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• W4385065034 abstract "Abstract 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 $$wedge $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mo>∧</mml:mo> </mml:math> and $$vee $$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mo>∨</mml:mo> </mml:math> 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." @default.
• W4385065034 created "2023-07-23" @default.
• W4385065034 creator A5057825333 @default.
• W4385065034 date "2023-07-21" @default.
• W4385065034 modified "2023-10-16" @default.
• W4385065034 title "The Logic of Lexical Connectives" @default.
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• W4385065034 doi "https://doi.org/10.1007/s10992-023-09708-5" @default.
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