A truth-functional logic for near-universal generalizations (Q751649)

This paper continues to solve the problems of logical analysis of ``almost all'' quantification, as have been formulated in E. W. Adams's papers. The ``near-universality'' is treated as ``a closure quantifier which can be embedded in Boolean combinations''. The resulting binary truth-semantics is obtained ``by replacing the limit concept in the definition of measure-entailment by a class of structures used to obtain that limit''. A natural deduction system for this ``m-entailment'' is introduced and its soundness and completeness proved. Remark: The considerations on p. 395\({}^{14-26}\) are unintelligible since the claim made on p. 395\({}^{17-18}\) is trivially false.