Britannica
Sources used in this answer
How do logical connectives determine the truth of molecular propositions?
Created from Britannica articles
using AI.
AI can make mistakes, so verify using Britannica articles.
Analytic philosophy
British philosopher and educator A.J. Ayer, late 1980s.
In analytic philosophy and formal logic, logical connectives determine the truth of molecular (compound) propositions by acting as truth-functions. This means the truth-value of a complex proposition is a quantity that depends entirely on the truth-values of its constituent atomic propositions.12
The logical properties of these connectives are defined by how they map the truth-values of their components to a resulting truth-value (true or false). These dependencies are systematically displayed using a truth table:123
- Conjunction (& or ·): True if and only if both component propositions are true.2
- Disjunction (∨): True if at least one of the component propositions is true.23
- Negation (~): True if the component proposition is false, and false if it is true.2
- Conditional (⊃): True in all cases except when the antecedent is true and the consequent is false.2
By evaluating these functions, one can determine the truth-value of complex formulas regardless of their internal content, a foundational principle in the propositional calculus.24