The primary aim of the paper is to introduce a new notion of relevance of the antecedent of a true implication statement to its consequent, and to sketch a formalization of the new notion. The formalization is set up in the framework of the so called 'Logic of Strict Processes (LSP)', as articulated by the author in collaboration with J. Podrouzek. Their approach to the relevance is presented as a natural part of a wider specter of logics, including modal and relevance logics. The formalization is compared with consequence relations in normal modal logic and in the relevance logic R. In conclusion the author outlines the most important problems of LSP, which still remain open.
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