The Pi-Calculus as a Theory in Linear Logic: Preliminary Results

Loading...
Thumbnail Image
Penn collection
Technical Reports (CIS)
Degree type
Discipline
Subject
Funder
Grant number
License
Copyright date
Distributor
Related resources
Author
Miller, Dale
Contributor
Abstract

The agent expressions of the π-calculus can be translated into a theory of linear logic in such a way that the reflective and transitive closure of π-calculus (unlabeled) reduction is identified with "entailed-by". Under this translation, parallel composition is mapped to the multiplicative disjunct ("par") and restriction is mapped to universal quantification. Prefixing, non-deterministic choice (+), replication (!), and the match guard are all represented using non-logical constants, which are specified using a simple form of axiom, called here a process clause. These process clauses resemble Horn clauses except that they may have multiple conclusions; that is, their heads may be the par of atomic formulas. Such multiple conclusion clauses are used to axiomatize communications among agents. Given this translation, it is nature to ask to what extent proof theory can be used to understand the meta-theory of the π-calculus. We present some preliminary results along this line for πo, the "propositional" fragment of the π-calculus, which lacks restriction and value passing (πo is a subset of CCS). Using ideas from proof-theory, we introduce co-agents and show that they can specify some testing equivalences for πo. If negation-as-failure-to-prove is permitted as a co-agent combinator, then testing equivalence based on co-agents yields observational equivalence for π0. This latter result follows from observing that co-agents directly represent formulas in the Hennessy-Milner modal logic.

Advisor
Date Range for Data Collection (Start Date)
Date Range for Data Collection (End Date)
Digital Object Identifier
Series name and number
Publication date
1992-10-01
Volume number
Issue number
Publisher
Publisher DOI
Journal Issue
Comments
University of Pennsylvania Department of Computer and Information Science Technical Report No. MS-CIS-92-48.
Recommended citation
Collection