Semantics
Like in other propositional t-norm fuzzy logics, algebraic semantics is predominantly used for MTL, with three main classes of algebras with respect to which the logic is complete:
- General semantics, formed of all MTL-algebras — that is, all algebras for which the logic is sound
- Linear semantics, formed of all linear MTL-algebras — that is, all MTL-algebras whose lattice order is linear
- Standard semantics, formed of all standard MTL-algebras — that is, all MTL-algebras whose lattice reduct is the real unit interval with the usual order; they are uniquely determined by the function that interprets strong conjunction, which can be any left-continuous t-norm
Read more about this topic: Monoidal T-norm Logic