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We investigate the notion of "semicomputability," intended to generalize the notion of recursive enumerability of relations to abstract structures. Two characterizations are considered and shown to be equivalent: one in terms of " partial computable functions' ' (for a suitable notion of computability over abstract structures) and one in terms of definability by means of Horn programs over such structures. This leads to the formulation of a "Generalized Church-Turing Thesis" for definability of relations on abstract structures. adoi:10.1016/0743-1066(92)90020-4 fatcat:ghcujd36yzaebmrd33x6yfy6by