Artificial Intelligence
General theory of cumulative inference
Proceedings of the 2nd international workshop on Non-monotonic reasoning
Theoretical foundations for non-monotonic reasoning in expert systems
Logics and models of concurrent systems
A note on non-monotonic modal logic
Artificial Intelligence
Handbook of logic in artificial intelligence and logic programming (vol. 3): nonmonotonic reasoning and uncertain reasoning
Logic and representation
For the sake of the argument: Ramsey test conditionals, inductive inference, and nonmonotonic reasoning
The learning power of belief revision
TARK '98 Proceedings of the 7th conference on Theoretical aspects of rationality and knowledge
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Recent foundational work on the nature of defeasible inference has appealed to an epistemic context principle (ECP): β follows defeasibly from α (α |~ β) if and only if β follows classically from C(α), where C(α) is the given epistemic context for α. Since nothing requires that C(α) ⊆ C(α Λ γ), the induced notion of consequence is nonmonotonic. We will focus on a particular manner of articulating ECP where C(α) is an autoepistemic (AE) extension of {α}. 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.