Formalisation in Predicate Logic

Question 1

Syntactic consistency

Answer 1

A set Γ of L2-sentences is syntactically consistent iff there is a sentence φ such that Γ does not entail φ.

Question 2

Scope of a quantifier or connective in L2

Answer 2

The scope of an occurrence of a quantifier or a connective in a sentence φ of L2 is the occurrence of the smallest L2-formula that contains that occurrence of the quantifier or connective and is part of φ.

Question 3

Logical truth, contradiction, consistency (predicate version)

Answer 3

(i) An English sentence is logically true in predicate logic iff its formalisation in predicate logic
is logically true.
(ii) An English sentence is a contradiction in predicate logic iff its formalisation in predicate logic
is a contradiction.
(iii) A set of English sentences is consistent in predicate logic iff the set of their formalisation in
predicate logic is semantically consistent.

Question 4

Validity (predicate version)

Answer 4

An argument in English is valid in predicate logic iff its formalisation in the language L2 of predicate logic is valid.