LTAG Semantics for Questions Aleksandar Savkov

Contents Introduction Hamblin’s idea Karttunen’s upgrade Goals of the paper Scope properties of wh-phrases Quantificational NPs Wh-phrases as quontifiers Multiple wh-questions Long-distance wh-dependencies Comparison to other approaches Embedded interrogatives Ambiguity in multiple wh-questions References

Introduction Hamblin’s semantics for questions Every question denotes a set of propositions expressed by its possible answers Who came? {‘Bill came.’, ‘John came.’, ‘Dan came.’…} Is it raining? {‘It’s raining.’, ‘It’s not raining.’}

Introduction Karttunen’s upgrade Every question denotes a set of propositions expressing only true answers

Introduction Goals of the paper (Romerom Kallmeyer, Babko-Malaya 2004) capture scope properties of quantificational elements within the question achieve the correct semantics for interrogatives embedded under e.g. know

Introduction Example of different scopes for wh- and non-wh-quantifiers:

Introduction Example for multiple wh- phrases:

Introduction Example for correct semantics of interrogatives:

Scope properties of wh- phrases Quantificational NPs Wh-phrases as quontifiers Multiple wh-questions Long-distance wh-dependencies Comparison to other approaches

Quantificational NPs We assume quantifiers as everybody have a multi-component set containing an auxiliary tree (contributes to the scope part) and an initial tree (contributes the predicate argument)

every(x,person(x,s0),laugh(x,s0))

disambiguation: 3 -> l3, 4 -> l1 every(x,person(x,s0),laugh(x,s0))

Wh-phrases as quantifiers Repeating the Karttunen style

Wh-phrases as quontifiers 5 -> l4, 9 -> l5, 10 -> l2, 7 -> l6, 14 -> l7, 15 -> l1 Q3:λp.p(s0) and some(x,person(x,s0), p=λs.every(y,person(y,s/s0), like(x,y,s)))

Multiple wh-questions To treat in situ wh-quantifiers correctly we need the minimal scope of any NP substitution node To achieve that we need both minimal scopes for wh- and non-wh-quantifiers We will use the feature WH for the wh- quantifier and P for the non-wh

Long-distance wh- dependencies In long distance wh-dependencies, one must make sure that the wh-quantifier scopes over all verbs in the sentence in order to provide argument for the most embedded one.

Long-distance wh- dependencies

Comparison to other approaches Karttunen style semantics Ginzburg and Sag, 2000 Our approach

Karttunen style semantics Draws distinction between wh-scope and non-wh-scope Uses different semantic types for all the relevant categories Wh-quantifiers combine with functions of type from situations to sets of propositions Thus all wh-quantifiers must scope over all non-wh-quantifiers

Ginzburg and Sag Ontological distinction between state- of-affairs (SOA) and propositions One builds propositions, questions, outcomes and facts from SOAs Non-wh-quantifiers have SOA nuclear scope and wh-quantifiers have proposition and thus the second one is wider

Our approach We use a ‘flat’ semantic framework in the style of MRS (Copestake et al.1999) Semantic contribution of the elementary and auxiliary trees is a set of formulas No type distinction can be made to which of the scope properties of wh- and non-wh-quantifiers could relate No distinction between SOA and propositions MAXS, WH and P features and feature unification are used to define appropriate scope windows.

Embedded interrogatives Unless bound by an operator situation arguments are replaced by the utterance situation In embedded interrogatives the issue is how to bind the situation variable

Embedded interrogatives

Ambiguity in multiple wh- questions Some multiple wh-questions are ambiguous Example: Who remembers where Mary keeps which book? This could be read in two different ways: 1) Bill remembers where Mary keeps which book. 2) Joe remembers where Mary keeps Aspects and Max remembers where Mary keeps Syntactic Structures

References LTAG Semantics for Questions (Romero, Kallmeyer, Babko-Malaya, 2004) Syntax and semantics for questions (Karttunen)