Abstract. This is an attempt to create a partial elementary logic system which would provide a basis for the construction of cylindric algebras describing properties of partial relations. The intended link between such partial logic and the corresponding cylindric algebra theory should be analogous to that which relates classic elementary logic to "classic" cylindric algebras. After introducing basic notions and elementary properties of the system, we prove a completeness theorem. The proof is based on a standard idea, even if its realization is non-standard due to the partiality of relations in models. The approach presented in this paper is, in some model-theoretic sense, a generalization of the presentation of classic relational systems and algebras (partial or total) in the first order language. Some arguments concerning the last statement are contained in the series of informal remarks of model-theoretic and categorical nature, carried on paralelly to the main stream of the work.

AMS Subject Classification (1991): 03B60, 03C07, 03C35, 03C52, 18A15

Received April 3, 1995 and in revised form February 11, 1997. (Registered under 6101/2009.)