Semantics and Tableaux

Question 1

In tableaux, what aspect of the sentence should you use for your branching?

Answer 1

The main connective of the sentence

Question 2

What sentences are easier to start with in tableaux?

Answer 2

• Double negation
• Conjugation
• Negated disjunction
• Negated Conditional

Question 3

How do you find counter-models in tableaux?

Answer 3

Trace up an open branch and, for every atomic p, assign ν(p)=1, and for every negated atomic ¬p, assign ν(p)=0

E.g.
Let ν(p) = 0 and ν(q) = 1. To see that this really is a counter-model we note that it makes the premises true and the conclusion false. In particular, by the classical meaning for ‘⊃’ when ν(q)=1 we have ν(p⊃q) = 1.

Question 4

What is a good rule to use when looking for main connectives?

Answer 4

They will be inside the fewest parentheses

Question 5

According to classical logics, which arguments are valid?

Answer 5

Exactly the same args

C = TC = NC

Question 6

When is v(AB) = 1?

Answer 6

Iff v(A) = v(B)