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Game-theoretical semantics (GTS) is one of the most important approaches to logical and semantical theory. (For a survey, see Hintikka and Sandu (1997).) It has prompted several new developments in different directions. Among other things, it has helped to bring out the prima facie surprising fact that the received first-order logic (quantification theory) is not a satisfactory theory of that basic part of logic that is supposed to be a theory of, that is, a satisfactory theory of quantifiers and propositional connectives. The main reason for this inadequacy is that in the received first-order logic we cannot express all the possible patterns of dependence and independence among quantifiers and therefore not all possible patterns of dependence and independence among variables. This defect can be corrected by introducing an independence indicator / (slash) which helps to exempt a quantifier, say (Q²y) from its dependence on another quantifier, say (Q ¹x), in whose syntactical scope it occurs, viz., by writing it (Q²y/Q¹x). The result is a stronger logic, independence friendly (IF) first-order logic. (For it, see e.g., Hintikka (1996) and (2002a).) It is the true basic logic, not the received first-order logic.

DOI: 10.1007/978-94-017-0249-2_5

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