Peter Jipsen

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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)
In the present paper, which is a sequel to [20, 4, 12], we investigate further the structure theory of quasi-MV algebras and √ quasi-MV algebras. In particular: we provide a new representation of arbitrary √ qMV algebras in terms of √ qMV algebras arising out of their MV* term sub-reducts of regular elements; we investigate in greater detail the structure(More)
Concurrent Kleene algebras were introduced by Hoare, Möl-ler, Struth and Wehrman in [HMSW09,HMSW09a,HMSW11] as idem-potent bisemirings that satisfy a concurrency inequation and have a Kleene-star for both sequential and concurrent composition. Kleene algebra with tests (KAT) were dened earlier by Kozen and Smith [KS97]. Concurrent Kleene algebras with tests(More)