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Expressivity of coalgebraic modal logic: The limits and beyond
 IN FOUNDATIONS OF SOFTWARE SCIENCE AND COMPUTATION STRUCTURES, VOLUME 3441 OF LNCS
, 2005
"... Modal logic has a good claim to being the logic of choice for describing the reactive behaviour of systems modeled as coalgebras. Logics with modal operators obtained from socalled predicate liftings have been shown to be invariant under behavioral equivalence. Expressivity results stating that, c ..."
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Cited by 39 (13 self)
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Modal logic has a good claim to being the logic of choice for describing the reactive behaviour of systems modeled as coalgebras. Logics with modal operators obtained from socalled predicate liftings have been shown to be invariant under behavioral equivalence. Expressivity results stating that, conversely, logically indistinguishable states are behaviorally equivalent depend on the existence of separating sets of predicate liftings for the signature functor at hand. Here, we provide a classification result for predicate liftings which leads to an easy criterion for the existence of such separating sets, and we give simple examples of functors that fail to admit expressive normal or monotone modal logics, respectively, or in fact an expressive (unary) modal logic at all. We then move on to polyadic modal logic, where modal operators may take more than one argument formula. We show that every accessible functor admits an expressive polyadic modal logic. Moreover, expressive polyadic modal logics are, unlike unary modal logics, compositional.
Semigroup and ring theoretical methods in probability
, 2004
"... This is an expanded version of a series of four lectures designed to show algebraists how ring theoretical methods can be used to analyze an interesting family of finite Markov chains. The chains happen to be random walks on semigroups, and the analysis is based on a study of the associated semigrou ..."
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Cited by 18 (0 self)
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This is an expanded version of a series of four lectures designed to show algebraists how ring theoretical methods can be used to analyze an interesting family of finite Markov chains. The chains happen to be random walks on semigroups, and the analysis is based on a study of the associated semigroup algebras. The paper
Conditional semiThue Systems for Presenting Monoids
 PROC. STACS'92
, 1992
"... There are well known examples of monoids in literature which do not admit a finite and canonical presentation by a semiThue system over a fixed alphabet, not even over an arbitrary alphabet. We introduce conditional Thue and semiThue systems similar to conditional term rewriting systems as defined ..."
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There are well known examples of monoids in literature which do not admit a finite and canonical presentation by a semiThue system over a fixed alphabet, not even over an arbitrary alphabet. We introduce conditional Thue and semiThue systems similar to conditional term rewriting systems as defined by Kaplan. Using these conditional semiThue systems we give finite and canonical presentations of the examples mentioned above. Furthermore we show, that each finitely generated monoid with decidable word problem is embeddable in a monoid which has a finite canonical conditional presentation.
RISCLinz Report Series No. 0811
, 2008
"... on Unification (UNIF 2008). The workshop was held in the Castle of Hagenberg, Austria on July 18, 2008 and collocated with the 19th International Conference on Rewriting Techniques and Applications (RTA 2008). The aim of UNIF 2008 is to bring together people interested in unification, present recent ..."
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on Unification (UNIF 2008). The workshop was held in the Castle of Hagenberg, Austria on July 18, 2008 and collocated with the 19th International Conference on Rewriting Techniques and Applications (RTA 2008). The aim of UNIF 2008 is to bring together people interested in unification, present recent (even unfinished) work, and discuss new ideas and trends in unification and related fields. This includes scientific presentations, but also descriptions of applications and software using unification as a strong component.