PP201704: Enqvist, Sebastian and Seifan, Fatemeh and Venema, Yde (2017) Completeness for mucalculi: a coalgebraic approach. [Preprint] (Unpublished)

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Abstract
We set up a generic framework for proving completeness results for variants of the modal mucalculus, using tools from coalgebraic modal logic. We illustrate the method by proving two new completeness results: for the graded mucalculus (which is equivalent to monadic secondorder logic on the class of unranked tree models), and for the monotone modal mucalculus. Besides these main applications, our result covers the KozenWalukiewicz completeness theorem for the standard modal mucalculus, as well as the lineartime mucalculus and modal fixpoint logics on ranked trees. Completeness of the lineartime mucalculus is known, but the proof we obtain here is different and places the result under a common roof with Walukiewicz' result. Our approach combines insights from the theory of automata operating on potentially infinite objects, with methods from the categorical framework of coalgebra as a general theory of statebased evolving systems. At the interface of these theories lies the notion of a coalgebraic modal onestep language. One of our main contributions here is the introduction of the novel concept of a disjunctive basis for a modal onestep language. Generalizing earlier work, our main general result states that in case a coalgebraic modal logic admits such a disjunctive basis, then soundness and completeness at the onestep level transfers to the level of the full coalgebraic modal mucalculus.
Item Type:  Preprint 

Report Nr:  PP201704 
Series Name:  Prepublication (PP) Series 
Year:  2017 
Subjects:  Computation Logic 
Depositing User:  Yde Venema 
Date Deposited:  21 Mar 2017 12:12 
Last Modified:  23 Mar 2017 17:16 
URI:  https://eprints.illc.uva.nl/id/eprint/1530 
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