The π-calculus as a theory in linear logic: Preliminary results

The π-calculus as a theory in linear logic: Preliminary results (1993)

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by Dale Miller

Venue:	3rd Workshop on Extensions to Logic Programming, LNCS 660
Citations:	99 - 17 self

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Datum	Value	Source
TITLE	The π-calculus as a theory in linear logic: Preliminary results	INFERENCE
AUTHOR NAME	Dale Miller	SVM HeaderParse 0.2
AUTHOR AFFIL	Computer Science Department; University of Pennsylvania	SVM HeaderParse 0.2
AUTHOR ADDR	Philadelphia, PA 19104-6389 USA	SVM HeaderParse 0.2
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 π0, the “propositional ” fragment of the π-calculus, which lacks restriction and value passing (π0 is a subset of CCS). Using ideas from proof-theory, we introduce co-agents and show that they can specify some testing equivalences for π0. 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. 1	SVM HeaderParse 0.2
YEAR	1993	INFERENCE
VENUE	3rd Workshop on Extensions to Logic Programming, LNCS 660	INFERENCE
VENUE TYPE	CONFERENCE	INFERENCE
PAGES	242--265	INFERENCE
CITATIONS	15 found	ParsCit 1.0