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Coalgebraic Logic (1999)
| Venue: | Annals of Pure and Applied Logic |
| Citations: | 110 - 0 self |
BibTeX
@ARTICLE{Moss99coalgebraiclogic,
author = {Lawrence S. Moss},
title = {Coalgebraic Logic},
journal = {Annals of Pure and Applied Logic},
year = {1999},
volume = {96}
}
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Abstract
We present a generalization of modal logic to logical systems which are interpreted on coalgebras of functors on sets. The leading idea is that infinitary modal logic contains characterizing formulas. That is, every model-world pair is characterized up to bisimulation by an infinitary formula. The point of our generalization is to understand this on a deeper level. We do this by studying a frangment of infinitary modal logic which contains the characterizing formulas and is closed under infinitary conjunction and an operation called 4. This fragment generalizes to a wide range of coalgebraic logics. We then apply the characterization result to get representation theorems for final coalgebras in terms of maximal elements of ordered algebras. The end result is that the formulas of coalgebraic logics can be viewed as approximations to the elements of the final coalgebra. Keywords: infinitary modal logic, characterization theorem, functor on sets, coalgebra, greatest fixed point. 1 Intr...
Keyphrases
coalgebraic logic infinitary modal logic model-world pair final coalgebra characterization theorem maximal element characterization result end result final coalgebras infinitary formula representation theorem wide range modal logic characterizing formula ordered algebra infinitary conjunction logical system
