THE LATTICE OF SUPER-BELNAP LOGICS

Abstract We study the lattice of extensions four-valued Belnap–Dunn logic, called super-Belnap logics by analogy with superintuitionistic logics. describe global structure this splitting it into several subintervals, and prove some new completeness theorems for The crucial technical tool purpose will be so-called antiaxiomatic (or explosive) part operator. logic turn out to particular interest owing their connection graph theory: finitary is isomorphic upsets in homomorphism order on finite graphs (with loops allowed). In particular, there a continuum Moreover, non-finitary can constructed help isomorphism. As algebraic corollaries we obtain existence antivarieties De Morgan algebras prevariety which not quasivariety.