Results 11  20
of
34
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
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 ".
Logic Programming and MultiAgent Systems: A Synergic Combination for Applications and Semantics
 IN THE LOGIC PROGRAMMING PARADIGM  A 25YEAR PERSPECTIVE
, 1999
"... ..."
Using Linear Logic to Reason About Sequent Systems
 PROCEEDINGS OF TABLEAUX 2002, LNAI 2381
, 2002
"... Linear logic can be used as a metalogic for the specification of some sequent calculus proof systems. We explore in this paper properties of such linear logic specifications. We show that derivability of one proof system from another has a simple decision procedure that is implemented simply vi ..."
Abstract

Cited by 22 (4 self)
 Add to MetaCart
Linear logic can be used as a metalogic for the specification of some sequent calculus proof systems. We explore in this paper properties of such linear logic specifications. We show that derivability of one proof system from another has a simple decision procedure that is implemented simply via bounded logic programming search. We also provide conditions to ensure that an encoded proof system has the cutelimination property and show that this can be decided again by simple, bounded proof search algorithms.
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 21 (10 self)
 Add to MetaCart
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.
Substructural Operational Semantics as Ordered Logic Programming
"... We describe a substructural logic with ordered, linear, and persistent propositions and then endow a fragment with a committed choice forwardchaining operational interpretation. Exploiting higherorder terms in this metalanguage, we specify the operational semantics of a number of object language f ..."
Abstract

Cited by 12 (9 self)
 Add to MetaCart
We describe a substructural logic with ordered, linear, and persistent propositions and then endow a fragment with a committed choice forwardchaining operational interpretation. Exploiting higherorder terms in this metalanguage, we specify the operational semantics of a number of object language features, such as callbyvalue, callbyname, callbyneed, mutable store, parallelism, communication, exceptions and continuations. The specifications exhibit a high degree of uniformity and modularity that allows us to analyze the structural properties required for each feature in isolation. Our substructural framework thereby provides a new methodology for language specification that synthesizes structural operational semantics, abstract machines, and logical approaches. 1
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 ..."
Abstract

Cited by 10 (1 self)
 Add to MetaCart
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...
A Logic for Reasoning with HigherOrder Abstract Syntax
"... Logical frameworks based on intuitionistic or linear logics with highertype quantification have been successfully used to give highlevel, modular, and formal specifications of many important judgments in the area of programming languages and inference systems. Given such specifications, it is natu ..."
Abstract

Cited by 7 (2 self)
 Add to MetaCart
Logical frameworks based on intuitionistic or linear logics with highertype quantification have been successfully used to give highlevel, modular, and formal specifications of many important judgments in the area of programming languages and inference systems. Given such specifications, it is natural to consider proving properties about the specified systems in the framework: for example, given the specification of evaluation for a functional programming language, prove that the language is deterministic or that the subjectreduction theorem holds. One challenge in developing a framework for such reasoning is that higherorder abstract syntax (HOAS), an elegant and declarative treatment of objectlevel abstraction and substitution,is difficult to treat in proofs involving induction. In this paper, we present a metalogic that can be used to reason about judgments coded using HOAS; this metalogic is an extension of a simple intuitionistic logic that admits higherorder quantification over simply typedterms (key ingredients for HOAS) as well as induction and a notion of definition. The latter concept of a definition is a prooftheoretic device that allows certain theories to be treated as “closed ” or as defining fixed points. The resulting metalogic can specify various logical frameworks and a large range of judgments regarding programming languages and inference systems. We illustrate this point through examples, including the admissibility of cut for a simple logic and subject reduction, determinacy of evaluation, and the equivalence of SOS and natural semantics presentations of evaluation for a simple functional programming language. 1.
A New Framework for Declarative Programming
, 2001
"... We propose a new indexedcategory syntax and semantics of Weak Hereditarily Harrop logic programming with constraints, based on resolution over taucategories:finite product categories with canonical structure. ..."
Abstract

Cited by 6 (3 self)
 Add to MetaCart
We propose a new indexedcategory syntax and semantics of Weak Hereditarily Harrop logic programming with constraints, based on resolution over taucategories:finite product categories with canonical structure.
Lógica Linear E a Especificação De Sistemas Computacionais
, 2001
"... In recent years, intuitionistic logic and type systems have been used in numerous computational logical systems as frameworks for the specification of natural deduction proof systems. As we shall illustrate here, linear logic can be similarly used to specify the more general setting of sequent calcu ..."
Abstract

Cited by 6 (2 self)
 Add to MetaCart
In recent years, intuitionistic logic and type systems have been used in numerous computational logical systems as frameworks for the specification of natural deduction proof systems. As we shall illustrate here, linear logic can be similarly used to specify the more general setting of sequent calculus proof systems and provides rich forms of analysis and deduction of properties of the specified systems. We shall present several example encodings of sequent calculus proof systems using the Forum presentation of linear logic: linear logic is a resource conscious logic developed by Girard, and Forum is an abstract logic programming language associated to it, due to Miller. We start by proposing an encoding of sequents, rules and systems. Then a correctness result is proved for these encodings and it is observed that metalevel proofs match closely the objectlevel ones. The encoding of an objectlevel proof system as Forum clauses has certain advantages over encoding them as inference figures. For example, Forum specifications do not deal with context explicitly and instead it only focuses on the formulas that are directly involved in the inference rule. The distinction between making the inference rule additive or multiplicative is achieved in inference rule figures by explicitly presenting contexts and either splitting or copying them. The Forum clause representation achieves the same distinction using metalevel additive or multiplicative connectives. Objectlevel quantifiers can be handled directly using the metalevel quantification. Similarly, the structural rules of contraction and weakening can be captured together using the ? modal. Finally, since the encoding of proof systems is natural and direct, we are able to use the rich metatheory of linear logic to help ...
Specifying Properties of Concurrent Computations in CLF
, 2004
"... CLF (the Concurrent Logical Framework) is a language for specifying and reasoning about concurrent systems. Its most significant feature is the firstclass representation of concurrent executions as monadic expressions. We illustrate the representation techniques available within CLF by applying the ..."
Abstract

Cited by 5 (4 self)
 Add to MetaCart
CLF (the Concurrent Logical Framework) is a language for specifying and reasoning about concurrent systems. Its most significant feature is the firstclass representation of concurrent executions as monadic expressions. We illustrate the representation techniques available within CLF by applying them to an asynchronous picalculus with correspondence assertions, including its dynamic semantics, safety criterion, and a type system with latent effects due to Gordon and Jeffrey.