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Understanding Universal Disjunction via Normal Forms using Venn diagrams

Author:

Goodwin, Garry

Category:

Research Papers

Sub-Category:

Philosophy

Language:

English

Date Published:

February 02, 2026

File:

/Research Papers-Philosophy/Download/9979

Downloads:

423

Keywords:

Quantificational logic, Universal disjunction, normal forms, Venn diagrams

Abstract:

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 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.