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.
Normal Forms and Free Algebras for Some Extensions of MTL / S. Aguzzoli, B. Gerla. - In: FUZZY SETS AND SYSTEMS. - ISSN 0165-0114. - 159:10(2008), pp. 1131-1152. [10.1016/j.fss.2007.12.003]
Normal Forms and Free Algebras for Some Extensions of MTL
S. AguzzoliPrimo
;
2008
Abstract
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.
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