Conservativity

In formal semantics conservativity is a proposed linguistic universal which states that any determiner $D$ must obey the equivalence $D(A,B)\leftrightarrow D(A,A\cap B)$ . For instance, the English determiner "every" can be seen to be conservative by the equivalence of the following two sentences, schematized in generalized quantifier notation to the right.^[1]^[2]^[3]

Every aardvark bites. $\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \rightsquigarrow every(A,B)$
Every aardvark is an aardvark that bites. $\ \ \rightsquigarrow every(A,A\cap B)$

Conceptually, conservativity can be understood as saying that the elements of $B$ which are not elements of $A$ are not relevant for evaluating the truth of the determiner phrase as a whole. For instance, truth of the first sentence above does not depend on which biting non-aardvarks exist.^[1]^[2]^[3]

Conservativity is significant to semantic theory because there are many logically possible determiners which are not attested as denotations of natural language expressions. For instance, consider the imaginary determiner $shmore$ defined so that $shmore(A,B)$ is true iff $|A|>|B|$ . If there are 50 biting aardvarks, 50 non-biting aardvarks, and millions of non-aardvark biters, $shmore(A,B)$ will be false but $shmore(A,A\cap B)$ will be true.^[1]^[2]^[3]

Some potential counterexamples to conservativity have been observed, notably, the English expression "only". This expression has been argued to not be a determiner since it can stack with bona fide determiners and can combine with non-nominal constituents such as verb phrases.^[4]

Only some aardvarks bite.
This aardvark will only [VP bite playfully.]

Different analyses have treated conservativity as a constraint on the lexicon, a structural constraint arising from the architecture of the syntax-semantics interface, as well as constraint on learnability.^[5]^[6]^[7]

Notes

^ a b c Dag, Westerståhl (2016). "Generalized Quantifiers". In Aloni, Maria; Dekker, Paul (eds.). Cambridge Handbook of Formal Semantics. Cambridge University Press. ISBN 978-1-107-02839-5.
^ a b c Gamut, L.T.F. (1991). Logic, Language and Meaning: Intensional Logic and Logical Grammar. University of Chicago Press. pp. 245–249. ISBN 0-226-28088-8.
^ a b c Barwise, Jon; Cooper, Robin (1981). "Generalized Quantifiers and Natural Language". Linguistics and Philosophy. 4 (2): 159–219. doi:10.1007/BF00350139.
^ von Fintel, Kai (1994). Restrictions on quantifier domains (PhD). University of Massachusetts Amherst.
^ Hunter, Tim; Lidz, Jeffrey (2013). "Conservativity and learnability of determiners". Journal of Semantics. 30 (3): 315–334. doi:10.1093/jos/ffs014.
^ Romoli, Jacopo (2015). "A structural account of conservativity". Semantics-Syntax Interface. 2 (1).
^ Steinert-Threlkeld, Shane; Szymanik, Jakub (2019). "Learnability and semantic universals". Semantics and Pragmatics. 12 (4): 1. doi:10.3765/sp.12.4. hdl:11572/364230. S2CID 54087074.

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[cambridgehbk-1] Dag, Westerståhl (2016). "Generalized Quantifiers". In Aloni, Maria; Dekker, Paul (eds.). Cambridge Handbook of Formal Semantics. Cambridge University Press. ISBN 978-1-107-02839-5.

[gamut-2] Gamut, L.T.F. (1991). Logic, Language and Meaning: Intensional Logic and Logical Grammar. University of Chicago Press. pp. 245–249. ISBN 0-226-28088-8.

[barwisecooper-3] Barwise, Jon; Cooper, Robin (1981). "Generalized Quantifiers and Natural Language". Linguistics and Philosophy. 4 (2): 159–219. doi:10.1007/BF00350139.

[4] von Fintel, Kai (1994). Restrictions on quantifier domains (PhD). University of Massachusetts Amherst.

[5] Hunter, Tim; Lidz, Jeffrey (2013). "Conservativity and learnability of determiners". Journal of Semantics. 30 (3): 315–334. doi:10.1093/jos/ffs014.

[6] Romoli, Jacopo (2015). "A structural account of conservativity". Semantics-Syntax Interface. 2 (1).

[7] Steinert-Threlkeld, Shane; Szymanik, Jakub (2019). "Learnability and semantic universals". Semantics and Pragmatics. 12 (4): 1. doi:10.3765/sp.12.4. hdl:11572/364230. S2CID 54087074.

Conservativity

See also

Notes