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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