Abstract
In binary propositional constructions S1 con
S2, the Strong Kleene connectives explain filtering of S1’s and S2’s presuppositions depending on their logical relations with their
non-presuppositional content. However, the
presuppositions derived by the Strong Kleene
connectives are weak conditional presuppositions, which raise the “proviso problem” in
cases where no filtering is motivated. Weak
Kleene connectives do not face this problem,
but only because their presuppositions are often too strong, and hence do not account for
filtering phenomena altogether. While various
mechanisms have been proposed to allow filtering without the proviso problem, their relations with the standard trivalent Kleene systems have remained unclear. This paper shows
that by sacrificing truth-functionality, we uncover a rich domain of possibilities in trivalent semantics in between the Weak Kleene
and Strong Kleene connectives. These systems
derive presupposition filtering while avoiding
the proviso problem. The Kleene-style operators studied are generalized to arbitrary binary
functions, which further clarifies the connection between their different “repair” strategies
and presupposition projection.
S2, the Strong Kleene connectives explain filtering of S1’s and S2’s presuppositions depending on their logical relations with their
non-presuppositional content. However, the
presuppositions derived by the Strong Kleene
connectives are weak conditional presuppositions, which raise the “proviso problem” in
cases where no filtering is motivated. Weak
Kleene connectives do not face this problem,
but only because their presuppositions are often too strong, and hence do not account for
filtering phenomena altogether. While various
mechanisms have been proposed to allow filtering without the proviso problem, their relations with the standard trivalent Kleene systems have remained unclear. This paper shows
that by sacrificing truth-functionality, we uncover a rich domain of possibilities in trivalent semantics in between the Weak Kleene
and Strong Kleene connectives. These systems
derive presupposition filtering while avoiding
the proviso problem. The Kleene-style operators studied are generalized to arbitrary binary
functions, which further clarifies the connection between their different “repair” strategies
and presupposition projection.
Original language | English |
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Title of host publication | Proc. of Mathematics of Language |
Pages | 27–39 |
Number of pages | 13 |
DOIs | |
Publication status | Published - 2019 |