Cognitive Science > Introduction to Semantics > Syntax and Semantic Interpretation

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[edit] Set and Function

  • set and functional (lamda) definition: interchangeable
  • set: only 'in' or 'out', not 'undefined'
    • useful in presuppositions
    • -> function view more handy
  • relations can be expressed as functions

[edit] Currying/Schönfinkelization

  • [|parent|] as function
    • LaTex: \lambda <x,y>\in\{ <x,y>|x\in Person\}[y is a parent of xLaTex: ]
    • LaTex: \lambda x\in Person[\lambda y\in Person[y is a parent of xLaTex: ]]
  • advantages
    • arguments are normally not symmetric
    • one argument is usually closer than the other

[edit] Binary Branching

  • [|Hannes likes Cassandra|] denotated: [|like|]([|Cassandra|]) LaTex: \lambda x[LaTex: \lambda y[y likes x]]
  • Evidence for binary branching can be accounted for by this mechanism.
  • Transitive Verbs
    • add to lexicon: function that takes individual first and then a function (like an intransitive verb)

[edit] Semantic Types

  • e = entitiy
  • t = truth value
    -> saturated denotations, basic types
  • <e,t> functions form individual to truth values
  • <e,<e,t>> functions ...
  • <t,t> 'it is not the case that'
  • <t,<t,t>> 'and', 'or'
    -> unsaturated denotations
  • D_e = domain of e, etc.
    -> new rule: type driven interpretation

[edit] General Semantic Principles

  • TN
    If LaTex: \alpha is a terminal node and LaTex: [|\alpha|] is in the domain of LaTex: \lbrack\rbrack, then LaTex: \lbrack |\alpha|\rbrack is given in the lexicon.
  • NN
    non-branching
  • FA
    branching
  • Interpretability principle
    A tree LaTex: \alpha is interpretable iff all of its nodes are in the domain of LaTex: \lbrack \rbrack.

[edit] Syntax & Semantics

  • separate models?
Source: http://wiki.stuhlmueller.info/Cognitive_Science/Introduction_to_Semantics/Syntax_and_Semantic_Interpretation