9. PL syntax

Question 1

Syntax (3)

Answer 1

A) the study of language as a closed-off system
B) regardless of the world
C) regardless of meaning

Question 2

Semantics (2)

Answer 2

A) the study of language as it relates to the world
B) focus on the meanings that are conveyed by language

Question 3

Well-Formed Formulas WFF (5)

Answer 3

A) every atomic proposition is a wff
B) if α is a wff and β is a wff, then (α ∧ β) is also a wff
C) if α is a wff and β is a wff, then (α ∨ β) is also a wff
D) if α is a wff, then ¬α is also a wff
E) nothing else is a wff

Question 4

Parse Tree (3)

Answer 4

A) Every WFF has a unique parse tree, if it has two or more then it is not a WFF
B) Parse trees follow WFF rules (∧, ∨, ¬)
C) Bracketing rules help avoid scope ambiguities in WFF

Well form formula Non-well formed formula
3. ((P ∨ Q) ∧ R) P ∨ Q ∧ R
2. (P ∨ Q) R P ∨ Q R | P Q ∧ R
1. P Q P Q | Q R

Question 5

Main Connective (2)

Answer 5

A) first connective that is removed (P.Tree top-bottom)
B) last connective that is added (P.Tree bottom-top)

The conjunction ∧ Is the Main-Connective
3. ((P ∨ Q) ∧ R)
2. (P ∨ Q) R
1. P Q

Question 6

Subformula (2)

Answer 6

A) Components of a P.Tree, anything that occurs within it
B) The result of of a P.Tree is a subformula (limit case)

Subformulas of ‘((P ∨ Q) ∧ R):
((P ∨ Q) ∧ R), R, (P ∨ Q), P, Q

Question 7

Scope of a Connective

Answer 7

A) Lowermost,first, occurence of a connective in a P.Tree
B) DIff occurrences have different scopes
C) Scope of main connecter is always the whole WFF

3. (((P ∨ Q) ∨ H) ∧ R) Scope of ∧ (((P ∨ Q) ∨ H) ∧ R) = WFF
4. ((P ∨ Q) ∨ H) R Second Scope of ∨ is ((P ∨ Q) ∨ H)
5. (P ∨ Q) H Scope of ∨ is (P ∨ Q)
6. P Q