Robert Stalnaker proposed in [25] a substantial way of understanding this defeasible notion of AE-consequence. The gist of the proposal is: (P) what is non-monotonically entailed by a sentence α is what is meant or implicated, but not explicitly said by uttering α. He suggested that a defeasible notion of consequence (explicated via ECP) could be used to formally encode Grice’s notion of conversational implicature — and to understand its context-dependent behavior.

This article makes three main contributions. First, we will focus on the tenability of (P). Paul Grice considered in [10] some minimal constraints on implicature needed in order to handle G.E. Moore’s paradox of ‘saying and disbelieving’. We will show that (P) is incompatible with those constraints. Secondly we will offer an alternative account of AE consequence based on several remarks made by Grice in [10]. According to this account C(α) encodes the body of full beliefs to which someone is committed after uttering α. Thirdly we will offer a preliminary account of the formal properties of this new notion of consequence.

AE logic assumes that introspective reasoners do not subscribe to the alethic principle (T) — establishing that the AE-operator L obeys L(A) → A. This is due to a tacit interpretation of L as an operator of ‘weak’ belief. This is done even when (T) is satisfied post hoc in every AE-extension. The price paid by this maneuver is that AE logic, unlike most defeasible logics, is not cumulative — although (T) is satisfied in every extension, the principle cannot be used in the reasoning to arrive at the extension (see [13], page 228). We verify that our notion of AE-consequence is not affected by this problem by showing that (with certain provisos) the notion is cumulative.