LTAG Semantics on the Derivation Tree Presented by Maria I. Tchalakova

Papers for analysis: Factoring Predicate Argument and Scope Semantics: Underspecified Semantics with LTAG, Kallmeyer and Joshi (2003) Compositional Semantics with Lexicalized Tree-Adjoining Grammar (LTAG): How Much Underspecification is Necessary?, Joshi and Vijay-Shanker (1999)

Can the TAG derivation tree reepresent a semantic graph? An answer in the light of Meaning-Text Theory, Candito and Kahane (1998)

The elementary trees encapsulate only the syntactic/semantic arguments of the lexical anchor. All the recursion is factored away  elementary trees are extended projections of the lexical items. The elementary trees posses an extended domain of locality.

This extended domain of locality helps for formulating a syntax-semantic interface as a relation between elementary trees and semantic representations. Because of the extended domain of locality “ flat ” semantic representations can be used (one needs not represent (reproduce the internal structure of the elementary trees))

Localization of the arguments of the lexical items  Defining compositional semantics for LTAG with respect to the derivation tree. The derivation tree indicates how to combine the semantic representations.

A domain of locality – a domain over which various syntactic or semantic dependencies can be specified. Every formalism specifies such domain of locality and many of the properties of the formalism follow from the initial specification of the domain of locality. In CFG – domain of locality is the one level tree corresponding to a rule in a CFG.  arguments are not in the same local domain

Two important issues: 1.lexicalization of each elementary domain of locality 2.encapsulation of the arguments of the lexical anchor in the elementary domain Adjoining viewed as: 1.inserting a tree 2.a pair of substitutions

(any CFG can be strongly lexicalized by an LTAG) Increasing the domain of locality leads to: 1.lexicalization of each elementary domain 2.introducing adjoining 3.strong lexicalization of CFGs. The factoring of recursion allows all dependencies to be localized in the elementary domains.

An alternative perspective on adjoining The tree to which another three is to be adjoined could be viewed as made up of two threes (supertree and subtree at X) Wrapping operation: wrapping these two trees around the tree, which is to be adjoined – seen as a substitution and adjoining.

The wrapping perspective can be formalized by MC-LTAG. The elementary objects can be sets of trees. Here only two components are used. Using only tree-local MC-LTAG – adopting the constraint that the tree receiving multi- component attachments must be an elementary tree.

The scope ambiguity is reflected in the derivation tree. Generally, in other approaches the scope ambiguity is represented at another level of representation.

COMPOSING SEMANTICS WITH LTAG Every elementary tree is connected with a semantic representation. How these semantic representation combine depends on the derivation structure. Each edge represents one derivation step in the LTAG. Substitution (inserting a new argument, relating a predicate to its arguments) – direction from the mother to the daughters. Adjoining – the other way round.

Example: John always loves Mary. Semantic representation consists of a conjunctively interpreted set of formulas and a set of argument variables.

A partial assignment function f is applied  the union of the two semantic representation is built. Separation of Scope Information from Predicate Arguments Relations.

Problematic cases – quantifiers: the contribution of a quantifier is connected to its syntactic position, according to which an argument is added to the semantic representation. However, quantifiers can rise.

Considering quantifiers in the traditional way: quantifying phrases take two properties and give back a proposition. Every dog barks. every(x, dog(x), bark(x))

The contribution of a quantifier consists of two parts: 1.every(x,p1,p2) – responsible for the scope relations 2. P(x) and x – restrict the quantifier, inserts the semantic argument  Separate the contribution of a quantifying phrase into two elementary trees: 1. Auxiliary tree (scope contribution) 2. Initial tree (predicate argument contribution)  use MC-LTAG

Also, we need a restricted use of multiple adjunctions. Because of the tree-locality restriction, the right amount of underspecification needed to treat scope ambiguity is allowed.

Underspacified Quontifier Scope Description of underspecified representation  Hole semantics - Using only propositional holes – hopefully sufficient.

(A partial order on holes and labels describes the structure of a semantic representation). Labels, holes variables  between the hole and the label quantifiers might come in

Adjunct scope Pat allegedly usually drives a Cadillac. usually - in the scope of allegedly, adverbs – VP- modifiers Assumption: for tree sets containing single auxiliary trees, multiple adjunctions of several such trees at one and the same node are not allowed.

Allow multiple component adjunction in a restricted way – obtain the syntactic derivations for quantifiers. Adjoining: - at the VP-node - at the node with label ADV

Towards the Formal Definition of the Syntax-Semantic Interface … Derivations considering: Tree-local derivation Restriction on multiple-adjunctions Definition: Scope auxiliary trees: Let G be a TAG and β an auxiliary tree. Β is a scope auxiliary tree iff - β consists of only one single node u - and, the top and bottom feature structures of u are empty

Consider MC-TAG: Derivations must be tree-local Multiple adjunction is only allowed for scope auxiliary trees that form a tree set together with one initial tree. After an adjunction step, there is a node that is considered as being part of the old tree and at the same time part of the adjoined auxiliary tree.

All operations take place at certain positions in the tree that is already derived. The derived order is the same, no matter which linear order is chosen for the sisters. This, however, might be important for the corresponding semantic representation. A semantic representation is a set of terms with together with constraints on scope order.

Combining Semantic Representations: When applying one semantic representations to another some of the arguments of the first representation are mapped to free variables, holes or labels from the other representation, and apart from this the union of the of the two semantic representations is built.

The Syntax-semantic interface is a set of triples, each of these triples consisting of an elementary tree from the syntactic MC-TAG, a semantic representation, and a relation between the argument variables of the semantic representation and positions of substitution nodes in the representation.

For the syntax-semantic interface, in order to obtain the semantic representation, it is not necessary to consider the specific syntactic trees or tree sets. The derivation structure is sufficient to determine how to put the corresponding semantic representations together.

Viewing the derivation of a sentence as a set of attachments: Considering substitution and adjunction as attachments – attachments of one tree to another tree. The order of attachments need not be reflected in the semantics.

Monotonicity vs. non-monotonicity. Generally, the semantic is build monotonically. Underspecification

Analyzing Pat allegedly usually drives a Cadillac considering allegedly to recursively modify usually and not the whole VP – different auxiliary tree, different semantic representation for allegedly: the elementary tree of allegedly adjoins at the ADV-node of the elementary tree of usually