SoSe22: Constraint-based Semantics 2

LRS as assumed in the course

Conventions for the LRS-specific features

DR: Discourse referent

Intuition: The discourse referent that a constituent refers to.

• For verbs: the predicate contributed by the verb.
  

(Note: This is different from the way it is done in the textbook, because we don't use an eventuality variable in our course)

• For proper names: the name symbol contributed by the name

• For common nouns: the variable bound by the logical determiner that combines with this noun

• For determiners: the same as the DR value of the noun that they combine with; the variable that is bound by the logical determiner contributed by the determiner.

EXTERNAL-CONTENT (EXC, EXCONT, EX-CONT)

• For utterances: the semantic representation (logical form) that represents the truth conditions of the utterance

• For proper names: just the name symbol

• For quantified NPs: the quantified formula in which the DR value of the NP is bound

• For determiners: The EXTERNAL content and the INTERNAL-CONTENT are identical.

INTERNAL-CONTENT (INC, INCONT, IN-CONT)

Intuition: The scopally lowest element contributed by the lexical head of a phrase.
Typically, the main predicate associated with the lexical head combined with its semantic arguments.

• For proper names: just the name symbol

• For common nouns: their predicate applied to their DR value (plus other arguments if the predicate has more than just one argument)

• For ``ordinary´´verbs: their predicate (i.e. their DR value) applied to their semantic arguments
• For modal auxliaries, such as can, may, must, ...:
  Their DR value is the modal operator Can, May, Must, etc. Their INCONT value is identical with that of their VP complement.
  In this class, we specify this directly in the lexical entry of the auxiliary.
• For intensional verbs such as search, look (for), be missing, we assume a lexical decomposition into a lower predicate and a higher predicate. The DR value is identical with the higher predicate, and the INCONT with the lower predicate, applied to its arguments.
  For example look (for) is decomposed into try(x,...find(x,y)...). The DR value is the predicate try, the INCONT value is the expression find(x,y).

• For determiners: the quantified formula consisting of the logical determiner contributed by the word, binding the determiner's DR value

PARTS

The list of all meaning contributions made by a sign or its components.

LRS Principles

For a list of ``official LRS principles´´see the appendix of the textbook: https://www.lexical-resource-semantics.de/wiki/index.php/Appendix_LRS_Principles

Content Principle

In any headed phrase,
the DR value of the mother and the head daughter are identical.

(Note: This differs from the textbook version, as we only have the feature DR and no feature MAIN in this class.)

LRS Projection Principle


(final version going back to Penn and Richter (2004)):

In every headed phrase,

1. The EXTERNAL-CONTENT value of the mother and the head daughter are identical.
2. The INTERNAL-CONTENT value of the mother and the head daughter are identical.
3. The PARTS list of a phrase is the concatenation of the PARTS lists of its daughters.

Semantics Principle

In every headed phrase,

1. If the nonhead is a determiner with an INCONT of the form Qx(φ:ψ), then the INCONT of the head is a component of φ and the head and the nonhead have identical EXCONT values.
2. For each nonhead that is a quantified NP with an EXCONT value of the form Qx(φ:ψ), the INCONT of the head is a component of ψ.

External Content Principle

1. In every phrase, the EXTERNAL-CONTENT value of a non head daughter is an element of its PARTS list.
2. In every utterance, every subexpression of the EXTERNAL-CONTENT value of the utterance is an element of its PARTS list, and every element of the utterance's PARTS list is a subexpression of its EXTERNAL-CONTENT value.

Meeting 02: Introduction

Note: The meeting takes place asynchronically!

Please watch the video for this meeting:

Definition of a model

The following material is an adapted form of material created by student participants of the project e-Learning Resources for Semantics (e-LRS). Involved participants: Lisa, Marthe, Elisabeth, Isabelle.

Watch a short podcast what first-order models look like.

Based on this podcast, we can define a model as follows:

• Universe: U = {LittleRedRidingHood, Grandmother, Wolf}
  
• Properties:
  red-hood = { < x> | x wears a read hood } = { <LittleRedRidingHood> }
  female = { <x> | x is female } = { <LittleRedRidingHood>, <Grandmother> }
  big-mouth = { <x> | x has a big mouth } = { <Wolf> }
  live-in-forest = { < x> | x lives in the forest } = { <Grandmother>, <Wolf>}
  
• Relations:
  grand-child-of = { <x,y> | x is y 's grandchild } = { <LittleRedRidingHood,Grandmother > }
  afternoon-snack-of = { <x,y> | x is y 's afternoon snack } = { <LittleRedRidingHood,Wolf > }

Computation of the truth value of atomic formulae

The following video presents the step-by-step computation of the truth value of two atomic formulae. The example uses a model based on Shakespeare's play Macbeth. The two formulae are:

• kill(macbeth,duncan)
• kill(lady-macbeth,macbet)

Computation of the truth value of complex formulae

The following video presents the step-by-step computation of the truth value of two formulae with connectives. The example uses a model based on Shakespeare's play Macbeth. The two formulae are:

• ¬ king(lady-macbeth)
• king(duncan) ∨ king(lady-macbeth)

The next video shows how the truth value of a more complex formula can be computed. The example contains two connectives:

kill(malcom,lady-macbeth) ∨ ¬thane(macbeth)

The video shows two different methods: top down and bottom up.

Quantifiers

Video introducing determiners into our logical language. (The video is based on the scenario of Romeo and Juliett.)

Meeting 01

(no meeting)