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Residuation is a fundamental concept of ordered structures and categories. In this survey we consider the consequences of adding a residuated monoid operation to lattices. The resulting residuated lattices have been studied in several branches of mathematics, including the areas of lattice-ordered groups, ideal lattices of rings, linear logic and(More)
We prove that there is no algorithm that decides whether a nite relation algebra is representable. Representability of a nite relation algebra A is determined by playing a certain two player game G(A) overàtomic A-networks'. It can be shown that the second player in this game has a winning strategy if and only if A is representable. Let be a nite set of(More)
Generalized basic logic algebras (GBL-algebras for short) have been introduced in [JT02] as a generalization of Hájek's BL-algebras, and constitute a bridge between algebraic logic and ℓ-groups. In this paper we investigate normal GBL-algebras, that is, integral GBL-algebras in which every filter is normal. For these structures we prove an analogue of Blok(More)
Approved: Date: ACKNOWLEDGEMENTS I wish to express my deepest gratitude to Bjarni Jónsson for all his advice, encouragement and patience. He directed me to this area of research and posed many interesting problems, some of which ultimately lead to this dissertation. His love and concern for mathematics are inspiring and will remain with me in the years to(More)
We will give here a purely algebraic proof of the cut elimination theorem for various sequent systems. Our basic idea is to introduce mathematical structures, called Gentzen structures, for a given sequent system without cut, and then to show the completeness of the sequent system without cut with respect to the class of algebras for the sequent system with(More)