Global view on reactivity: Switch graphs and their logics

Dov Gabbay; Sérgio Marcelino

doi:10.1007/s10472-012-9316-8

Global view on reactivity: Switch graphs and their logics

Dov Gabbay, Sérgio Marcelino

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

The notion of reactive graph generalises the one of graph by allowing the base accessibility relation to change when its edges are traversed. Can we represent these more general structures using points and arrows? We prove this can be done by introducing higher order arrows: the switches. The possibility of expressing the dependency of the future states of the accessibility relation on individual transitions by the use of higher-order relations, that is, coding meta-relational concepts by means of relations, strongly suggests the use of modal languages to reason directly about these structures. We introduce a hybrid modal logic for this purpose and prove its completeness.

Original language	English
Pages (from-to)	131-162
Number of pages	32
Journal	Annals of Mathematics and Artificial Intelligence
Volume	66
Issue number	1
DOIs	https://doi.org/10.1007/s10472-012-9316-8
State	Published - Dec 2012

Bibliographical note

Funding Information:
The author Sérgio Marcelino thanks the support of FCT and EU FEDER, via the postdoc scholarship SFRH/BPD/76513/2011, the project FCT PEst-OE/EEI/LA0008/2011 of IT, the FP7-PEOPLE-2012-IRSES GetFun Marie Curie International Research Staff Exchange Scheme Fellowship within the 7th European Community Framework Programme, as well as the PQDR initiative of SGIQ.

Funding

The author Sérgio Marcelino thanks the support of FCT and EU FEDER, via the postdoc scholarship SFRH/BPD/76513/2011, the project FCT PEst-OE/EEI/LA0008/2011 of IT, the FP7-PEOPLE-2012-IRSES GetFun Marie Curie International Research Staff Exchange Scheme Fellowship within the 7th European Community Framework Programme, as well as the PQDR initiative of SGIQ.

Funders	Funder number
FP7-PEOPLE-2012-IRSES GetFun Marie Curie
Fundação para a Ciência e a Tecnologia
Seventh Framework Programme
European Regional Development Fund	SFRH/BPD/76513/2011, PEst-OE/EEI/LA0008/2011

Keywords

Dynamic logics
Dynamic models
Hybrid logic
Modal logic
Reactive graphs
Reactive logics
Switch graphs

Access to Document

10.1007/s10472-012-9316-8

Cite this

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abstract = "The notion of reactive graph generalises the one of graph by allowing the base accessibility relation to change when its edges are traversed. Can we represent these more general structures using points and arrows? We prove this can be done by introducing higher order arrows: the switches. The possibility of expressing the dependency of the future states of the accessibility relation on individual transitions by the use of higher-order relations, that is, coding meta-relational concepts by means of relations, strongly suggests the use of modal languages to reason directly about these structures. We introduce a hybrid modal logic for this purpose and prove its completeness.",

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Global view on reactivity: Switch graphs and their logics

Abstract

Bibliographical note

Funding

Keywords

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