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33
The Logic of Bunched Implications
 BULLETIN OF SYMBOLIC LOGIC
, 1999
"... We introduce a logic BI in which a multiplicative (or linear) and an additive (or intuitionistic) implication live sidebyside. The propositional version of BI arises from an analysis of the prooftheoretic relationship between conjunction and implication; it can be viewed as a merging of intuition ..."
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Cited by 194 (38 self)
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We introduce a logic BI in which a multiplicative (or linear) and an additive (or intuitionistic) implication live sidebyside. The propositional version of BI arises from an analysis of the prooftheoretic relationship between conjunction and implication; it can be viewed as a merging of intuitionistic logic and multiplicative intuitionistic linear logic. The naturality of BI can be seen categorically: models of propositional BI's proofs are given by bicartesian doubly closed categories, i.e., categories which freely combine the semantics of propositional intuitionistic logic and propositional multiplicative intuitionistic linear logic. The predicate version of BI includes, in addition to standard additive quantifiers, multiplicative (or intensional) quantifiers # new and # new which arise from observing restrictions on structural rules on the level of terms as well as propositions. We discuss computational interpretations, based on sharing, at both the propositional and predic...
A metanotation for protocol analysis
 in: Proc. CSFW’99
, 1999
"... Most formal approaches to security protocol analysis are based on a set of assumptions commonly referred to as the “DolevYao model. ” In this paper, we use a multiset rewriting formalism, based on linear logic, to state the basic assumptions of this model. A characteristic of our formalism is the w ..."
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Cited by 142 (33 self)
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Most formal approaches to security protocol analysis are based on a set of assumptions commonly referred to as the “DolevYao model. ” In this paper, we use a multiset rewriting formalism, based on linear logic, to state the basic assumptions of this model. A characteristic of our formalism is the way that existential quantification provides a succinct way of choosing new values, such as new keys or nonces. We define a class of theories in this formalism that correspond to finitelength protocols, with a bounded initialization phase but allowing unboundedly many instances of each protocol role (e.g., client, server, initiator, or responder). Undecidability is proved for a restricted class of these protocols, and PSPACEcompleteness is claimed for a class further restricted to have no new data (nonces). Since it is a fragment of linear logic, we can use our notation directly as input to linear logic tools, allowing us to do proof search for attacks with relatively little programming effort, and to formally verify protocol transformations and optimizations. 1
A concurrent logical framework I: Judgments and properties
, 2003
"... The Concurrent Logical Framework, or CLF, is a new logical framework in which concurrent computations can be represented as monadic objects, for which there is an intrinsic notion of concurrency. It is designed as a conservative extension of the linear logical framework LLF with the synchronous con ..."
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Cited by 73 (25 self)
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The Concurrent Logical Framework, or CLF, is a new logical framework in which concurrent computations can be represented as monadic objects, for which there is an intrinsic notion of concurrency. It is designed as a conservative extension of the linear logical framework LLF with the synchronous connectives# of intuitionistic linear logic, encapsulated in a monad. LLF is itself a conservative extension of LF with the asynchronous connectives #, & and #.
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 28 (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
Logic Programming and MultiAgent Systems: A Synergic Combination for Applications and Semantics
 IN THE LOGIC PROGRAMMING PARADIGM  A 25YEAR PERSPECTIVE
, 1999
"... ..."
A Relevant Analysis of Natural Deduction
 Journal of Logic and Computation
, 1999
"... Linear and other relevant logics have been studied widely in mathematical, philosophical and computational logic. We describe a logical framework, RLF, for defining natural deduction presentations of such logics. RLF consists in a language together, in a manner similar to that of Harper, Honsell and ..."
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Cited by 23 (7 self)
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Linear and other relevant logics have been studied widely in mathematical, philosophical and computational logic. We describe a logical framework, RLF, for defining natural deduction presentations of such logics. RLF consists in a language together, in a manner similar to that of Harper, Honsell and Plotkin's LF, with a representation mechanism: the language of RLF is the lLcalculus; the representation mechanism is judgementsastypes, developed for relevant logics. The lLcalculus type theory is a firstorder dependent type theory with two kinds of dependent function spaces: a linear one and an intuitionistic one. We study a natural deduction presentation of the type theory and establish the required prooftheoretic metatheory. The RLF framework is a conservative extension of LF. We show that RLF uniformly encodes (fragments of) intuitionistic linear logic, Curry's l I calculus and ML with references. We describe the CurryHowardde Bruijn correspondence of the lLcalculus with a s...
Frühwirth: A LinearLogic Semantics For Constraint Handling Rules
 Proceedings of CP 2005
, 2005
"... Abstract. We motivate and develop a linear logic declarative semantics for CHR ∨ , an extension of the CHR programming language that integrates concurrent committed choice with backtrack search and a predefined underlying constraint handler. We show that our semantics maps each of these aspects of t ..."
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Cited by 23 (10 self)
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Abstract. We motivate and develop a linear logic declarative semantics for CHR ∨ , an extension of the CHR programming language that integrates concurrent committed choice with backtrack search and a predefined underlying constraint handler. We show that our semantics maps each of these aspects of the language to a distinct aspect of linear logic. We show how we can use this semantics to reason about derivations in CHR ∨ and we present strong theorems concerning its soundness and completeness. 1
Analysis of Security Protocols
 IN CALCULATIONAL SYSTEM DESIGN, SERIES F: COMPUTER AND SYSTEMS SCIENCES
, 1999
"... Several approaches have been developed for analyzing security protocols. Most formal approaches are based on a set of assumptions commonly referred to as the "DolevYao model." In this paper, we use a formalism based on multiset rewriting to describe these modeling assumptions and explain how the ..."
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Cited by 21 (4 self)
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Several approaches have been developed for analyzing security protocols. Most formal approaches are based on a set of assumptions commonly referred to as the "DolevYao model." In this paper, we use a formalism based on multiset rewriting to describe these modeling assumptions and explain how they are used in protocol analysis.
Efficient implementation of a linear logic programming language
 Proceedings of the 1998 Joint International Conference and Symposium on Logic Programming
, 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 14 (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 significant performance advantages relative to their traditional Prolog implementations.
A Bottomup Semantics for Linear Logic Programs
 In Proceedings of PPDP'00
, 2000
"... The operational semantics of linear logic programming languages is given in terms of goaldriven sequent calculi. The prooftheoretic presentation is the natural counterpart of the topdown semantics of traditional logic programs. In this paper we investigate the theoretical foundation of an alterna ..."
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Cited by 8 (8 self)
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The operational semantics of linear logic programming languages is given in terms of goaldriven sequent calculi. The prooftheoretic presentation is the natural counterpart of the topdown semantics of traditional logic programs. In this paper we investigate the theoretical foundation of an alternative operational semantics based on a bottomup evaluation of linear logic programs via a fixpoint operator. The bottomup fixpoint semantics is important in applications like active databases, and, more in general, for program analysis and verification. As a first casestudy, we consider Andreoli and Pareschi's LO [4] enriched with the constant 1. For this language, we give a fixpoint semantics based on an operator defined in the style of TP . We give an algorithm to compute a single application of the fixpoint operator where constraints are used to represent in a finite way possibly infinite sets of provable goals. Furthermore, we show that the fixpoint semantics for propositional LO without the const...