The Logic of “Most” and “Mostly”
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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.
KeywordsModal predicate logic Generalized quantifiers Adverbs of quantification Logical probability Common sense reasoning Non-monotonic logic
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.
- Adams EW (1975) The logic of conditionals. An application of probability to deductive logic. D. Reidel Publishing Company, DodrechtGoogle Scholar
- Carnap R (1962) Logical foundations of probability, 2nd edn. The University of Chicago Press, ChicagoGoogle Scholar
- 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/
- Lewis D (1998) Adverbs of quantification. In: Papers in philosophical logic. Cambridge University Press, pp 5–20Google Scholar
- Peters S, Westerstahl D (2006) Quantifiers in language and logic. Oxford Clarendon Press, OxfordGoogle Scholar