Results 1  10
of
24
Decision Problems for Propositional Linear Logic
, 1990
"... Linear logic, introduced by Girard, is a refinement of classical logic with a natural, intrinsic accounting of resources. We show that unlike most other propositional (quantifierfree) logics, full propositional linear logic is undecidable. Further, we prove that without the modal storage operator, ..."
Abstract

Cited by 111 (19 self)
 Add to MetaCart
Linear logic, introduced by Girard, is a refinement of classical logic with a natural, intrinsic accounting of resources. We show that unlike most other propositional (quantifierfree) logics, full propositional linear logic is undecidable. Further, we prove that without the modal storage operator, which indicates unboundedness of resources, the decision problem becomes pspacecomplete. We also establish membership in np for the multiplicative fragment, npcompleteness for the multiplicative fragment extended with unrestricted weakening, and undecidability for certain fragments of noncommutative propositional linear logic. 1 Introduction Linear logic, introduced by Girard [14, 18, 17], is a refinement of classical logic which may be derived from a Gentzenstyle sequent calculus axiomatization of classical logic in three steps. The resulting sequent system Lincoln@CS.Stanford.EDU Department of Computer Science, Stanford University, Stanford, CA 94305, and the Computer Science Labo...
Multiset Rewriting and the Complexity of Bounded Security Protocols
 Journal of Computer Security
, 2002
"... We formalize the DolevYao model of security protocols, using a notation based on multiset rewriting with existentials. The goals are to provide a simple formal notation for describing security protocols, to formalize the assumptions of the DolevYao model using this notation, and to analyze the ..."
Abstract

Cited by 74 (9 self)
 Add to MetaCart
We formalize the DolevYao model of security protocols, using a notation based on multiset rewriting with existentials. The goals are to provide a simple formal notation for describing security protocols, to formalize the assumptions of the DolevYao model using this notation, and to analyze the complexity of the secrecy problem under various restrictions. We prove that, even for the case where we restrict the size of messages and the depth of message encryption, the secrecy problem is undecidable for the case of an unrestricted number of protocol roles and an unbounded number of new nonces. We also identify several decidable classes, including a dexpcomplete class when the number of nonces is restricted, and an npcomplete class when both the number of nonces and the number of roles is restricted. We point out a remaining open complexity problem, and discuss the implications these results have on the general topic of protocol analysis.
A Brief Guide to Linear Logic
, 1993
"... An overview of linear logic is given, including an extensive bibliography and a simple example of the close relationship between linear logic and computation. ..."
Abstract

Cited by 56 (10 self)
 Add to MetaCart
An overview of linear logic is given, including an extensive bibliography and a simple example of the close relationship between linear logic and computation.
HigherOrder, Linear, Concurrent Constraint Programming
, 1992
"... We present a very simple and powerful framework for indeterminate, asynchronous, higherorder computation based on the formulaasagent and proofascomputation interpretation of (higherorder) linear logic [Gir87]. The framework significantly refines and extends the scope of the concurrent constrai ..."
Abstract

Cited by 34 (6 self)
 Add to MetaCart
We present a very simple and powerful framework for indeterminate, asynchronous, higherorder computation based on the formulaasagent and proofascomputation interpretation of (higherorder) linear logic [Gir87]. The framework significantly refines and extends the scope of the concurrent constraint programming paradigm [Sar89] in two fundamental ways: (1) by allowing for the consumption of information by agents it permits a direct modelling of (indeterminate) state change in a logical framework, and (2) by admitting simplytyped terms as dataobjects, it permits the construction, transmission and application of (abstractions of) programs at runtime. Much more dramatically, however, the framework can be seen as presenting higherorder (and if desired, constraintenriched) versions of a variety of other asynchronous concurrent systems, including the asynchronous ("input guarded") fragment of the (firstorder) ßcalculus, Hewitt's actors formalism, (abstract forms of) Gelernter's Lin...
Chu spaces and their interpretation as concurrent objects
, 2005
"... A Chu space is a binary relation =  from a set A to an antiset X defined as a set which transforms via converse functions. Chu spaces admit a great many interpretations by virtue of realizing all small concrete categories and most large ones arising in mathematical and computational practice. Of pa ..."
Abstract

Cited by 34 (0 self)
 Add to MetaCart
(Show Context)
A Chu space is a binary relation =  from a set A to an antiset X defined as a set which transforms via converse functions. Chu spaces admit a great many interpretations by virtue of realizing all small concrete categories and most large ones arising in mathematical and computational practice. Of particular interest for computer science is their interpretation as computational processes, which takes A to be a schedule of events distributed in time, X to be an automaton of states forming an information system in the sense of Scott, and the pairs (a, x) in the =  relation to be the individual transcriptions of the making of history. The traditional homogeneous binary relations of transition on X and precedence on A are recovered as respectively the right and left residuals of the heterogeneous binary relation =  with itself. The natural algebra of Chu spaces is that of linear logic, made a process algebra by the process interpretation.
Petri Nets as Models of Linear Logic
 Proceedings of Colloquium on Trees in Algebra and Programming
, 1990
"... The chief purpose of this paper is to appraise the feasibility of Girard's linear logic as a specification language for parallel processes. To this end we propose an interpretation of linear logic in Petri nets, with respect to which we investigate the expressive power of the logic. 1 Intro ..."
Abstract

Cited by 34 (2 self)
 Add to MetaCart
The chief purpose of this paper is to appraise the feasibility of Girard's linear logic as a specification language for parallel processes. To this end we propose an interpretation of linear logic in Petri nets, with respect to which we investigate the expressive power of the logic. 1 Introduction Girard's linear logic has sparked off a great deal of interest in how it might be useful in the theory of parallelism, not least because of Girard's initial claims for it [Gir87]. Linear logic has been described as a "resource conscious" logic by Mart'iOliet and Meseguer [MOM89]; in its proofs occurrences of propositions cannot be used more than once or disappear unless they are explicitly created or used up by the rules of inference. People were not long in spotting a relationship with Petri nets where there are similar ideas. Places in a Petri net hold to certain nonnegative multiplicities forming a multiset of places, traditionally called a marking; as transitions occur, multipliciti...
A Concurrent Logical Framework: The Propositional Fragment
, 2003
"... We present the propositional fragment CLF0 of the Concurrent Logical Framework (CLF). CLF extends the Linear Logical Framework to allow the natural representation of concurrent computations in an object language. The underlying type theory uses monadic types to segregate values from computations ..."
Abstract

Cited by 31 (3 self)
 Add to MetaCart
(Show Context)
We present the propositional fragment CLF0 of the Concurrent Logical Framework (CLF). CLF extends the Linear Logical Framework to allow the natural representation of concurrent computations in an object language. The underlying type theory uses monadic types to segregate values from computations. This separation leads to a tractable notion of definitional equality that identifies computations di#ering only in the order of execution of independent steps. From a logical point of view our type theory can be seen as a novel combination of lax logic and dual intuitionistic linear logic. An encoding of a small Petri net exemplifies the representation methodology, which can be summarized as "concurrent computations as monadic expressions ".
Deciding Provability of Linear Logic Formulas
 Advances in Linear Logic
, 1994
"... Introduction There are many interesting fragments of linear logic worthy of study in their own right, most described by the connectives which they employ. Full linear logic includes all the logical connectives, which come in three dual pairs: the exponentials ! and ?, the additives & and \Phi, ..."
Abstract

Cited by 30 (0 self)
 Add to MetaCart
(Show Context)
Introduction There are many interesting fragments of linear logic worthy of study in their own right, most described by the connectives which they employ. Full linear logic includes all the logical connectives, which come in three dual pairs: the exponentials ! and ?, the additives & and \Phi, and the multiplicatives\Omega and . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........ . SRI International Computer Science Laboratory, Menlo Park CA 94025 USA. Work supported under NSF Grant CCR9224858. lincoln@csl.sri.com http://www.csl.sri.com/lincoln/lincoln.html Patrick Lincoln For the most part we will consider fragments of linear logic built up using these connectives in any combination. For example, full linear logic formulas may employ any connective, while multiplic
Interpreting Strands in Linear Logic
, 2000
"... The adoption of the DolevYao model, an abstraction of security protocols that supports symbolic reasoning, is responsible for many successes in protocol analysis. In particular, it has enabled using logic effectively to reason about protocols. One recent framework for expressing the basic assumptio ..."
Abstract

Cited by 24 (13 self)
 Add to MetaCart
(Show Context)
The adoption of the DolevYao model, an abstraction of security protocols that supports symbolic reasoning, is responsible for many successes in protocol analysis. In particular, it has enabled using logic effectively to reason about protocols. One recent framework for expressing the basic assumptions of the DolevYao model is given by strand spaces, certain directed graphs whose structure reflects causal interactions among protocol participants. We represent strand constructions as relatively simple formulas in firstorder linear logic, a refinement of traditional logic known for an intrinsic and natural accounting of process states, events, and resources. The proposed encoding is shown to be sound and complete. Interestingly, this encoding differs from the multiset rewriting definition of the DolevYao model, which is also based on linear logic. This raises the possibility that the multiset rewriting framework may differ from strand spaces in some subtle way, although the two settings are known to agree on the basic secrecy property. 1 Introduction In recent years, a variety of methods have been developed for analyzing and reasoning about protocols based on cryptographic primitives. Although there are many differences among these proposals, most current formal approaches use the socalled "DolevYao" model of adversary capabilities, which appears to be drawn from positions taken in [34] and from a simplified model presented in [11]. In this idealized setting, a protocol adversary is allowed to nondeterministically choose among possible actions. Messages are composed of indivisible abstract values, not sequences of bits, and encryption is modeled in an idealized way. The adversary may only send messages comprised of data it "knows" as the result of overhearing past transmissions.
Linear Logic
, 1992
"... this paper we will restrict attention to propositional linear logic. The sequent calculus notation, due to Gentzen [10], uses roman letters for propositions, and greek letters for sequences of formulas. A sequent is composed of two sequences of formulas separated by a `, or turnstile symbol. One may ..."
Abstract

Cited by 23 (1 self)
 Add to MetaCart
(Show Context)
this paper we will restrict attention to propositional linear logic. The sequent calculus notation, due to Gentzen [10], uses roman letters for propositions, and greek letters for sequences of formulas. A sequent is composed of two sequences of formulas separated by a `, or turnstile symbol. One may read the sequent \Delta ` \Gamma as asserting that the multiplicative conjunction of the formulas in \Delta together imply the multiplicative disjunction of the formulas in \Gamma. A sequent calculus proof rule consists of a set of hypothesis sequents, displayed above a horizontal line, and a single conclusion sequent, displayed below the line, as below: Hypothesis1 Hypothesis2 Conclusion 4 Connections to Other Logics