R. Goldblatt. A calculus of terms for coalgebras of polynomial functors. In Marina Lenisa Andrea Corradini and Ugo Montanari, editors, Coalgebraic Methods in Computer Science (CMCS'2001), volume 44 of Electr. Notes in Theoret. Comp. Sci., 2001.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....(or cofree) coalgebras. This allows to give final semantics to systems and to use coinduction as a proof and definition principle. In the view of coalgebras as systems, logics for coalgebras are specification languages for systems. Examples of different approaches to logics for coalgebras include [17, 14, 22, 10, 4, 18]. These examples show that due to the generality provided by functors as signatures there is no uniform syntax for specification languages for coalgebras. The purpose of this paper is not to develop a new logical syntax for coalgebras (although we make the proposal to use modal logics with a ....

....Note that the formulas of a logic are preserved under : iff every definable class of coalgebras is closed under : Formulas of Hennessy Milner logic are preserved under subcoalgebras, quotients, coproducts, and domains of quotients. The same holds for the logics of the above cited papers [17, 14, 22, 10, 4, 18]. Of interest for us are also the notions of covariety and quasi covariety which dualise the corresponding notions from algebra. Behavioural covarieties dualise ground varieties. Definition 5 ( quasi )covariety, behavioural covariety) A quasi covariety is a class of coalgebras closed under ....

Robert Goldblatt. A calculus of terms for coalgebras of polynomial functors. In A. Corradini, M. Lenisa, and U. Montanari, editors, Coalgebraic Methods in Computer Science (CMCS'01), volume 44.1 of ENTCS. Elsevier, 2001.

....are now also accepted as a semantics for classes in object oriented programming and speci cation, see [12] for the initial paper. Recently, there was a lot of work centred around the mentioned duality, especially to establish coalgebraic versions of Birkho s variety theorem, see e.g. 6] 2] [1]. It is commonly seen as one of the biggest advantages of coalgebras that they deliver standard notions like bisimulation, observational equality and (path wise) modal operators for free . Also, many people see coalgebras as generalisations of transition systems. However, some parts of this ....

R. Goldblatt. A calculus of terms for coalgebras of polynomial functors. In A. Corradini, M. Lenisa, and U. Montanari, editors, Coalgebraic Methods in Computer Science, volume 44 of ENTCS, pages 160-183, April 2001.

....of models of such formulas. An approach of this kind was intitiated in [15] for coalgebras of certain monomial Philip Hall used the term in this way in lectures in the 1940 s (information supplied by Paul Cohn and Bernhard Neumann) 15 functors, and extended to polynomial functors in [14, 13]. It involves a new notion of ultra lter enlargement of a coalgebra, an analogue of the Stone space of a Boolean algebra. These ideas can be illustrated with the functor T on Set that has TX = X f0; 1g. The transition structure of a T coalgebra A comprises in essence a pair of functions A : ....

Robert Goldblatt. A calculus of terms for coalgebras of polynomial functors. Electronic Notes in Theoretical Computer Science, 44, Issue 1, 2001. http://www.elsevier.nl/ locate/entcs.

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R. Goldblatt. A calculus of terms for coalgebras of polynomial functors. In Marina Lenisa Andrea Corradini and Ugo Montanari, editors, Coalgebraic Methods in Computer Science (CMCS'2001), volume 44 of Electr. Notes in Theoret. Comp. Sci., 2001.

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