Quantifiers and Logical Reductions
In Chapter 6 we have seen that least fixed-point logic FO(LFP) captures PTIME, but does not strongly capture PTIME. In fact, it is open until now, whether there is any “natural” logic strongly capturing PTIME. At a first glance the following idea might be successful: Consider, for example, FO(LFP). One could think of strengthening it by adding some PTIME concepts, thereby enlarging its expressive power just up to PTIME. In traditional model theory there is a well-established method to enrich logics by new concepts, namely by adjoining so-called Lindström quantifiers. We have already met such quantifiers, for example, the counting quantifiers (cf. section 2.4).
KeywordsEquality Type Turing Machine Logical Reduction Relation Symbol Input Tape
Unable to display preview. Download preview PDF.