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<embedvideo service="youtube" dimensions="400">http://www.youtube.com/watch?v=ZWdltj5Mqdc</embedvideo>
<embedvideo service="youtube" dimensions="400">http://www.youtube.com/watch?v=ZWdltj5Mqdc</embedvideo>


= Videos with example computations =


== Formulae with connectives ==
== Formulae with connectives ==
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<embedvideo service="youtube" dimensions="400">http://youtu.be/C1rjU104R54</embedvideo>
<embedvideo service="youtube" dimensions="400">http://youtu.be/C1rjU104R54</embedvideo>


= Logical determiners/quantifiers =
= Logical determiners/quantifiers =

Revision as of 15:46, 13 October 2019


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.

Based on this podcast, we can define a model as follows:

  • Universe: U = {LittleRedRidingHood, Grandmother, Wolf}
  • Properties:
    red-hood = { < x> | x wears a read hood } = { <LittleRedRidingHood> }
    female = { <x> | x is female } = { <LittleRedRidingHood>, <Grandmother> }
    big-mouth = { <x> | x has a big mouth } = { <Wolf> }
    live-in-forest = { < x> | x lives in the forest } = { <Grandmother>, <Wolf>}
  • Relations:
    grand-child-of = { <x,y> | x is y 's grandchild } = { <LittleRedRidingHood,Grandmother > }
    afternoon-snack-of = { <x,y> | x is y 's afternoon snack } = { <LittleRedRidingHood,Wolf > }

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)


Connectives

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 pq it true if and only if p is true and q is true.

Truthtable AND

Truthtable AND1.png

OR (∨)

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

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

Truthtable OR

Truthtable OR1.png

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)

An implication pq is true if and only if p is false or q is true (or both).
In other words: An implication pq is true if and only if whenever p is true, q is true as well.

Truthtable IF/THEN

Truthtable IF THEN2.png

NOT (¬)

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

A negated formula ¬p is true if and only if p is false.

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

Truthtable NOT

Truthtable NOT.png

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.


Formulae with connectives

The following video presents the step-by-step computation of the truth value of two formulae with connectives. The example uses a model based on Shakespeare's play Macbeth. The two formulae are:

  • ¬ king(lady-macbeth)
  • king(duncan) ∨ king(lady-macbeth)

The next 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.

Logical determiners/quantifiers

Video introducing determiners into our logical language. (The video is based on the scenario of Romeo and Juliett.)

Links

Predicate logic in the Virtual Linguistics Campus

There are short lectures by Jürgen Hanke (Virtual Linguistics Campus) related to the topics of Chapter 2:

  • Predicates and their arguments
  • Logical connectives
  • Quantifiers ("∀" and "∃")
    • Note: The video mentions the terms "restrictor" and "scope" of a quantifier but uses the conventional first-order representation of quantifiers. This means that the restrictor and the scope are linked by an implication ("⊃") in the case of a universal quantifier and by a conjunction ("∧") in the case of the existential quantifier.
      So, where we write: ∀ x (φ : ψ), the traditional notation is: ∀ x (φ ⊃ ψ),
      and where we write ∃ x (φ : ψ), the traditional notation is ∃ x (φ ∧ ψ)
    • Note: In the video, the symbol "¬" is called "the negative quantifier". This is to be seen as short hand for "¬∃"

Pine's Essential Logic: Basic Reasoning Skills for the 21st Century

Ronald C. Pine is profesor of philosophy at the Honolulu Community College. He has put online a number of courses and a version of his book on logic, entitled Essential Logic: Basic Reasoning Skills for the 21st Century:

Pine, Ronald C.: Essential Logic: Basic Reasoning Skills for the 21st Century. Harcourt, 1996; Oxford University Press, 2001; online edition, 2011.
URL: http://home.honolulu.hawaii.edu/~pine/EL/Essential-Logic.html

The book's content goes far beyond what we cover in our textbook.


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