In formal semantics conservativity is a proposed linguistic universal which states that any determiner ${\displaystyle D}$ must obey the equivalence ${\displaystyle D(A,B)\leftrightarrow D(A,A\cap B)}$. 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]

1. Every aardvark bites. ${\displaystyle \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \rightsquigarrow every(A,B)}$
2. Every aardvark is an aardvark that bites. ${\displaystyle \ \ \rightsquigarrow every(A,A\cap B)}$

Conceptually, conservativity can be understood as saying that the elements of ${\displaystyle B}$ which are not elements of ${\displaystyle A}$ 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 ${\displaystyle shmore}$ defined so that ${\displaystyle shmore(A,B)}$ is true iff ${\displaystyle |A|>|B|}$. If there are 50 biting aardvarks, 50 non-biting aardvarks, and millions of non-aardvark biters, ${\displaystyle shmore(A,B)}$ will be false but ${\displaystyle shmore(A,A\cap B)}$ 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]

1. Only some aardvarks bite.
2. 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

1. ^ 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.
2. ^ 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.
3. ^ a b c 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. S2CID 54087074.