We find several large classes of equations with the property that every automorphism of the lattice of equational theories of commutative groupoids fixes any equational theory generated by such equations, and every equational theory generated by finitely many such equations is a definable element of the lattice. We conjecture that the lattice has no non-identical automorphisms.

derivations, equational logic and interpolation (extended abstract) Gerard R. Renardel de Lavalette Department of Mathematics and Computing Science University of Groningen, the Netherlands Abstract. We define abstract derivations for equational logic and use them to prove the interpolation property. We define abstract derivations for equational logic and use them to prove the interpolation prop...

We prove that the equational theory of the process algebra BCCSP modulo completed simulation equivalence does not have a finite basis. Furthermore, we prove that with a finite alphabet of actions, the equational theory of BCCSP modulo ready simulation equivalence does not have a finite basis. In contrast, with an infinite alphabet, the latter equational theory does have a finite basis.

We propose a design for the integration of decision procedures in reflective rewritingbased equational theorem provers. Rewriting-based equational theorem provers use term rewriting as their basic proof engine; they are particularly well suited for proving properties of equational specifications. A reflective rewriting-based theorem prover is itself an executable equational specification, which...

It is well known that bisimulation on μ-expressions cannot be finitely axiomatised in equational logic. Complete axiomatisations such as those of Milner and Bloom/Ésik necessarily involve implicational rules. However, both systems rely on features which go beyond pure equational Horn logic: either the rules are impure by involving non-equational side-conditions, or they are schematically infini...

The following classes of equational theories, which are important in unification theory, are presented: permutative, finite, Noetherian, simple, almost collapse free, collapse free, regular, and ~-free theories. The relationships between the particular theories are shown and the connection between these classes and the unification hierarchy is pointed out. We give an equational theory that alwa...