We formalize equational propositional logic, prove that it is sound and complete, and compare the equational-proof style with the more traditional Hilbert style.

We propose an extension of purely equational reasoning with an induction rule, to obtain an intermediate between the equational theory of an algebraic specification and its !-closure.

We show that for every quasivariety K of relational structures there is a semilattice S with operators such that the lattice of quasiequational theories of K (the dual of the lattice of sub-quasivarieties of K) is isomorphic to Con(S,+, 0, F). As a consequence, new restrictions on the natural quasi-interior operator on lattices of quasi-equational theories are found. 1. Motivation and terminolo...

This paper studies the (in)equational theory of simulation preorder and equivalence over the process algebra BCCSP. We prove that in the presence of a finite alphabet with at least two actions, the (in)equational theory of BCCSP modulo simulation preorder or equivalence does not have a finite basis. In contrast, in the presence of an alphabet that is infinite or a singleton, the equational theo...