TY - GEN

T1 - Logic of trace languages

AU - Rabinovich, Alexander

N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1992.

PY - 1992

Y1 - 1992

N2 - Usually, laws established in process calculi have the format of equations and/or inequations between process-terms. Though such set of laws captures important properties of the underlying algebra it cannot reveal some basic logical properties of the algebra. From the logical point of view, the consequence relation associated with an algebra is much more fundamental than the set of laws valid in it. That is why in this paper our main concern is about consequence relation which provides the answer to questions in the following format (the formalization is in terms of sequents): what terms are equal under the assumption that some other pairs of terms are equal. We compare two algebras: algebra of linear trace languages and algebra of relations. The fundamental operations in trace algebra are synchronization (parallel composition) of two trace languages, nondeterministic choice and hiding of a port in a language. The corresponding operations in relational algebra are join, union and projection. We show that these algebras have the same laws, i.e. two terms have the same meaning in all trace interpretations iff they have the same meaning in all relational interpretations. Moreover, we show that these algebras have the same consequence relations. We embed both algebras into first order logic and through this embedding obtain sound and complete proof systems for reasoning about the consequence relations in these algebras.

AB - Usually, laws established in process calculi have the format of equations and/or inequations between process-terms. Though such set of laws captures important properties of the underlying algebra it cannot reveal some basic logical properties of the algebra. From the logical point of view, the consequence relation associated with an algebra is much more fundamental than the set of laws valid in it. That is why in this paper our main concern is about consequence relation which provides the answer to questions in the following format (the formalization is in terms of sequents): what terms are equal under the assumption that some other pairs of terms are equal. We compare two algebras: algebra of linear trace languages and algebra of relations. The fundamental operations in trace algebra are synchronization (parallel composition) of two trace languages, nondeterministic choice and hiding of a port in a language. The corresponding operations in relational algebra are join, union and projection. We show that these algebras have the same laws, i.e. two terms have the same meaning in all trace interpretations iff they have the same meaning in all relational interpretations. Moreover, we show that these algebras have the same consequence relations. We embed both algebras into first order logic and through this embedding obtain sound and complete proof systems for reasoning about the consequence relations in these algebras.

UR - http://www.scopus.com/inward/record.url?scp=0347011708&partnerID=8YFLogxK

U2 - 10.1007/bfb0084812

DO - 10.1007/bfb0084812

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AN - SCOPUS:0347011708

SN - 9783540558224

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 504

EP - 517

BT - CONCUR 1992 - 3rd International Conference on Concurrency Theory, Proceedings

A2 - Cleaveland, W. Rance

PB - Springer Verlag

T2 - 3rd International Conference on Concurrency Theory, CONCUR 1992

Y2 - 24 August 1992 through 27 August 1992

ER -