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Temporal logic with reference pointers

V. Goranko. Temporal logic with reference pointers. In Temporal logic, LNCS, pp. 133–148, Berlin: Springer, 1994.

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Abstract:

An extension of the propositional temporal language is introduced with a simple syntactic device, called `reference pointer', which provides for making references within a formula to `instants of reference' specified in the formula. The language with reference pointers $\scr L\sb \rm trp$ has a great expressive power (e.g. Kamp's and Stavi's operators as well as Prior's clock variables are definable in it), especially compared to its frugal syntax, perspicuous semantics and simple deductive system. The minimal temporal logic $K\sb \rm trp$ of this language is axiomatized and a strong completeness theorem is proved for it and extended to an important class of extensions of $K\sb \rm trp$. Validity in $\scr L\sb \rm trp$ is proved to be undecidable.

BibTeX: (download)

@INCOLLECTION{goranko94:_tempor,
  author = {V. Goranko},
  title = {Temporal logic with reference pointers},
  booktitle = {Temporal logic},
  publisher = {Berlin: Springer},
  year = {1994},
  volume = {827},
  series = {LNCS},
  pages = {133--148},
  abstract = {
	An extension of the propositional temporal language is introduced
	with a simple syntactic device, called `reference pointer', which
	provides for making references within a formula to `instants of reference'
	specified in the formula. The language with reference pointers $\scr
	L\sb {\rm trp}$ has a great expressive power (e.g. Kamp's and Stavi's
	operators as well as Prior's clock variables are definable in it),
	especially compared to its frugal syntax, perspicuous semantics and
	simple deductive system. The minimal temporal logic $K\sb {\rm trp}$
	of this language is axiomatized and a strong completeness theorem
	is proved for it and extended to an important class of extensions
	of $K\sb {\rm trp}$. Validity in $\scr L\sb {\rm trp}$ is proved
	to be undecidable. },
  editors = {Gabbay, D. and H. Ohlbach}
}

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