Understanding Universal Disjunction via Normal Forms using Venn Diagrams

The difference in meaning between the two versions of universal disjunction is a fundamental feature of quantificational logic, yet it is rarely subjected to sustained semantic analysis. Working within a limited fragment of quantificational logic, a Venn diagram semantics is used to identify twelve distinct meanings, yielding normal forms that distinguish disjunctions of universally quantified sentences from cases in which a universal quantifier is distributed over a disjunctive matrix. The difference between the two is reflected in the differing lengths of their respective normal forms.