From: Chris Date: Sun, 12 Apr 2015 01:34:41 +0000 (-0400) Subject: edits X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=commitdiff_plain;h=aa3fa8ee79bd50b6371da340227b2144026ae3a7 edits --- diff --git a/topics/_week10_gsv.mdwn b/topics/_week10_gsv.mdwn index 1cd25a80..63bd0711 100644 --- a/topics/_week10_gsv.mdwn +++ b/topics/_week10_gsv.mdwn @@ -9,51 +9,46 @@ GSV are interested in developing and establishing a reasonable theory of discourse update. One way of looking at this paper is like this: - GSV = GS + V, where + GSV = GS + V, where - GS = Dynamic theories of binding of Groenendijk and Stokhof, e.g., - Dynamic Predicate Logic L&P 1991: dynamic binding, donkey anaphora - Dynamic Montague Grammar 1990: generalized quantifiers, discourse referents + GS = Dynamic theories of binding of Groenendijk and Stokhof, e.g., + Dynamic Predicate Logic L&P 1991: dynamic binding, donkey anaphora + Dynamic Montague Grammar 1990: generalized quantifiers, discourse referents - V = a dynamic theory of epistemic modality, e.g., - Veltman, Frank. "Data semantics." - In Truth, Interpretation and Information, Foris, Dordrecht (1984): 43-63. + V = a dynamic theory of epistemic modality, e.g., + Veltman, Frank. "Data semantics." + In Truth, Interpretation and Information, Foris, Dordrecht + (1984): 43-63, or + Veltman, Frank. "Defaults in update semantics." Journal of + philosophical logic 25.3 (1996): 221-261. That is, Groenendijk and Stokhof have a well-known theory of dynamic semantics, and Veltman has a well-known theory of epistemic modality, and this fragment brings both of those strands together into a single system. -We will be interested in this paper both from a theoretical point of -view and from a practical engineering point of view. On the -theoretical level, these scholars are proposing a strategy for -managing the connection between variables and the objects they -designate in way that is flexible enough to be useful for describing -natural language. - ## Basics of GSV's fragment The fragment in this paper is unusually elegant. We'll present it on -its own terms, with the exception that we will not use pegs. See the -digression below concerning pegs for an explanation. After presenting -the paper, we'll re-engineering the fragment using explicit monads. - -In this fragment, points of evaluation are not just worlds, but a pair -of a world and an assginment function. This is familiar from Heim's -1983 File Change Semantics. We'll follow GSV and call a -world-assignment pair a "possibility". Then a context is a set (an -"information state") is a set of possiblities. Infostates -simultaneously track both information about the world (which possible -worlds are live possibilities?) as well as information about the -discourse (which objects to the variables refer to?). - -Worlds in general settle all matters of fact in the world. In -particular, they determine the extensions of predicates and relations. +its own terms, with the exception that we will not use GSV's "pegs". +See the discussion below below concerning pegs for an explanation. +After presenting the paper, we'll re-engineering the fragment using +explicit monads. + +In this fragment, points of evaluation are not just worlds, but pairs +consisting of a world and an assginment function. This conception of +an evaluation point is familiar from Heim's 1983 File Change +Semantics. Following GSV, we'll call a world-assignment pair a +"possibility", and so a context (an "information state") will be set +of possiblities. As GSV emphasize, infostates simultaneously track +information about the world (which possible worlds are live +possibilities?) as well as information about the discourse (which +objects to the variables refer to?). The formal language the fragment interprets is Predicate Calculus with -equality, existential and universal quantification, along with one -unary modality (box and diamond, corresponding to epistemic necessity -and epistemic possibility). +equality, existential and universal quantification, and on 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. [[An implementation @@ -63,17 +58,16 @@ 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 possibility: - ref(i, t) = t if t is an individual, and + ref (i,t) = t if t is an individual, and g(t) if t is a variable, where i = (w,g) -Here are the main clauses for update (their definition 3.1). - -Following GSV, we'll write `update(s, φ)` (the update of information -state `s` with the information in φ) as `s[φ]`. +Immediately following are the recipes for context update (GSV's +definition 3.1). Following GSV, we'll write `update(s, φ)` (the +update of information state `s` with the information in φ) as `s[φ]`. - s[P(t)] = {i in s | w(P)(ref(i,t))} + s[P(t)] = {(w,g) in s | w P (ref((w,g),t))} -So `man(x)` is the set of live possibilities `i = (w,g)` in s such that +So `man(x)` is the set of live possibilities `(w,g)` in s such that the set of men in `w` given by `w(man)` maps the object referred to by `x`, namely, `g("x")`, to `true`. That is, update with "man(x)" discards all possibilities in which "x" fails to refer to a man.