The use of coalgebras for the specification of dynamical systems with a hidden state space is receiving more and more attention in the years, as a valid alternative to algebraic methods based on observational equivalences. However, to our knowledge, the coalgebraic framework is still lacking a complete equational deduction calculus which enjoys properties similar to those stated in Birkhoff's completeness theorem for the algebraic case. In this paper we present a sound and complete equational calculus for a restricted class of coalgebras. We compare our notion of coalgebraic equation to others in the literature, and we hint at possible extensions of our framework.
A Completeness result for equational deduction in coalgebraic specification
CORRADINI, ANDREA
1998-01-01
Abstract
The use of coalgebras for the specification of dynamical systems with a hidden state space is receiving more and more attention in the years, as a valid alternative to algebraic methods based on observational equivalences. However, to our knowledge, the coalgebraic framework is still lacking a complete equational deduction calculus which enjoys properties similar to those stated in Birkhoff's completeness theorem for the algebraic case. In this paper we present a sound and complete equational calculus for a restricted class of coalgebras. We compare our notion of coalgebraic equation to others in the literature, and we hint at possible extensions of our framework.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
