1 Quantification and the subformula property.................. 3 1.2 Ground forward sequent calculus......................... 5 1.3 Lifting to free variables............................... 10
Resourcedistribution via Boolean constraints
 Proceedings of CADE14
, 1997
"... We consider the problem of searching for proofs in sequential presentations of logics with multiplicative (or intensional) connectives. Specifically, we start with the multiplicative fragment of linear logic and extend, on the one hand, to linear logic with its additives and, on the other, to the ..."
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Cited by 31 (8 self)
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We consider the problem of searching for proofs in sequential presentations of logics with multiplicative (or intensional) connectives. Specifically, we start with the multiplicative fragment of linear logic and extend, on the one hand, to linear logic with its additives and, on the other, to the additives of the logic of bunched implications, BI. We give an algebraic method for calculating the distribution of the sideformul in multiplicative rules which allows the occurrence or nonoccurrence of a formula on a branch of a proof to be determined once sufficient information is available. Each formula in the conclusion of such a rule is assigned a Boolean expression. As a search proceeds, a set of Boolean constraint equations is generated. We show that a solution to such a set of equations determines a proof corresponding to the given search. We explain a range of strategies, from the lazy to the eager, for solving sets of constraint equations. We indicate how to apply our methods systematically to large family of relevant systems. 1
Composition of semantic web services using linear logic theorem proving
 Information Systems
, 2005
"... This paper introduces a method for automatic composition of semantic web services using Linear Logic (LL) theorem proving. The method uses semantic web service language (DAMLS) for external presentation of web services, while, internally, the services are presented by extralogical axioms and proofs ..."
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Cited by 30 (5 self)
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This paper introduces a method for automatic composition of semantic web services using Linear Logic (LL) theorem proving. The method uses semantic web service language (DAMLS) for external presentation of web services, while, internally, the services are presented by extralogical axioms and proofs in LL. LL, as a resource conscious logic, enables us to define attributes of web services formally (including qualitative and quantitative values of nonfunctional attributes). The subtyping rules that are used for semantic reasoning are presented with LL inference figures. We propose a system architecture where the DAMLS Translator, LL Theorem Prover and Semantic Reasoner can operate together. This architecture has been implemented in Java.
Efficient implementation of a linear logic programming language
, 1998
"... A number of logic programming languages based on Linear Logic [3] have been proposed. However, the implementation techniques proposed for these languages have relied heavily on the copying and scanning of large data structures to ensure that linearity conditions have been met, and thus have been mos ..."
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Cited by 15 (8 self)
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A number of logic programming languages based on Linear Logic [3] have been proposed. However, the implementation techniques proposed for these languages have relied heavily on the copying and scanning of large data structures to ensure that linearity conditions have been met, and thus have been most suited to the creation of interpreters written in highlevel languages. In this paper we present a new formulation of the logic of the language Lolli that is conducive to the creation of both more efficient interpreters, as well as compilers based on extensions of the standard WAM model. We present such an extension which implements a useful fragment of Lolli. Resource conscious algorithms executed using this system show signiflcant performance advantages relative to their traditional Prolog implementations.
Backtrackable State with Linear Affine Implication and Assumption Grammars
, 1996
"... . A general framework of handling state information for logic programming languages on top of backtrackable assumptions (linear affine and intuitionistic implications ranging over the current continuation) is introduced. Assumption Grammars (AGs), a variant of Extended DCGs handling multiple streams ..."
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Cited by 14 (12 self)
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. A general framework of handling state information for logic programming languages on top of backtrackable assumptions (linear affine and intuitionistic implications ranging over the current continuation) is introduced. Assumption Grammars (AGs), a variant of Extended DCGs handling multiple streams without the need of a preprocessing technique, are specified within our framework. Equivalence with DCGs is shown through a translation from AGs to DCGs and through use of an implementationindependent metainterpreter, customized for handling both DCGs and AGs. For AGs, efficiency comparable to that of preprocessing based DCG is obtained through a WAMlevel implementation which uses space only for nondeterministic execution while collapsing to a form of inplace update in case of deterministic execution. AGs have been fully integrated in BinProlog 5.00 (available by ftp from clement.info.umoncton.ca) and have been used as an alternative to DCGs in various applications. Not restricted to P...
Forum as a Logic Programming Language: Preliminary Report
 Proceedings of the Linear Logic '96 Meeting
, 1996
"... When Miller introduced Forum he called it a specification logic, rather than a logic programming language. In this paper we outline those features that create problems in attempting to implement an interpreter for the language, and describe solutions to those problems. We show how techniques used in ..."
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Cited by 11 (1 self)
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When Miller introduced Forum he called it a specification logic, rather than a logic programming language. In this paper we outline those features that create problems in attempting to implement an interpreter for the language, and describe solutions to those problems. We show how techniques used in the implementation of Lolli can be extended naturally to Forum. Finally, we show two Forum programs in order to demonstrate some of the paradigms that arise in using the language. 1 Introduction Forum, a fragment of Linear Logic introduced by Dale Miller in 1994, is distinguished by two key features. First, it is complete for all of Linear Logic, in the sense that Linear Logic operators that are not part of Forum can be mapped to Forum by a provabilitypreserving translation. Second, a form of goaldirected proof search (as characterized by uniform proofs) is complete. Historically, logics for which uniform proofs are complete, such as Horn Clauses, Hereditary Harrop Formulas, and Linear H...
Logic Programming with Linear Logic
, 1997
"... Programming languages are the basic tools of computer science. The design of a good programming language is a tradeoff between many factors. Perhaps the most important and difficult tradeoff is between execution efficiency and programmer efficiency. Higher level languages reduce the amount of work ..."
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Cited by 7 (2 self)
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Programming languages are the basic tools of computer science. The design of a good programming language is a tradeoff between many factors. Perhaps the most important and difficult tradeoff is between execution efficiency and programmer efficiency. Higher level languages reduce the amount of work the programmer has to do; however they have, to date, been less efficient than lower level languages. That lower level languages are necessarily more efficient is a piece of folklore which is under attack  higher level languages are constantly coming closer to the performance of the lower level languages. A consequence of this constantly closing performance gap is that the abstraction level of programming languages is slowly but inevitably rising. A class of programming languages which has been described as "very high level" is declarative programming languages. Declarative programming languages have simple formal semantics and are easier to reason about and to construct tools for than m...
Some Applications of the Linear Logic Programming Language Lygon
 IN KOTAGIRI RAMAMOHANARAO, EDITOR, AUSTRALASIAN COMPUTER SCIENCE CONFERENCE
, 1996
"... We describe and discuss the applications of a logic programming language called Lygon. This language is based on linear logic, a logic designed with bounded resources in mind. Linear logic may be thought of as a generalisation of classical logic, and as a result Lygon contains various features which ..."
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Cited by 6 (4 self)
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We describe and discuss the applications of a logic programming language called Lygon. This language is based on linear logic, a logic designed with bounded resources in mind. Linear logic may be thought of as a generalisation of classical logic, and as a result Lygon contains various features which do not exist in (pure) Prolog, whilst maintaining all the features of (pure) Prolog. In this paper we describe various applications of this language, which include graph problems, and problems involving states and actions. In logic programming languages based on classical logic, it is possible to write elegant solutions for problems over acyclic graphs. By making use of properties of linear logic, it is possible to write similarly elegant solutions for cyclic graphs as well. As linear logic enables changes of state to be neatly expressed, it is straightforward to give Lygon solutions to problems such as the Yale shooting problem and the blocks world, and we give example solutions to each. ...
Deriving Logic Programming Languages
, 1996
"... Given a logic we would like to derive from it a programming language. In order to do this we need to have a formal litmus test which identifies logic programming languages. The standard test is uniformity introduced by Miller, Nadathur, Pfenning and Scedrov. Uniformity suffers from a number of short ..."
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Cited by 5 (5 self)
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Given a logic we would like to derive from it a programming language. In order to do this we need to have a formal litmus test which identifies logic programming languages. The standard test is uniformity introduced by Miller, Nadathur, Pfenning and Scedrov. Uniformity suffers from a number of shortcomings, one of the major ones being that it works best in logics which allow only a single conclusion. This report looks at a variety of intuitions which distinguish logic programming from theorem proving. Some of these intuitions are formalised and applied to a variety of languages which have been proposed in the literature. We then introduce a mechanism by which the proof search can be guided by atomic goals. This enables us to propery generalise uniformity to multiple conclusioned logics. We propose an extended version of single conclusion uniformity and two versions of multiple conclusion uniformity all of which remedy the problems which plague uniformity. 1 Department of Computer Scie...
A Survey of Linear Logic Programming
 Computational Logic
, 1995
"... Abstract. Logic programming can be given a foundation in sequent calculus, viewing computation as the process of building a cutfree sequent proof from the bottomup. Earliest accounts of logic programming were based in classical logic and then later in intuitionistic logic. The use of linear logic ..."
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Abstract. Logic programming can be given a foundation in sequent calculus, viewing computation as the process of building a cutfree sequent proof from the bottomup. Earliest accounts of logic programming were based in classical logic and then later in intuitionistic logic. The use of linear logic to design new logic programming languages was inevitable given that it allows for more dynamics in the way sequents change during the search for a proof and since it can account for logic programming in these other logics. We overview how linear logic has been used to design new logic programming languages and describe some applications and implementation issues for such languages. §1. Introduction. It is now common place to recognize the important role of logic in the foundations of computer science in general and programming languages more specifically. For this reason, when a major new advance is made in our understanding of logic, we can expect to see that advance ripple into other areas of computer science. Such rippling has been observed during the years