How Not to Combine Modal Logics

This paper describes a failed attempt to decompose the fusion of two non-normal modal logics as a composition of iterated nonnormal modalisations. That strategy had already succeeded in the transfer of soundness, completeness and decidability for normal modal logics, but we show here why it fails for the transference of some of these properties in the fusion non-normal modal logics. The possibility of the transference of these properties is not ruled out by this result. We also show that the fusion of some of the more common non-normal modal logics transfers completeness, relying directly on the properties of each of the component modal logics.

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