WiSe22/23: Constraint-based Semantics 2
HPSG-neutral notation for LRS
Constraints
Metavariables: α, β, ɣ, ..., φ, ψ, ...
Contribution constraints:
- call(x)
The semantic representation of a sign with a contribution constraint of the form call(x) must be an expression containing call(x) as a subexpression - ¬α
The semantic representation of a sign with a contribution constraint of the form ¬α must be an expression containing ¬α as a subexpression where α can be any expression.
Embedding constraints:
- α[call(x)]
The metavariable α is any expression containing call(x) as a subexpression.
Combinatorial semantics
When two signs combine,
- all constraints on the combining signs' semantic representation also apply to the resulting combination, and
- additional constraints may be added through principles of grammar.
Internal content
internal content: The scopally lowest contributed element, marked in curly brackets: {φ}
- call: {call(x)}
- everyone: ∀x({person(x)} : β[x])
External content
external content: The semantic representation of a complete sign, marked by underlining: φ
- everyone: ∀x({person(x)} : β[x])
Combinatorially added constraints
Internal content raisers
When an auxiliary combines with its VP complement, the internal content of the complement must be the internal content of the auxiliary.
Example:
- call: {call(x)}
- didn't: ¬α[{α'}]
- didn't call: β[call(x), ¬α[{α'}, α'≡call(x) ]
This constraint can be expressed more compactly as: β[¬α[{call(x)}]]
Determiner-noun combinations
When a determiner combines with a head, the head's internal content is a subexpression of the determiner's restrictor.
Example:
- book: {book(x)}
- every: {∀}x(φ[x] : ψ[x])
- every book: α[{book(x)}, {∀}x(φ[x] : ψ[x]), φ[book(x)]
This constraint can be expressed more compactly as: α[{∀}x(φ[x, {book(x)}] : ψ[x])]
Quantified NPs as non-heads
When a quantified NP combines with a head, the head's internal content is a subexpression of the quantifier's restrictor.
Example:
- called: {call(x)}
- someone: ∃x({person(x)} : ψ[x])
- Someone called.: α[{call(x)}, ∃x({person(x)} : ψ[x]), ψ[call(x)]]
This constraint can be expressed more compactly as: α[∃x({person(x)} : ψ[x,{call(x)}])]
External content principle
The semantic representation of an utterance
- can only contain the constants, variables, and operators that occur in the constraints contributed by lexical items and
- it must respect all constraints contributed by the lexical and non-lexical items contained in the utterance
Modality
Basic assumptions
We assume:
- Our model contains a set of possible worlds W, and a set of accessiblity relations ACC (ACC ∈ Pow(WW), i.e. M = < U, I, W, ACC >
- There is a special variable, w0 or @ that refers to the current world: [[w0]]M,w = w
- There are special predicates for the different accessibility relations (modal bases):
- Alethic: ALETHsst
- Deontic: DEON1sst and DEON2esst
- Epistemic: EPISTsst
- Dynamic: DYNAMesst
- Bouletic: BOULesst
Example formulae
Sentences are translated as formulae with a free occurrence of the world variable @.
Alex called. call(@,alex) -- also written as call@(alex)
Modal expressions introduce an explicit quantification over worlds (modal force):
Necessity modality: &Box; ⋄