Normal forms and free algebras for some extensions of MTL
We introduce a semantical definition of minterms and maxterms which generalizes the usual notion in Boolean logic to a class of many-valued logics. We apply this notion to get normal forms for logics G, NM, NMG. Then we obtain a combinatorial description of the n-generated free algebras in the varieties constituting the algebraic semantics of those logics. Specifically, we represent via combinatorial posets the embedding of the n-generated free algebra into the direct product of all n-generated chains in the variety. (c) 2008 Elsevier B.V. All rights reserved.
normal forms free algebras mtl algebraic semantics nilpotent minimum and godel logic wnm