Logics of quasiary predicates of quantifier-equational level

Abstract

First-order composition-nominative logics of partial single-valued, total multiple valued and partial multiple-valued quasiary predicates of quantifierequational level are studied. We define basic semantic properties of the introduced logics, particularly the properties of the relations of logical consequence for sets of formulas and the Х–Y-valued relations of logical consequence. On this basis we construct sequent calculi for logics of single-valued quasi-ary predicates of quantifier-equational level