This chapter emphasizes that the approach taken in which a formal semantics for sentential modal logic can be constructed, is the first taken in the history of this subject. It describes as an extension of the matrix semantics that was developed for sentential logic prior to the addition of modal operators, i.e. the matrix semantics of the sentential logic of modal free CN-formulas. This type of semantics is particularly important in so-called many-valued logics, i.e. logics in which it assumed that there can be truth values other than truth and falsehood. The chapter concludes that, despite the historical priority of this approach, no finite matrix (and therefore no finite system of “truth-values” provides an adequate semantics for the kinds of normal modal systems described in the previous chapter.
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