Formalisation in Propositional Logic

Question 1

Truth-functionality

Answer 1

A connective is truth-functional iff the truth-value of the compound sentence cannot be changed by replacing a direct subsentence with another sentence having the same truth-value.

Question 2

Scope of a connective in L1

Answer 2

The scope of an occurrence of a connective in a sentence φ of L1 is the occurrence of the smallest subsentence of φ that contains this occurrence of the connective.

Question 3

Tautology (propositional version)

Answer 3

An English sentence is a tautology iff its formalisation in propositional logic is logically true.

Question 4

Contradiction (propositional version)

Answer 4

An English sentence is a contradiction iff its formalisation in propositional logic is a contradiction.

Question 5

Consistency (propositional version

Answer 5

A set of English sentences is propositionally consistent iff the set of all their formalisations in propositional logic is semantically consistent.

Question 6

Propositional validity

Answer 6

An argument in English is propositionally valid iff its formalisation in L1 is valid.