Multimodal logic as a base of algorithmic logic. (English) Zbl 0533.03004

Mirkowska, Grażyna

Seminarber., Humboldt-Univ. Berlin, Sekt. Math. 52, 65-68 (1983).

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