We report a recent Tarski-style semantics for a language which includes the branching quantifiers on which Andrzej Ehrenfeucht made the first breakthrough in 1958. The semantics is equivalent to Henkin's game-theoretic semantics, but unlike Henkin's it is compositional. We use second-order formulas to give a new (and with any luck, more manageable) description of this Tarski-style semantics. Finally we apply the new description to present a compositional and fully abstract semantics for the slightly more limited syntax of Hintikka and Sandu, answering a question of Sandu.
CITATION STYLE
Hodges, W. (1997). Some strange quantifiers (pp. 51–65). https://doi.org/10.1007/3-540-63246-8_4
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