Interpolation and the Robinson property for logics not closed under the Boolean operations.

A variant of the Robinson property (ROB) is introduced. The property ROB is equivalent to the usual Robinson property and hence is equivalent also to the interpolation property, in any compact logic closed under the Boolean operations. On the other hand, it will be shown that ROB is not always equal to the interpolation property, if a logic is not closed under them. Next, we will study ROB and various interpolation properties for equational logics, which are typical examples of compact logics not closed under the Boolean operations. It will be shown that an equational logic has ROB if and only if it has the amalgamation property for isomorphic embeddings. [ABSTRACT FROM AUTHOR]