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Axiomathes

, Volume 28, Issue 1, pp 107–124 | Cite as

The Logic of “Most” and “Mostly”

  • Corina StrößnerEmail author
Original Paper
  • 116 Downloads

Abstract

The paper suggests a modal predicate logic that deals with classical quantification and modalities as well as intermediate operators, like “most” and “mostly”. Following up the theory of generalized quantifiers, we will understand them as two-placed operators and call them determiners. Quantifiers as well as modal operators will be constructed from them. Besides the classical deduction, we discuss a weaker probabilistic inference “therefore, probably” defined by symmetrical probability measures in Carnap’s style. The given probabilistic inference relates intermediate quantification to singular statements: “Most S are P” does not logically entail that a particular individual S is also P, but it follows that this is probably the case, where the probability is not ascribed to the propositions but to the inference. We show how this system deals with single case expectations while predictions of statistical statements remain generally problematic.

Keywords

Modal predicate logic Generalized quantifiers Adverbs of quantification Logical probability Common sense reasoning Non-monotonic logic 

Notes

Acknowledgements

I would like to thank the anonymous reviewers for their comments, Niko Strobach for supervision at the early stage of this research and Joanna Kuchacz for her encouragement.

References

  1. Adams EW (1974) The logic of ‘almost all’. J Philos Log 3:3–17CrossRefGoogle Scholar
  2. Adams EW (1975) The logic of conditionals. An application of probability to deductive logic. D. Reidel Publishing Company, DodrechtGoogle Scholar
  3. Barwise J, Cooper R (1981) Generalized quantifiers and natural language. Linguist Philos 4:159–219CrossRefGoogle Scholar
  4. Carnap R (1962) Logical foundations of probability, 2nd edn. The University of Chicago Press, ChicagoGoogle Scholar
  5. Hájek A (2012) Interpretations of probability. In: Zalta (ed) The stanford encyclopedia of philosophy (Winter 2012 edn). https://plato.stanford.edu/archives/win2012/entries/probability-interpret/
  6. Keenan E (2002) Some properties of natural language quantifiers: generalized quantifier theory. Linguist Philos 25:627–654CrossRefGoogle Scholar
  7. Kraus S, Lehmann D, Magidor M (1990) Nonmonotonic reasoning, preferential models and cumulative logics. Artif Intell 44(1–2):167–207CrossRefGoogle Scholar
  8. Lewis D (1998) Adverbs of quantification. In: Papers in philosophical logic. Cambridge University Press, pp 5–20Google Scholar
  9. Peters S, Westerstahl D (2006) Quantifiers in language and logic. Oxford Clarendon Press, OxfordGoogle Scholar
  10. Priest G (2008) An introduction to non-classical logic. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  11. Reiter R (1980) A logic for default reasoning. Artif Intell 13:81–132CrossRefGoogle Scholar
  12. Reiter R (1987) Nonmonotonic reasoning. Ann Rev Comput Sci 2:147–186CrossRefGoogle Scholar
  13. Schurz G (2001) What is ‘normal’? An evolution-theoretic foundation for normic laws and their relation to statistical normality. Philos Sci 68:476–497CrossRefGoogle Scholar
  14. Strößner C (2015) Normality and majority: towards a statistical understanding of normality statements. Erkenntnis 80:793–809CrossRefGoogle Scholar
  15. van Benthem J (1984) Questions on quantifiers. J Symb Log 49(2):443–466CrossRefGoogle Scholar
  16. van Benthem J (2003) Conditional probability meets update logic. J Log Lang Inf 12:409–421CrossRefGoogle Scholar
  17. Veltman F (1996) Defaults in update semantics. J Philos Log 25:221–261CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Heinrich Heine University DüsseldorfDüsseldorfGermany

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