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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)

- ROBIN HIRSCH, IAN HODKINSON, Peter Jipsen, Maarten Marx, Szabolcs Mikulás, Mark Reynolds +1 other
- 1999

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)

- 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, John Rafter, Steven Tschantz, Mark Ellingham, Gordon Royle, Cary Timar +1 other

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)

- Nikolaos Galatos, Ralph McKenzie, Steven Tschantz, Jonathan Farley, Alan Peters, Peter Jipsen +4 others
- 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)

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