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The dynamic interpretation of a formula as a binary relation (inducing transitions) on states is extended by alternative treatments of implication, universal quantification, negation and disjunction that are more "dynamic" (in a precise sense) than the usual reductions to tests from quantified dynamic logic (which, nonetheless, can be recovered from the new connectives). An analysis of the "donkey" sentence followed by the assertion "It will kick back" is provided. | The donkey strikes back Extending the dynamic interpretation constructively Tim Fernando fernandoQcwi.nl Centre for Mathematics and Computer Science P.O. Box 4079 1009 AB Amsterdam The Netherlands Abstract The dynamic interpretation of a formula as a binary relation inducing transitions on states is extended by alternative treatments of implication universal quantification negation and disjunction that are more dynamic in a precise sense than the usual reductions to tests from quantified dynamic logic which nonetheless can be recovered from the new connectives . An analysis of the donkey sentence followed by the assertion It will kick back is provided. 1 Introduction The line If a farmer owns a donkey he beats it I from Geach 6 is often cited as one of the success stories of the so-called dynamic approach to natural language semantics by which is meant Kamp 12 Heim 9 Barwise 1 and Groenendijk and Stokhof 7 among others . But add the note It will kick back 2 and the picture turns sour processing 1 may leave no beaten donkey active. Accordingly providing a referent for the pronoun it in 2 would appear to call for some non-compositional surgery that may upset many a squeamish linguist . The present paper offers as a preventive a dynamic form of implication applied to 1 . Based on a constructive conception of discourse analysis an overhaul of Groenendijk and Stokhof 7ps Dynamic Predicate Logic DPL is suggested although can also be introduced less destructively so as to extend DPI conservatively. Thus the reader who prefers the old static interpretation of 1 can still make that choice and declare the continuation 2 to be semantically ill-formed. On the other hand Groe-nendijk and Stokhof 7 themselves concede that at least in certain contexts we need alternative externally dynamic interpretations of universal quantification implication and negation a both internally and externally dynamic treatment of disjunction. A proposal for such connectives is made below extending .
