Chapter 3: Formalisation in Propositional Logic

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.

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.

An English sentence is a tautology iff…

its formalisation in propositional logic is logically true.

An English sentence is a propositional contradiction iff…

its formalisation in propositional logic is a contradiction.

A set of English sentences is propositionally consistent iff…

the set of all their formalisations in propositional logic is semantically consistent.

An argument in English is propositionally valid iff…

its formalisation in 𝐿₁ is valid.