Natural language does not express all connectives definable in classical logic as simple lexical items. Coordination in English is expressed by conjunction and, disjunction or, and negated disjunction nor. Other languages pattern similarly. Non-lexicalized connectives are typically expressed compositionally: in English, negated conjunction is typically expressed by combining negation and conjunction (not both). This is surprising: if \(\wedge \) and \(\vee \) are duals, and the negation of the latter can be expressed lexically (nor), why not the negation of the former? I present a two-tiered model of the semantics of the binary connectives. The first tier captures the expressive power of the lexicon: it is a bilateral state-based semantics that, under a restriction, can express all and only the distinctions that can be expressed by the lexicon of natural language (and, or, nor). This first tier is characterized by rejection as non-assertion and a Neglect Zero assumption. The second tier is obtained by dropping the Neglect Zero assumption and enforcing a stronger notion of rejection, thereby recovering classical logic and thus definitions for all Boolean connectives. On the two-tiered model, we distinguish the limited expressive resources of the lexicon and the greater combinatorial expressive power of the language as a whole. This gives us a logic-based account of compositionality for the Boolean fragment of the language.

自然语言并不将经典逻辑中可定义的所有连接词表达为简单的词汇项。英语中的并列由连词and、析取or和否定析取Nor来表示。其他语言的模式也类似。非词汇化连接词通常以组合方式表达：在英语中，否定连词通常通过组合否定和连词（而不是两者）来表达。这是令人惊讶的：如果\(\wedge \)和\(\vee \)是对偶，并且后者的否定可以在词法上表达（也不），为什么不是前者的否定呢？我提出了二元连接词语义的两层模型。第一层捕获了词典的表达能力：它是一种基于双边状态的语义，在限制下，可以表达所有且仅能由自然语言词典可以表达的区别（and、or、nor）。）。第一层的特点是拒绝作为非断言和忽略零假设。第二层是通过放弃忽略零假设并强制执行更强的拒绝概念来获得的，从而恢复经典逻辑以及所有布尔连接词的定义。在两层模型上，我们区分了词典有限的表达资源和整个语言更大的组合表达能力。这为我们提供了该语言布尔片段的组合性的基于逻辑的解释。