Completeness of the equational semantics for Basic LOTOS

The logical correspondence between the equational semantics of Basic LOTOS and is standard, derivational one is proven. A derivational semantics is traditionally given by means of a set of axioms and deduction rules which define a deduction system. With such semantics, some difficulties arise when dealing with deduction rules with negative premises; also, the proof that a transition cannot take place cannot be carried out within the formal system. On the other hand, in the equational semantics approach, a transition is viewed as the application of a triadic predicate. Such a function is defined by a set of equations, and this, in a natural way, allows for the use of negative information within the system. It is shown that for Basic LOTOS, when restricted to guarded recursion, both formal reasoning systems strongly correspond. >