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Hierarchies of modal and temporal logics with reference pointers

V. Goranko. Hierarchies of modal and temporal logics with reference pointers. Journal of Logic, Language and Information, 5(1):1–24, 1996.

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Abstract:

We introduce and study hierarchies of extensions of propositional modal and temporal languages with pairs of new syntactic devices: `point of reference--reference pointer', which enable semantic references to be made within a formula. We propose three different but equivalent semantics for the extended languages, and we discuss and compare their expressiveness. The languages with reference pointers are shown to have great expressive power (especially when their frugal syntax is taken into account), perspicuous semantics, and simple deductive systems. For instance, Kamp's and Stavi's temporal operators, as well as nominals (names, clock variables), are definable in them. Universal validity in these languages is proved undecidable. The basic modal and temporal logics with reference pointers are uniformly axiomatized and a strong completeness theorem is proved for them and extended to some classes of their extensions.

BibTeX: (download)

@ARTICLE{goranko96:_hierar,
  author = {V. Goranko},
  title = {Hierarchies of modal and temporal logics with reference pointers},
  journal = {Journal of Logic, Language and Information},
  year = {1996},
  volume = {5},
  pages = {1--24},
  number = {1},
  abstract = { We introduce and study hierarchies of extensions of propositional
	modal and temporal languages with pairs of new syntactic devices:
	`point of reference--reference pointer', which enable semantic references
	to be made within a formula. We propose three different but equivalent
	semantics for the extended languages, and we discuss and compare
	their expressiveness. The languages with reference pointers are shown
	to have great expressive power (especially when their frugal syntax
	is taken into account), perspicuous semantics, and simple deductive
	systems. For instance, Kamp's and Stavi's temporal operators, as
	well as nominals (names, clock variables), are definable in them.
	Universal validity in these languages is proved undecidable. The
	basic modal and temporal logics with reference pointers are uniformly
	axiomatized and a strong completeness theorem is proved for them
	and extended to some classes of their extensions. }
}

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