Algorithmic logic. Multiple-valued extensions

Extended algorithmic logic (EAL) as introduced in 18] is a modified version of extended ⁺-valued algorithmic logic. Only two-valued predicates and two-valued propositional variables occur in EAL. The role of the ⁺-valued logic is restricted to construct control systems (stacks) of pushdown algorithms whereas their actions are described by means of the two-valued logic. Thus EAL formalizes a programming theory with recursive procedures but without the instruction CASE.The aim of this paper is to discuss EAL and prove the completeness theorem. A complete formalization of EAL was announced in 20] but no proof of the completeness theorem was given.