Global view on reactivity: switch graphs and their logics (bibtex)

by D. M. Gabbay, S. Marcelino

Abstract:

The notion of reactive graph generalises the one of graph by allowing the\text[D?]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\text[D?]by introducing higher order arrows: the switches.\text[D?]The possibility of expressing the dependency of the future states of the accessibility relation on individual transitions by the use of higher-order relations,\text[D?]that is, coding meta-relational concepts by means of relations, strongly suggests the use of\text[D?]modal languages to reason directly about these structures. We introduce a hybrid\text[D?]modal logic for this purpose and prove its completeness.

Reference:

Global view on reactivity: switch graphs and their logics (D. M. Gabbay, S. Marcelino), In , Springer, 2012.

Bibtex Entry:

@Article{10993/15852, Title = {Global view on reactivity: switch graphs and their logics}, Author = {Gabbay, D. M. and Marcelino, S.}, Year = {2012}, Abstract = {The notion of reactive graph generalises the one of graph by allowing the\text{[D?]}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\text{[D?]}by introducing higher order arrows: the switches.\text{[D?]}The possibility of expressing the dependency of the future states of the accessibility relation on individual transitions by the use of higher-order relations,\text{[D?]}that is, coding meta-relational concepts by means of relations, strongly suggests the use of\text{[D?]}modal languages to reason directly about these structures. We introduce a hybrid\text{[D?]}modal logic for this purpose and prove its completeness.}, Publisher = {Springer}, Timestamp = {2015.01.26} }

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