Coatoms, Molecules and Creators in MTL-algebras and Their Counterparts in Multivalued Logics

Abstract

MTL-Algebras are the algebraic counterpart of Monoidal t-norm logic, whose truth values are real numbers in. More generally, logics whose truth value set forms an MTL-Algebra are called MTL-valued logics; their deductive systems are studied. Many results known to hold for BL-Algebras are updated to apply to all MTL-Algebras. Coatoms, molecules, creators, and essential deductive systems are defined on MTL-Algebras. Coatoms and molecules are particular elements of an MTL-Algebra and creators are duals of annihilators known in MV-Algebra theory. These new algebraic concepts have a logic origin that is discussed. Creators are particular deductive systems. Their relation to coatoms, molecules and prime, Boolean, and maximal deductive systems is studied. Essential deductive systems on MTL-Algebras are analyzed.