10. PL Semantics

Question 1

Interpreting Atomic Propositions (by Glossary)

Answer 1

Based on the meaning of words, semantics, the truth condition is locked.
P: Lorenz is a logician. If situations where Lorenze is a Logician P is true and situations where he isn’t P is false.

Question 2

Interpreting Molecular Propositions

Answer 2

Based on multiple schematic variables and their conjunction with connectives.

Question 3

Determinacy

Answer 3

Given a possible situation s, every wff is either true in s or false in s.

Question 4

Truth values and valuations

Answer 4

A) there are exactly two truth values: 0 & 1
B) valuation of wff’s assigns exactly one truth value
C) Truth valuation of the whole WFF is based on
1) the truth values assigned to the atoms
2) the truth conditions of the connectives

Question 5

Parallelism between syntax and semantics

Answer 5

A) a string of symbols is well-formed (syntactic criterion) if and only if it has a unique truth value (semantic criterion)
B) They share perfectly parallel sematic and syntactic trees.

Question 6

Short working

Answer 6

A) It’s more economical to use truth tables than semantic trees to valuate WFFs.
B) Taking into account the truth function of connectives we can move pass evaluating both atomic propositions.
EX:
A∧B, if A is 0, we know the truth table for A∧B is 0. We must not examine it any further.
A∨B, if A is 1, we know the truth table for A∨Bis 1.