Algebraic Semantics of Refinement Modal Logic
Identifieur interne : 000044 ( Main/Exploration ); précédent : 000043; suivant : 000045Algebraic Semantics of Refinement Modal Logic
Auteurs : Zeinab Bakhtiari [France] ; Hans Van Ditmarsch [France] ; Sabine Frittella [Pays-Bas]Source :
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Abstract
In the present paper we develop algebraic semantics of refinement modal logic using duality theory. Refinement modal logic has been introduced by Bozzelli et al.[7]. A Refinement is like a bisimulation, except that from the three relational requirements only 'atoms' and 'back' have to be satisfied. We study the dual notion of refinement on algebras and present algebraic semantics of refinement modal logic. For this end, we proceed as follows: (1) we present the algebraic semantics of action model logic quantifier, (2) we introduce an algebraic model based on semantics of refinement quantifier in terms of refinement relation. Then we show that refinement modal logic is sound and complete with respect to the algebraic semantics introduced.
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Box 5031, 2600GA Delft The Netherlands</addrLine><country key="NL"></country></address><ref type="url">http://www.ewi.tudelft.nl</ref></desc><listRelation><relation active="#struct-84531" type="direct"></relation></listRelation><tutelles><tutelle active="#struct-84531" type="direct"><org type="institution" xml:id="struct-84531" status="VALID"><orgName>Delft University of Technology [[Delft]</orgName><desc><address><addrLine>Delft University of Technology Postbus 5 2600 AA Delft</addrLine><country key="NL"></country></address><ref type="url">http://www.tudelft.nl/</ref></desc></org></tutelle></tutelles></hal:affiliation><country>Pays-Bas</country></affiliation></author></analytic></biblStruct></sourceDesc></fileDesc><profileDesc><textClass><keywords scheme="mix" xml:lang="en"><term>Refinement modal logic</term><term>algebraic semantics</term><term>arbitrary action model logic</term><term>dynamic epistemic logic</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">In the present paper we develop algebraic semantics of refinement modal logic using duality theory. Refinement modal logic has been introduced by Bozzelli et al.[7]. A Refinement is like a bisimulation, except that from the three relational requirements only 'atoms' and 'back' have to be satisfied. We study the dual notion of refinement on algebras and present algebraic semantics of refinement modal logic. For this end, we proceed as follows: (1) we present the algebraic semantics of action model logic quantifier, (2) we introduce an algebraic model based on semantics of refinement quantifier in terms of refinement relation. Then we show that refinement modal logic is sound and complete with respect to the algebraic semantics introduced.</div></front></TEI><affiliations><list><country><li>France</li><li>Pays-Bas</li></country><region><li>Grand Est</li><li>Lorraine (région)</li></region><settlement><li>Metz</li><li>Nancy</li></settlement><orgName><li>Université de Lorraine</li></orgName></list><tree><country name="France"><region name="Grand Est"><name sortKey="Bakhtiari, Zeinab" sort="Bakhtiari, Zeinab" uniqKey="Bakhtiari Z" first="Zeinab" last="Bakhtiari">Zeinab Bakhtiari</name></region><name sortKey="Van Ditmarsch, Hans" sort="Van Ditmarsch, Hans" uniqKey="Van Ditmarsch H" first="Hans" last="Van Ditmarsch">Hans Van Ditmarsch</name></country><country name="Pays-Bas"><noRegion><name sortKey="Frittella, Sabine" sort="Frittella, Sabine" uniqKey="Frittella S" first="Sabine" last="Frittella">Sabine Frittella</name></noRegion></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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