Dynamic Semantics with Orderings

Hopefully, I have shown how the order-theoretic method is a better method for representing salience than the choice-functional method. However, as we saw in Section 2, explaining anaphoric definite

description utterances requires not only representing salience but also modeling salience change. So far, the only way of modeling salience change that I have presented is DSCF, which utilizes salience functions. As

such, despite its weaknesses, we might think that we are forced to use the choice-functional method, lest we be unable to explain anaphoric definite description utterances.

To reject this conclusion, I will show how salience change can be modeled using salience orderings, by altering DSCF so that it utilizes salience orderings. The system I will define I will callDynamic Semantics with Orderings (DSO). The first difference between the two systems that needs to be accounted for is the

salience updating function. Rather than the salience function update functionupd3, we need a salience ordering update function upd, defined as follows:

upd(≥, x) =≥0 such that∀y, z        y≥zand zy ifx=y y≥ziffy≥z otherwise

This function formalizes the claim I made above that mentioning something raises it to the highest level of salience (in every applicable category). Next we need to redefine the world change potentials and salience change potentials of the English fragment I discussed in Section 2. The world change potentials of DSCF do not invoke salience representations directly, and therefore they do not have to be redefined. Note that the world change potentials for subject-predicate sentences are defined in terms of the referent of their subject term. Supposing the subject term is a definite description, this world change potential will utilize the choice-functional principle (SP) in DSCF and the order-theoretic principle (SO) in DSO. However, either way the world change potentialitself does not need to be redefined, and either way it implements

(one version or another of) the salience analysis.

That just leaves the salience change potentials to be redefined. In DSO, salience change potentials must return salience orders, rather than salience functions. As before, I will assume that utterances of predicates do not affect salience, so the salience change potentials of atomic sentences do not need to be redefined, and no salience change potentials need to be defined for predicates. Thus, we can start our redefinition with the salience change potential of ‘Albert’:

scp(Albert)(c) =upd(≥c,Albert)

This definition entails that an utterance of ‘Albert’ will make Albert the most salient entity in the context, and therefore the most salient entity inevery category Albert is a member of. There is then no need to

specify a particular category Albert is the most salient member of. This definition accords with the discussion in the previous subsection. In line with this, we can redefine the salience change potential of ‘the

F’: scp(theF)(c) =        upd(≥c,ktheFk c ) if ktheFkc is defined ≥c otherwise

Again, this definition entails that an utterance of ‘theF’ will make the most salientF the most salient

entity in the context, and therefore the most salient entity in every category that entity is a member of. This entity will already be the most salientF, as well as the most salient member of every subset of theFs

(given the monotone decreasing property of salience). However, the entity need not be the most salient member of anysupersetsof theFs, which means that this salience update need not be trivial. There is no

sense here in which the referent of ‘theF’ is specifically made the most salientF, and as such there is no

need to justify this particular choice.

Finally, the salience change potential of conjunctive sentences, like the salience change potential of subject-predicate sentences, makes no direct reference to salience representations, and therefore also does not need to be redefined. We now have the tools to analyze the example sentence ‘Albert is in NZ and the cat will stay there’. For convenience, I will abbreviate the contexthwc, upd(≥c,Albert)iascO.

wcp(Albert is in NZ and the cat will stay there)(c) =

wcp(the cat will stay there)(hwcp(Albert is in NZ)(c), scp(Albert is in NZ)(c)i₎

wcp(Albert is in NZ and the cat will stay there)(c) =

      

wcp(the cat will stay there)(cO_{) ifAlbert∈ kis in NZk}c

wcp(Albert is in NZ and the cat will stay there)(c) =        wc ifAlbert∈ kis in NZk c

andAlbert∈ kwill stay therekcO

nothing otherwise

scp(Albert is in NZ and the cat will stay there)(c) =

scp(the cat will stay there)(hwcp(Albert is in NZ)(c), scp(Albert is in NZ)(c)i)

scp(Albert is in NZ and the cat will stay there)(c) =

      

scp(the cat will stay there)(cO) if Albert∈ kis in NZkc

nothing otherwise

scp(Albert is in NZ and the cat will stay there)(c) =       

scp(the cat)(cO_{) ifAlbert∈ kis in NZk}c

nothing otherwise

scp(Albert is in NZ and the cat will stay there)(c) =       

upd(≥c,Albert) ifAlbert∈ kis in NZk c

nothing otherwise

The context change potential defined here is identical to the one defined by DSCF, except that the salience functions are exchanged with salient orderings. Thus we can see that DSO also predicts that an utterance of ‘Albert is in NZ and the cat will stay there’ will contain an anaphoric definite description utterance of ‘the cat’. Furthermore, under DSO, the result of uttering this sentence, supposing it is true, is to update the salience choice function so that Albert is the most salient entity, in accordance with the salience principles discussed above. Thus, we can see that explaining anaphoric definite description utterances does

not require the use of salience functions, and as such we have no reason to favor the choice-functional method over the order-theoretical method.