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- P. Jipsen, C. Tsinakis
- 2002

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)

- Francesco Belardinelli, Peter Jipsen, Hiroakira Ono
- Studia Logica
- 2004

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)

- Peter Jipsen, John Rafter, +4 authors Hermann Johannes Carl Jipsen

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)

Residuated frames provide relational semantics for substructural logics and are a natural generalization of Kripke frames in intuitionistic and modal logic, and of phase spaces in linear logic. We explore the connection between Gentzen systems and residuated frames and illustrate how frames provide a uniform treatment for semantic proofs of cut-elimination,… (More)

- Peter Jipsen
- 1992

- P. Jipsen, F. Montagna
- 2007

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)

- Peter Jipsen
- Studia Logica
- 2004

- Jules Desharnais, Peter Jipsen, Georg Struth
- RelMiCS
- 2009

We axiomatise and study operations for relational domain and antidomain on semigroups and monoids. We relate this approach with previous axiomatisations for semirings, partial transformation semigroups and dynamic predicate logic.

- Nikolaos Galatos, Ralph McKenzie, +7 authors Miklós Maróti
- 2003

ACKNOWLEDGMENTS This thesis wouldn't have been possible without the help and support of certain people. I could not possibly itemize my gratitude in detail, but I would like to mention some of the most important names. First and foremost, I would like to thank my advisor, Constantine Tsinakis, for introducing me to the subject of residuated lattices, and… (More)

- P. Jipsen, F. Montagna
- 2008

The poset product construction is used to derive embedding theorems for several classes of generalized basic logic algebras (GBL-algebras). In particular it is shown that every n-potent GBL-algebra is embedded in a poset product of finite n-potent MV-chains, and every normal GBL-algebra is embedded in a poset product of totally ordered GMV-algebras.… (More)