Conservativity

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

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

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