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2010

A Note on Expressive Coalgebraic Logics for Finitary Set Functors

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A Note on Expressive Coalgebraic Logics for Finitary Set Functors
This paper has two purposes. The first is to present a final coalgebra construction for finitary endofunctors on Set that uses a certain subset L∗ of the limit L of the first ω terms in the final sequence. L∗ is the set of points in L which arise from all coalgebras using their canonical morphisms into L, and it was used earlier for different purposes in Kurz and Pattinson [5]. Viglizzo in [11] showed that the same set L∗ carried a final coalgebra structure for functors in a certain inductively defined family. Our first goal is to generalize this to all finitary endofunctors; the result is implicit in Worrell [12]. The second goal is to use the final coalgebra construction to propose coalgebraic logics similar to those in [6] but for all finitary endofunctors F on Set. This time one can dispense with all conditions on F, construct a logical language LF directly from it, and prove that two points in a coalgebra satisfy the same sentences of LF iff they are identifi...
Lawrence S. Moss
Added 29 Jan 2011
Updated 29 Jan 2011
Type Journal
Year 2010
Where LOGCOM
Authors Lawrence S. Moss
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