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Multimodal logic as a base of algorithmic logic. (English) Zbl 0533.03004
This paper considers propositional modal logics with a bundle of modalities. Each modality is intended intuitively to be the input-output relationship of a program, yielding a binary relation of the so-called Kripke sort formally. After claiming the completeness theorem, the author considers within this framework how we should characterize program connectives of algorithmic logic such as ”either $$\alpha$$ or $$\beta$$ ” syntactially, only to leave the characterization of the elusive connective ”while P do $$\alpha$$ ” open.
Reviewer: H.Nishimura
##### MSC:
 03B45 Modal logic (including the logic of norms) 68Q65 Abstract data types; algebraic specification
##### Keywords:
modal logic; algorithmic logic; Kripke semantics