Partial algebras for Łukasiewicz logics and its extensions
|Title:||Partial algebras for Łukasiewicz logics and its extensions|
|Journal:||Archive for Mathematical Logic|
|Pages:||913 - 933|
We consider several logics differing from Lukasiewicz logics in that they contain further connectives: the logic PL, PL', PL'Δ, and LΠ. For their algebraic counterparts, we characterise the corresponding type of partial algebras; and we moreover consider the representing f-rings, constructed in a transparent way from the partial algebras - just like po-groups from effect algebras. All in all, we get three-fold correspondences: the total algebras - the partial algebras - the representing rings.