**Abstract ** We proposed a syntactical format, the _path_ format, for
structured operational semantics in which predicates may occur. We proved
that strong bisimulation is a congruence for all the operators that can
be defined within the _path_ format. To show that this format is useful
we provided many examples that we took from the literature about CCS,
CSP, and ACP; they do satisfy the _path_ format but no formats proposed
by others. The examples include concepts like termination, convergence,
divergence, weak bisimulation, a zero object, side conditions, functions,
real time, discrete time, sequencing, negative premises, negative
conclusions, and priorities (or a combination of these notions).

Keywords and Phrases: structured operational semantics, term deduction system, transition system specification, structured state system, labelled transition system, strong bisimulation, congruence theorem, predicate.

1980 Mathematics Suject Classification (1985 Revision): 68Q05, 68Q55. CR Categories: D.3.1, F.1.1, F.3.2, F.4.3.

Note: Partial support received from the European Communities under CONCUR 2, BRA 7166.

**Abstract** We prove a general conservative extension theorem for
transition system based process theories with easy-to-check and reasonable
conditions. The core of this result is another general theorem giving
sufficient conditions for a system of operational rules and an extension
ensuring that provable transitions from an original term in the extension
are the same as in the original system. As a simple corollary of the
conservative extension theorem we prove a completeness theorem. As a
first application of our conservativity results, we prove a general
theorem giving sufficient conditions to reduce the question of ground
confluence modulo some equations for a large term rewriting system
associated with an equational process theory to a small term rewriting
system under the condition that the large system is a conservative
extension of the small one. We provide many other applications to show
that our results are useful. The applications include (but are not
limited to) various real and discrete time settings in \ccs, \acp, and
\atp\ and the notions projection, renaming, state operator, priority,
recursion, the silent step (both the weak and branching variants),
and the empty process (or combinations of these notions).

Keyword Codes: F.1.2, F.3.2, F.4.3.

Keywords: Concurrency; Operational Semantics; Algebraic language theory.

**Abstract**
We prove a general conservative extension theorem for transition system
based process theories with easy-to-check and reasonable conditions.
The core of this result is another general theorem which gives sufficient
conditions for a system of operational rules and an extension of it in
order to ensure conservativity, that is,
provable transitions from an original term in the
extension are the same as in the original system. As a simple corollary
of the conservative extension theorem we prove a completeness theorem.
We also prove a general
theorem giving sufficient conditions to reduce the question of ground
confluence modulo some equations for a large term rewriting system
associated with an equational process theory to a small term rewriting
system under the condition that the large system is a conservative
extension of the small one. We provide many applications to
show that our results are useful.
The applications include (but are not
limited to) various real and discrete time settings in \acp, \atp, and
\ccs\ and the notions projection, renaming, state operator, priority,
recursion, the silent step, autonomous actions, the empty process,
divergence, etc.

1980 Mathematics Suject Classification (1985 Revision): 68Q05, 68Q10, 68Q42, 68Q55, 03C05.

CR Categories: D.3.1, F.1.1, F.3.2, F.4.3.

Keywords: structured operational semantics, term deduction system, transition system specification, semantic equivalence, semantic preorder, algebraic system, process algebra, conservative extension.