Semantics 1, SoSe 2016 (Sailer)

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.

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)zwisch	zwisch(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)

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.

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

p	q	r	zwisch¬ rzwisch	zwisch (p ∨ q)zwisch	zwisch((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)

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