--- up: - "[[S2 LOGOS]]" tags: - s/science/linguistique aliases: --- - [[compositionnality]] language meaning need to satisfy a constraint much more concrete than [[compositionnality]], namely [[incrementality]] : NL input is processed word by word : - A The train... - B Ah-ha - A ...from Paris... - B Go on - reactions to an "abandonned utterance" - encourage to continue : - A John... Oh never mind - B What about john ? - A He's a lovely chap but a bit disconnected - complete the sentence : - A Bill is... - B Yeah, don't say it, we know. - abandoned utterance in mid-word : - *context : A is in the kitchen searching for the always disappearing scissors* - A Who took the sci-... - scope ambiguity : when there are more than one QNP (quantified noun phrase) - " every student has a supervisor - " a supervisor manages every student - intuitively, NPs refer to individuals or sets of individuals - c yet there are problems - " i saw no one - " Who lost her notebook - [[logique des predicats du premier ordre|first order logic]] to the rescue ? - author:: [[Richard Montague]] - translation into logic : - $\text{An } N \mapsto \exists x (N'(x) \wedge \dots)$ - $\exists x P(x)$ iff there exists a witness $b$ such that $P(b)$ is true - Every / each $\mapsto$ $\forall x$ - $\vdots$ - = A famous supervisor directs every student here. - there are two interpretations : - $\exists x (\operatorname{fam-sup}'(x) \wedge \forall y (\operatorname{student}(y) \to \operatorname{Direct}(x, y)))$ - $\forall y (\operatorname{student}(y) \to \exists x(\operatorname{fam-sup}'(x) \wedge \operatorname{Direct}(x, y))$ - = no player injured herself - $\forall x (\operatorname{player}(x) \to \neg \operatorname{Injure}(x, x)$ - $\neg \exists x (\operatorname{player}(x) \wedge \operatorname{Injure}(x, x))$ -