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We describe relations between hyper MV-algebras and hyper K-algebras and prove that a finite hyper MV-algebra satisfying the condition $0\CirclePlus x = \{x\}$, used by many authors, is in fact an ordinary MV-algebra. We also characterize relations between the main types of deductive systems of hyper MV-algebras. [ABSTRACT FROM AUTHOR]

The paper introduces an original formalization of distributed systems which work in a concurrent way, especially multi-agent systems (MAS). The described deductive system, called RA-MAS, is based on elements of branching time temporal logic, epistemic logic and algorithmic logic. The established operators and modalities allow to compare different multi-agent systems on the basis of the same formal system. Moreover, the logic provides tools for modelling and characterizing mental features of agents as well as different forms of cooperation. The main aim of the paper is to present axiomatization and prove a strong completeness result for the logic. The proof is inspired by a combination of the algebraic method of Rasiowa and Sikorski for classical logic with the Kripke method for modal logic. [ABSTRACT FROM AUTHOR]