Many-Valued Relation Lifting and Moss’ Coalgebraic Logic

0425733 - ÚI 2014 RIV DE eng C - Conference Paper (international conference)
Bílková, Marta - Dostál, M.
Many-Valued Relation Lifting and Moss’ Coalgebraic Logic.
Algebra and Coalgebra in Computer Science. Berlin: Springer, 2013 - (Heckel, R.; Milius, S.), s. 66-79. Lecture Notes in Computer Science, 8089. ISBN 978-3-642-40205-0. ISSN 0302-9743.
[CALCO 2013. International Conference /5./. Warsaw (PL), 03.09.2013-06.09.2013]
R&D Projects: GA ČR GAP202/10/1826
Grant - others:SGS ČVUT(CZ) SGS12/060/OHK3/1T/13
Institutional support: RVO:67985807
Keywords : coalgebra * coalgebraic logic * relation lifting * many-valued logic
Subject RIV: BA - General Mathematics

The notion of relation lifting can be generalised to work with many-valued relations while retaining many vital properties of the “classical” relation lifting. We show that polynomial endofunctors of the category of sets and mappings admit V-relation lifting for relations taking values from a commutative quantale V. Using the technique of functor presentations, we then show that every finitary weak pullback preserving functor admits a V-relation lifting for V being a complete Heyting algebra. As an application of the many-valued lifting we inspect the notion of many-valued bisimulation and we introduce an expressive many-valued variant of Moss’ logic for T-coalgebras, parametric in the functor T.
Permanent Link: http://hdl.handle.net/11104/0231547