Applications of weak Kripke semantics to intermediate consequences

Studia Logica 45 (1):119 - 134 (1986)
Section 1 contains a Kripke-style completeness theorem for arbitrary intermediate consequences. In Section 2 we apply weak Kripke semantics to splittings in order to obtain generalized axiomatization criteria of the Jankov-type. Section 3 presents new and short proofs of recent results on implicationless intermediate consequences. In Section 4 we prove that these consequences admit no deduction theorem. In Section 5 all maximal logics in the 3 rd counterslice are determined. On these results we reported at the 1980 meeting on Mathematical Logic at Oberwolfach. This paper concerns propositional logic only.
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References found in this work BETA
Andrzej Wronski (1981). Quasivarieties of Heyting Algebras. Bulletin of the Section of Logic 10 (3):128-131.
Andrzej Wronski (1981). Splittings of Lattices of Quasivarieties. Bulletin of the Section of Logic 10 (3):128-129.

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Lloyd Humberstone (2013). Replacement in Logic. Journal of Philosophical Logic 42 (1):49-89.
Lloyd Humberstone (2000). Contra-Classical Logics. Australasian Journal of Philosophy 78 (4):438 – 474.

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