Disjunction and Negation in Dynamic Semantics
In Free Choice (fc) inferences, conjunctive meanings are derived from disjunctive modal sentences contrary to the prescriptions of classical logic:
- (1) Deontic fc [Kam73]
- You may go to the beach or to the cinema.
- ↝You may go to the beach and you may go to the cinema.
- (2) Epistemic fc [Zim00]
- Mr. X might be in Victoria or in Brixton.
- ↝ Mr. X might be in Victoria and he might be in Brixton.
[Alo22] presented a formal account of fc inferences in a bilateral state-basedmodal logic (BSML). The novel hypothesis at the core of that proposal was that fc and related inferences are a straightforward consequence of a tendency in human cognition to neglect models that verify sentences by virtue of some empty configurations (neglect-zero). Using tools from team semantics [YV17], [Alo22] showed that neglect-zero derives fc inferences (when interpreting disjunctions speakers associate each disjunct with a non-empty possibility) and their cancellation under negation. The latter result relied on the adopted bilateralism, where each connective comes with an assertion and a rejection condition and negation is defined in terms of the latter notion.
In this talk I will present DyBSML, a quantified dynamic version of BSML, which captures besides fc and related inferences also cross-sentential and donkey anaphora and their interactions with modality [GSV96, Alo00]. One difference with respect to classical dynamic semantics [e.g., GS91, GSV96] concerns the treatment of negation. Like BSML, DyBSML will validate double negation elimination and therefore provide an account of Barbara Partee’s bathroom example [KM95]:
- (3) Either there is no bathroom in this house or it’s in a funny place.
DyBSML will be further applied to capture the obligatory ignorance infer- ence triggered by epistemic indefinites in German and other languages [AOMB15, AP15]:
- (4) Epistemic indefinites (German)Epistemic indefinites (Germ an)
1. Irgendein Student hat angerufen #Rat mal wer?
Irgend-one student has called guess prt who?
2. Some student called – the speaker doesn’t know who
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- [Alo22] Maria Aloni. Logic and conversation: the case of free choice. Under review, 2022.
- [AOMB15] Luis Alonso-Ovalle and Paula Men ́endez-Benito. Epistemic Indefi- nites. Oxford University Press, 2015.
- [AP15] Maria Aloni and Angelika Port. Epistemic indefinites and meth- ods of identifications. In Luis Alonso-Ovalle and Paula Men ́endez- Benito, editors, Epistemic Indefinites. Oxford University Press, 2015.
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