quantificational

In the late 19th and early 20th century Frege, followed by Russell and Whitehead, showed how deductive logic could be represented in the kind of rigorous formal system we now call quantificational logic or predicate logic.

Inductive Logic Hawthorne, James 2008

One can treat (46) as a kind of quantificational claim, whether or not one follows Russell in treating names as disguised descriptions.

Logical Form Pietroski, Paul 2009

So if English overtly displaces question-words that are covertly displaced in other languages, we should not be surprised if English covertly displaces other quantificational expressions like

Logical Form Pietroski, Paul 2009

This suggests covert displacement of the quantificational question-word in Chinese; see Huang (1982, 1995).

Logical Form Pietroski, Paul 2009

P; so every S is D. Aristotle discussed a range of such inferences, called syllogisms, involving quantificational propositions indicated by words like

Logical Form Pietroski, Paul 2009

Together with subsequent developments, Montague's work showed that Frege's logic was compatible with the idea that quantificational constructions in natural language have a systematic semantics.

Logical Form Pietroski, Paul 2009

But this schema, which fails to reflect any quantificational structure in the predicates, is not valid.

Logical Form Pietroski, Paul 2009

But there can be still further quantificational structure in these predicates, and likewise for any such schema, no matter how complex.

Logical Form Pietroski, Paul 2009

If we add a modal sentential operator meaning “it is possible that” or “it is necessary that” to classical first-order quantificational logic, along with appropriate axioms and new rule of inference catering to the added operator, the resulting system yields a sentence meaning the following as a theorem:

Possible Objects Yagisawa, Takashi 2009

Abstracting from the technical details, one can specify an algorithm that pairs each natural language sentence with one or more quantificational expressions like

Logical Form Pietroski, Paul 2009