Logic and conversation: The case of free choice

Abstract

Free choice inferences represent a much discussed case of a divergence between logic and language (Kamp 1973, Zimmermann 2000. Grice influentially argued that the assumption that such divergence does in fact exist is a mistake originating "from inadequate attention to the nature and importance of the conditions governing conversation" (Grice 1989: p. 24). I will first show that when applied to free choice phenomena, the standard implementation of Grice's view, representing semantics and pragmatics as two separate components, is empirically inadequate. I will then propose a different account: a bilateral state-based modal logic modeling next to literal meanings also pragmatic factors and the additional inferences that arise

An Acceptance Semantics for Stable Modal Knowledge

“…The most unusual entry (cf. [21], [13], [1] and §4) is that for Kϕ: according to our semantics, 'Smith knows that ϕ' can be accepted exactly when it is established that every accessible refinement of Smith's knowledge state supports ϕ; 'Smith knows that ϕ' can be rejected exactly when it is established that an accessible refinement of Smith's knowledge state doesn't support ϕ.…”

“…§5 thus proposes a novel alternative theory, showcasing a related but distinct tradition of informationsensitive semantics: we propose a formal acceptance semantics (in the ballpark of [21], [20], [12], [13], [5], [1]) that delivers Ver and GeNT as desired. Our treatment of ˛p is essentially standard for such a framework; the more novel aspect is our account of Kϕ, and its interaction with ˛p.…”

“…State i is veridical at w when w P i. We evaluate sentences in L as true (1) or false (0) relative to a possible world w and an information state i: the valuation function r¨s w,i is as follows.…”

Assertion, Rejection, and Semantic Universals

“…The explanation developed in this paper has to do with structural (logical) constraints on informationtransmission in a conversational setting. 1 Following [14], a bilateral system of updates is dened in which ∧, ∨, and nor, can be straightforwardly expressed, but that lacks nand and all other connectives. Accordingly, semantic universals may depend on cognitive asymmetries in the dynamic processing of logically structured information.…”

“…The former is a form of "Free Choice" inference, in which a disjunction implies a conjunction [1]. The latter is a typical pattern of Informational Conjunction ⊗, an operator denable on distributive bilattices [2,8,10].…”