We investigate amalgamation properties of relational type algebras. Besides purely algebraic interest, amalgamation in a class of algebras is important because it leads to interpolation results for the logic corresponding to that class (cf. ). The multi-modal logic corresponding to relational type algebras became known under the name of “arrow logic” (cf. [18, 17]), and has been studied rather extensively lately (cf. ). Our research was inspired by the following result of Andréka et al. .
Let K be a class of relational type algebras such that
(i) composition is associative,
(ii) K is a class of boolean algebras with operators, and
(iii) K contains the representable relation algebras RRA.
Then the equational theory of K is undecidable.
On the other hand, there are several classes of relational type algebras (e.g., NA, WA denned below) whose equational (even universal) theories are decidable (cf. ). Composition is not associative in these classes. Theorem 5 indicates that also with respect to amalgamation (a very weak form of) associativity forms a borderline. We first recall the relevant definitions.