Oracles and Quantiiers

We describe a general way of building oracle Turing machines, thereby treating oracle queries as reductions. The model allows various types of reductions, which lead to the diierent oracle models known from the literature. For model theoretic purposes we deene a functional transducer model which, for many complexity classes, corresponds to logical interpretations. We thus get a notion of reduction (reduction) which is equivalent to logical reductions. Finally, applying-reductions to our new oracle model, we obtain results such as: if a logic L captures a complexity class D, then L(QK) captures D K .