Reichenbach, Prior and Montague: a semantic get-together

C. Areces and P. Blackburn. Reichenbach, Prior and Montague: a semantic get-together. In S. Artemov, H. Barringer, A. d'Avila Garcez, L. Lamb, and J. Woods, editors, We Will Show Them: Essays in Honour of Dov Gabbay, pp. 77–88, College Publications, 2005.

Download

[pdf] 

Abstract

The pioneer of the use of richer logics in natural language semantics was Richard Montague who (most famously in his paper The Proper Treatment of Quantification in Ordinary English [Montague, 1973]) showed that higher-order logic was a superb tool for semantic construction. The higher- order logic that Montague developed for this purpose was called IL (Intensional Logic) and it made use of Prior’s tense operators. Hence Prior and Montague have met up too. So why not bring all three together to Dov’s birthday party? That’s what this paper is about. We are going to hybridize Montague’s IL in the simplest possible way (we’ll simply add nominals) to form NIL (Nominal Intensional Logic). We’ll then show that the resulting system is capable of assigning nominal tense logical representations, which capture the insights of both Reichenbach and Prior, in a compositional way.

BibTeX

@InCollection{Areces2005,
  author =       "C. Areces and P. Blackburn",
  booktitle =    "We Will Show Them: Essays in Honour of Dov Gabbay",
  publisher =    "College Publications",
  title =        "Reichenbach, {P}rior and {M}ontague: a semantic
                 get-together",
  abstract =     "The pioneer of the use of richer logics in natural
                 language semantics was Richard Montague who (most
                 famously in his paper The Proper Treatment of
                 Quantification in Ordinary English [Montague, 1973])
                 showed that higher-order logic was a superb tool for
                 semantic construction. The higher- order logic that
                 Montague developed for this purpose was called IL
                 (Intensional Logic) and it made use of Prior’s tense
                 operators. Hence Prior and Montague have met up too. So
                 why not bring all three together to Dov’s birthday
                 party? That’s what this paper is about. We are going
                 to hybridize Montague’s IL in the simplest possible
                 way (we’ll simply add nominals) to form NIL (Nominal
                 Intensional Logic). We’ll then show that the
                 resulting system is capable of assigning nominal tense
                 logical representations, which capture the insights of
                 both Reichenbach and Prior, in a compositional way.",
  year =         "2005",
  editor =       "S. Artemov and H. Barringer and A. d'Avila Garcez and
                 L. Lamb and J. Woods",
  pages =        "77--88",
  volume =       "1",
  ISBN =         "978-1-904987-12-3",
}