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Originated in logic, algebra and computer science, spi-logics have two natural semantics: meet-semilattices with monotone operators providing Birkhoff-style calculi and first-order relational structures (aka Kripke frames) often used as the intended structures in applications. Here we lay foundations for a completeness theory that aims to answer the question whether the two semantics define the same consequence relations for a given spi-logic.<\/jats:p>","DOI":"10.1017\/jsl.2019.22","type":"journal-article","created":{"date-parts":[[2019,4,3]],"date-time":"2019-04-03T08:22:43Z","timestamp":1554279763000},"page":"533-588","source":"Crossref","is-referenced-by-count":8,"title":["KRIPKE COMPLETENESS OF STRICTLY POSITIVE MODAL LOGICS OVER MEET-SEMILATTICES WITH 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