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Understanding Universal Disjunction

Author:

Goodwin, Garry

Category:

Research Papers

Sub-Category:

Miscellaneous

Language:

English

Date Published:

January 17, 2026

File:

/Research Papers-Miscellaneous/Download/9979

Downloads:

303

Keywords:

Quantificational logic, Universal disjunction, normal forms

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 systematic analysis. Working within a limited fragment of quantificational logic, we introduce a semantics that identifies twelve distinct meanings, allowing us to distinguish disjunctions of universally quantified sentences from cases in which a universal quantifier is distributed over the disjunctive matrix.