Wiki-ch2

Additional Wiki pages for Chapter 2

Models

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.

<mediaplayer>http://youtu.be/4a3mXelw7H4</mediaplayer>

Truth tables

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.

Truth tables for connectives

AND (∧)

Symbol: ∧
Sentence: Harry is a student and Snape is a teacher.
Formulae: student(harry) ∧ teacher(snape)

A conjunction p ∧ q it true if and only if p is true and q is true.

Truthtable AND

OR (∨)

Symbol: ∨
Sentence: Harry is a student or Snape is a teacher.
Formulae: student(harry) ∨ teacher(snape)

A disjunction p ∨ q is true if and only if p is true or q is true (or both).

Truthtable OR

IF/THEN (⊃, →)

Symbol: ⊃, → (Note: We use the symbol ⊃ in the textbook as it is more common in the logical literature.)
Sentence: If Harry is a student then Snape is a teacher.
Formula: student(harry) ⊃ teacher(snape)

Truthtable IF/THEN

NOT (¬)

Symbol: ¬
Sentence: Harry is not a student.
Formula: ¬student(harry)

The original formula has to be false for the overall statement to be true.

Example: Only if student(harry) is false, ¬student(harry) is true.

Truthtable NOT

Truth tables for complex formulae

Truth tables are also useful to compute the truth value of complex formulae. This is shown in the following podcast, created by Lisa Günthner.

<mediaplayer>http://www.youtube.com/watch?v=ZWdltj5Mqdc</mediaplayer>