Coatoms, molecules, and creators in MTL-algebras and their counterparts in multivalued logics
Erja Turunen · Logic Journal of IGPL · 2025
Abstract MTL-algebras are the algebraic counterpart of Monoidal t-norm logic, whose truth values are real numbers in $[0,1]$. 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.