The Logic of ‘‘Most’’ and ‘‘Mostly’’
Received: 20 December 2016 / Accepted: 17 April 2017 / Published online: 28 April 2017
Ó Springer Science+Business Media Dordrecht 2017
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 sym-
metrical 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
1 Introduction: Between ‘‘All’’ and ‘‘Some’’
1. One can see the moon in cloudless nights.
2. Snow is white.
3. Birds can ﬂy.
4. Hearts pump blood.
& Corina Stro
Heinrich Heine University Du
Axiomathes (2018) 28:107–124