Author:
Citkin Alex,Muravitsky Alexei
Abstract
AbstractThe topic of this chapter is the treatment of a consequence relation in the framework of predicate languages with generalized quantifiers, which is called in this book Q-consequence. We discuss two patterns of Q-consequence: one is defined by Q-structures and the other, for specified languages, through deductive systems. Since the former is largely related to matrix consequence, we employ the Lindenbaum method for its characterization. Then, this method is used to consider models of the three kinds of Q-consequence given deductively. Completeness results are given for three Q-consequence relations, but only for a limited case, which, however, includes the subcase of all formal theorems.
Publisher
Oxford University PressOxford