Semantics 1, SoSe 2016 (Sailer): Difference between revisions
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The material for week 3 can be accessed [[Semantics_1,_SoSe_2016_(Sailer): Week 3|here]] | The material for week 3 can be accessed [[Semantics_1,_SoSe_2016_(Sailer): Week 3|here]] | ||
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== Links to our literary scenario == | == Links to our literary scenario == | ||
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** two formulae that are false in your mode. | ** two formulae that are false in your mode. | ||
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Revision as of 20:08, 3 May 2016
Additional material for week 5
Formulae with more than one connective
The 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.
Preparation for week 5
- Read Levine et al (in prep.), Chapter 2, section 2.
- Using your model from last week,
- Give 1 formula with ⊃.
- Give 1 formule with 2 different connectives (both distinct from ⊃)
- Provide the step-by-step computation of the truth of your 2 formulae.
Additional material for week 4
The material can be found on the page Semantics 1, SoSe 2016 (Sailer): Week 4
Additional material for week 3
The material for week 3 can be accessed here
Just like with names, we want to have symbols that we can use in the logical language. For our example, let's take the predicate symbols afternoon-snack-of_2 and father-of_2, and talks-with_2. (The number 2 indicates that the interpretation consists of pairs, not just of single individual) There interpretation is defined as follows:
I(afternoon-snack-of_2) = { < x, y > | x is y 's afternoon snack } = { <Redridinghood, Wolf >, <Grandmother, Wolf > }.
Task: For each of your properties, invent an appropriate predicate symbol. Define its interpretation.
Properties and predicate symbols
A property is a specification that either holds of an individual or not. In the little story, having a big mouth is a property of the Wolf, but of noone else in the story. Being female holds of both Little Red Riding Hood and the Grandmother.
We can think of a property as the set of individuals that have this property. Under this view, the property of being female would be the set {Redridinghood, Grandmother}.
Alternatively it is convenient to think of properties as 1-place relations. Under this view, the property of being female would be a set of lists of length 1. This is what the property of being female then looks like: { <Redridinghood>, <Grandmother> }
Task: Using your Game of Thrones universe, define two properties in the format of 1-place relations.
Just like before, we want to have symbols that we can use in the logical language. For our example, let's take the predicate symbols female_1 and has-big-mouth_1. There interpretation is defined as follows:
I(female_1) = { < x > | x is female } = { <Redridinghood>, <Grandmother> }.
Task: For each of your properties, invent an appropriate predicate symbol. Define its interpretation.
Computing 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)
For next week
- Work through this wiki page.
- Read Levine et al. (in prep.), Chapter 2, Section 1 [available on olat].
- Define a model and introduce the necessary name symbols and predicate symbols for our scenario with
- three individuals
- two relations
- two properties
- Use your model and your symbols and write down
- one formula that is true in your model and
- two formulae that are false in your mode.
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