非严格弗雷格自由逻辑

莱曼(S.Lehmann)的1994年的论文从三值逻辑角度处理语言中的空词项。弗雷格认为句子的所指是真值,包含空词项的句子缺乏所指,而只有涵义,那么这样的句子不真也不假。莱曼的文章刻画了弗雷格这一思想,但有两点不尽人意之处:其一、对量词进行特殊处理,使得量词公式是二值的;其二,把包含空词项的复合句一概归于第三值。针对上述两点,本文以一度衍推系统为基础,在语义上,以偏解释函数为基础构造了一个非严格弗雷格中性自由逻辑表列系统,使得量词公式是三值的,同时使得一部分包含空词项的复合公式或真或假。

Non-strict Fregean Free Logic

Lehmann’s paper in 1994 is a representative article that aims at dealing with empty terms in terms of three-valued logic. Frege hold that the reference of a sentence is truth-value, sentences which include empty terms have no references but senses , that is to say ,such sentences are neither true nor false. Lehmann’s paper in 1994 characterizes Frege’s idea, but there are two problems: first, the special treatment of quantification makes the quantification formulas having two-valued. Second, it concludes that all complex sentences with empty terms are neither true nor false. In order to avoid the problems, based on first degree entailment, this paper presents a non-strict Fregean neutral free logic by partial interpretation functions, the quantification formula can be three-valued and some complex sentences with empty terms can be either true or false.