X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=blobdiff_plain;f=topics%2F_week10_gsv.mdwn;fp=topics%2F_week10_gsv.mdwn;h=1cd25a800c4c03b671bdfcb37cc09fe044699913;hp=c557d08be3d63d066cfd12430ac1a6a153143911;hb=6e3c775751114918d3c5fb7be4708dc0c555315f;hpb=c75dc0d2008d79a4fcc31e5c7c76317d9d1228d8 diff --git a/topics/_week10_gsv.mdwn b/topics/_week10_gsv.mdwn index c557d08b..1cd25a80 100644 --- a/topics/_week10_gsv.mdwn +++ b/topics/_week10_gsv.mdwn @@ -56,7 +56,8 @@ unary modality (box and diamond, corresponding to epistemic necessity and epistemic possibility). An implementation in OCaml is available [[here|code/gsv.ml]]; consult -that code for details of syntax, types, and values. +that code for details of syntax, types, and values. [[An implementation +in Haskell|code/gsv.hs]] is available as well, if you prefer. Terms in this language are either individuals such as Alice or Bob, or else variables. So in general, the referent of a term can depend on a @@ -545,5 +546,49 @@ fact, their system is careful designed to guarantee that every variable is assigned a discourse referent distinct from all previous discourse referents. -End of digression on pegs. - +The addition of pegs tracks an active discussion in the dynamic +literature around the time of publication of the paper. Groenendijk +and Stokhof (Two theories of dynamic semantics, 1989) noted that it +was possible in DPL for information to be "lost". + + 18. (∃x.P(x)) & (∃x.Q(x)) & R(x) + +If the two existentials happen to bind the same variable (here, "x"), +then the second existential occludes the first. That is, at the point +at which we evalute R(x), all of the assignment functions will be +mapping the variable "x" to objects that have property Q. The +information that there exist objects with property P has been lost. +If you want your dynamic system to be eliminative---or in more general +terms, if you want the amount of information embodied by an updated +information state to be monotonically increasing---then this is a +problem. + +A syntactic solution is to require that the variable bound +by an existential to be chosen fresh. + +Vermeulen, Cees FM. "Merging without mystery or: Variables in dynamics +semantics." Journal of Philosophical Logic 24.4 (1995): 405-450 offers +a different approach, one based on *referent systems*. GSV's pegs are +a referent system. In the pegs system, when (18) is processed, the +information that there is an object that has property P is maintained +in the information state. Curiously, however, there is still no way +to refer to that object, at least, not with a variable, since there is +no variable that is associated with the peg that points to the +relevant object. So the information is present, but not accessible. + +That does not mean that there aren't other expression types that are +able to latch onto peg. An intriguing suggestion based on an example +in Vermeulen is that "former" might be able to provide access to a +hidden peg: + + 19. Someone entered. Someone spoke. The former was a woman. + +Presumably we want *the former* to be able to pick out the person who +entered, whether or not the two existentials bind the same variable or +not. If we allow "former" to latch onto the second most recently +established peg, no matter whether there is a variable still pointing +to that peg, the desired effect is achieved. + +But none of this is relevant for any of the explanations or analyses +provide by the GSV fragment, and it is considerably simpler to see +what their fragment is about if we leave referent systems out of it.