Semantics 1 (Sailer): Week 5

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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.

Truth tables

(The following exercises have been copied here from the page on exercises for truth tables.)

Click on the boxes for which the truth value would be true.

p q zwisch(p q)zwisch zwisch ¬(p q)zwischzwisch(q ⊃ ¬ (p ∧ q))zwisch
(both p and q are true)
(p is true, but not q)
(p is false, but q is true)
(both p and q are false)


Click on the boxes for which the truth value would be true.

p q r zwisch¬ rzwisch zwisch (p q)zwischzwisch((p ∨ q) ⊃ ¬r)zwisch
(p, q, and r are true)
(p and q are true, r is false)
(p and r are true, q is false)
(p is true, q and r are false)
(p is false, q and r are true)
(p and r are false, q is true)
(p and q are false, r is true)
(p, q, and r are false)


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.

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.

Back to the course overview.