Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Exploring Relevant Parts Between Legal Documents Using Substructure Matching Read chapter Read first chapter

2020 | OriginalPaper | Chapter

Variables vs. Parameters in the Interpretation of Natural Language

Authors : Jan Köpping, Thomas Ede Zimmermann

Published in: New Frontiers in Artificial Intelligence

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

This paper compares two systems of functional type logic that have been applied to the analysis of meaning composition in natural language: Montague’s Intensional Logic IL and its extensional substratum Ty2 of two-sorted type theory. The two systems differ in their treatment of reference and quantification over indices (like possible worlds or times): whereas the denotations of IL-formulae (inter alia) depend on indices as parameters, their Ty2-counterparts contain explicit free and bound variables for them. Building on earlier results, it is argued that, appearances to the contrary, the two systems are largely equivalent; that any differences in expressivity are irrelevant to said applications; and that the equivalence also extends to variations of the systems that make use of multiple indices (as in mixed systems of modal and temporal interpretation) or additional dimensions (as in standard accounts of context dependence).

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter Semantic Types: Two Is Better Than Too Many
next chapter From Discourse to Logic with Stanford CoreNLP and Treebank Semantics
Footnotes
1
With the variability of the underlying Logical Space of possibilities, the intensions are generalizations of Kripke’s [17] possible worlds, as propagated in [19].
 
2
The \(\lambda \)-operator indicates functional abstraction: \([\lambda x. \dots \ x \ \dots ]\) is that function f that assigns \(\dots \ u \ \dots \) to any u in its domain D (which is left implicit); given the set-theoretic account of functions we thus have:
$$ [\lambda x. \dots \ x \ \dots ] \ = \ \{(u,v) \vert u \in D \ \& \ v = \dots \ u \dots \}.$$
 
3
Following [20], the sets \(\textit{Con}_{(s,b)}\) are usually referred to as \(\textit{Con}_b\), which we feel is confusing (given their interpretation) and moreover leads to complications when it comes to comparing IL and Ty2.
 
4
See [20, p. 387] and [9, p. 15] for other, less transparent ways of defining conjunction.
 
5
It ought to be mentioned that there is every reason to believe that Montague had been aware of Theorem (6), given the very design of IL.
 
6
In fact, it is almost that fragment, except for a little twist concerning constants occurring without index argument; cf. [30, p. 75].
 
7
Tautologies are among the obvious exceptions.
 
8
Hint: (7-a) and (8-a) boil down to a cardinality condition on \(D_s\); and the \(^*\)-counterpart of (8-b) is:
  • \((\lambda F^{((s,t),t)}. \ (\lambda \upsilon ^s_0. \ ( \lambda p^{(s,t)}. \ (p(\upsilon ^s_0) \ = F)))) \ (\lambda p. p(\upsilon ^s_0)).\)
 
9
The classic elimination algorithm from [4, p. 189] cannot be applied directly because it outputs terms of types outside \(\textit{IT}^+\). Thanks are due to Oleg Kiselyov for bringing up the question during the discussion following the LENLS presentation.
 
10
The syntactic variable t indicates the surface position from which the underlying noun plush toys has been moved and corresponds to the \(\lambda \)-bound Ty2-variable P in (13-b). See [10, p. 199f.] for an early formulation (and a different motivation) of such an analysis.
 
11
\(\chi '\), too, would have to be subjected to a meaning postulate in order to make sure it denotes a choice function \(\chi \), i.e. that \(w\in \chi (p)\) whenever \(p \ne \emptyset \).
 
12
The exact nature of the representation relation between contexts and indices varies across different versions of two-dimensional semantics and need not concern us here.
 
13
Cf. [15, p. 510], where the ban is presented as a descriptive observation on English and related languages. The more natural interpretation, following [18], takes it to be a defining criterion for context-dependence: unlike indices, contexts comprise those denotation-determining factors that cannot be shifted.
 
14
Here we slightly simplify matters: contexts are usually taken to contain more components than indices (cf. [14]); alternatively, they may be taken to be fully specified (utterance) situations (cf. [18]). In any case, these complications are orthogonal to our concerns.
 
15
The reasoning runs parallel to the proof Corollary (50b) in [16, Sec. 2.6]; see the next sub-section for this connection.
 
16
The (contextual) truth conditions of (23) are captured by equating index time \(t_0\) and context time \(t^*\) in (24), which still need to be kept apart to account for embedded occurrences of (23).
 
17
Apart from that a further result was proved to the effect that denotational equivalence holds across all types at diagonal points; obviously, this result is also covered by (27).
 
18
The ‘Y’ stands for ‘Yanovich’ on whose account [29] of backwards-looking operators (25) and (26) are based.
 
Literature
1.
Bäuerle, R.: Pragmatisch-semantische Aspekte der NP-Interpretation. In: Faust, M., Harweg, R., Lehfeldt, W., Wienold, G. (eds.) Allgemeine Sprachwissenschaft, Sprachtypologie und Textlinguistik, pp. 121–131. Narr, Tübingen (1983)
2.
Carnap, R.: Meaning and Necessity. University of Chicago Press, Chicago (1947)MATH
3.
4.
Curry, H.B., Feys, R.: Combinatory Logic, vol. I. North-Holland Publishing Company, Amsterdam (1958)MATH
5.
6.
7.
Frege, G.: Über Sinn und Bedeutung. Zeitschrift für Philosophie und philosophische Kritik NF 100(1), 25–50 (1892)
8.
Friedman, J., Warren, D.S.: \(\lambda \)-normal forms in an intensional logic for English. Studia Logica XXXIX(2–3), 311–324 (1980)
9.
Gallin, D.: Intensional and Higher-order Modal Logic. North-Holland Pub. Company, Amsterdam (1975)MATH
10.
Groenendijk, J., Stokhof, M.: Semantic analysis of WH-complements. Linguist. Philos. 5(2), 175–233 (1982)CrossRef
11.
Heim, I., Kratzer, A.: Semantics in Generative Grammar. Blackwell Publishers Ltd., Oxford (1998)
12.
13.
14.
15.
Kaplan, D.: Demonstratives. An essay on the semantics, logic, metaphysics and epistemology of demonstratives and other indexicals. In: Almog, J., Perry, J., Wettstein, H. (eds.) Themes from Kaplan, pp. 481–563. Oxford University Press, Oxford (1989)
16.
Köpping, J., Zimmermann, T.E.: Looking backwards in type logic. Inquiry (forthcoming)
17.
Kripke, S.A.: Semantical considerations on modal logic. Acta Philosophica Fennica 16, 83–94 (1963)MathSciNetMATH
18.
Lewis, D.K.: Index, context, and content. In: Kanger, S., Öhman, S. (eds.) Philosophy and Grammar, pp. 79–100. Reidel, Dordrecht (1980)CrossRef
19.
Montague, R.: Pragmatics. In: Klibansky, R. (ed.) Contemporary Philosophy. Volume I: Logic and the Foundations of Mathematics, pp. 102–122. La Nuova Italia Editrice, Florence (1968)
20.
21.
Montague, R.: The proper treatment of quantification in ordinary English. In: Hintikka, J., Moravcsik, J., Suppes, P. (eds.) Approaches to Natural Language, pp. 221–242. Reidel, Dordrecht (1973)CrossRef
22.
Parsons, T.: Frege’s hierarchies of indirect senses and the paradox of analysis. In: French, P., Uehling, T., Wettstein, H. (eds.) Midwest Studies in Philosophy VI: The Foundations of Analytic Philosophy, pp. 37–57. University of Minnesota Press, Minneapolis (1981)
23.
Percus, O.: Constraints on some other variables in syntax. Nat. Lang. Semant. 9(1), 173–229 (2000)CrossRef
24.
Saarinen, E.: Backwards-looking operators in tense logic and in natural language. In: Hintikka, J., Niiniluoto, I., Saarinen, E. (eds.) Essays on Mathematical and Philosophical Logic, pp. 341–367. Reidel, Dordrecht (1979)CrossRef
25.
Scott, D.: Advice on modal logic. In: Lambert, K. (ed.) Philosophical Problems in Logic, pp. 143–173. Reidel, Dordrecht (1970)CrossRef
26.
Stalnaker, R.: A theory of conditionals. In: Rescher, N. (ed.) Studies in Logical Theory, pp. 41–55. Blackwell, Oxford (1968)
27.
28.
Stalnaker, R.: The problem of logical omniscience, II. In: Context and Content, pp. 255–273. Oxford University Press, Oxford (1999)
29.
30.
31.
Zimmermann, T.E.: Fregean compositionality. In: Ball, D., Rabern, B. (eds.) The Science of Meaning, pp. 276–305. Oxford University Press, Oxford (2018)
32.
Zimmermann, T.E.: Representing intensionality: variables vs. parameters. In: Gutzmann, D., Matthewson, L., Meier, C., Rullmann, H., Zimmermann, T.E. (eds.) The Wiley Blackwell Companion to Semantics. Oxford, Wiley (forthcoming)
Metadata
Title
Variables vs. Parameters in the Interpretation of Natural Language
Authors
Jan Köpping
Thomas Ede Zimmermann
Copyright Year
2020
Book
New Frontiers in Artificial Intelligence

Print ISBN: 978-3-030-58789-5

Electronic ISBN: 978-3-030-58790-1

Copyright Year: 2020

DOI
https://doi.org/10.1007/978-3-030-58790-1_11

Premium Partner

    Image Credits