SoSE15: Term paper project: Determiners

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Short description of the project

• Difference between "every", "some" and the definite article;
• Video about how to differentiate "some" and the definite article;
• Three exercises for each operator

The difference between logical quantifiers and definite descriptions

The universal and existential quantifiers have to be interpreted differently than the definite article.

The universal quantifier (every, all → ∀) indicates that every single person or thing in a model that has the features of the restrictor, also has the features of the scope.

The existential quantifier (some, a → ∃) states that there is at least one person or thing or more in a model that has both the features of the restrictor and the scope.

The definite article (the → ⍳) states that there is absolutely one person or thing and no more or less in a model that fits exactly the described features.

Model from the scenario "Frozen"

Characters:

• Elsa, the Snow Queen of Arendelle
• Anna, the Princess of Arendelle
• Kristoff, an iceman
• Sven, a reindeer
• Olaf, a snowman
• Hans, the Prince of the Southern Isles

Properties:

• royal1 = {<x> | x is royal} = {<Elsa>, <Anna>, <Hans>}
• prince1 = {<x> | x is a prince} = {<Hans>}
• human1 = {<x> | x is human} = {<Elsa>, <Anna>, <Kristoff>, <Hans>}
• male1 = {<x> | x is male} = {<Kristoff>, <Sven>, <Olaf>, <Hans>}

2-place-relations:

• sibling2 = {<x, y> | x is the sibling of y} = {<Elsa, Anna>, <Anna, Elsa>}
• get-engaged2 = {<x, y> | x and y get engaged} = {<Anna, Hans>, <Hans, Anna>}

Example for the universal quantifier

Example: Every royal is human.

Here, every is our determiner, royal is our restrictor and human is the scope. We will choose x as our variable. Therefore, the paraphrase would look like that:

For every x such that x is royal x is human.

The overall formula for this expression would look like that:

∀ x (royal1(x) : human1(x))

Now we will interpret our formula, so we have to check the truth values for all our individuals in the model:

Participants

• Monique Lanz

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