How to accept a conditional? F. P. Ramsey proposed the following test in (Ramsey 1990).(RT) If A, then B must be accepted with respect to the current epistemic state iff the minimal hypothetical change of it needed to accept A also requires accepting B.

The paper studies first order extensions of classical systems of modal logic (see (Chellas, 1980, part III)). We focus on the role of the Barcan formulas. It is shown that these formulas correspond to fundamental properties of neighborhood frames. The results have interesting applications in epistemic logic. In particular we suggest that the proposed models can be used in order to study monadic operators of probability (Kyburg, 1990) and likelihood (Halpern-Rabin, 1987).

How to accept a conditional? F. P. Ramsey proposed the following test in . 'If A, then B' must be accepted with respect to the current epistemic state iff the minimal hypothetical change of it needed to accept A also requires accepting B. In this article we propose a formulation of , which unlike some of its predecessors, is compatible with our best theory of belief revision, the so-called AGM theory , chapters 1-5 for a survey). The new test, which, (...) we claim, encodes some of the crucial insights defended by F. P. Ramsey in , is used to study the conditionals epistemically validated by the AGM postulates. Our notion of validity is compared with the notion of negative validity used by Gärdenfors in . It is observed that the notions of PV and NV will in general differ and that when these differences arise it is the notion of PV that is preferable. Finally we compare our formulation of the Ramsey test with a previous formulation offered by Gärdenfors . We show that any attempt to interpret as delivering acceptance conditions for Ramsey's conditionals is doomed to failure. (shrink)

The article focuses on representing different forms of non-adjunctive inference as sub-Kripkean systems of classical modal logic, where the inference from □A and □B to □A ∧ B fails. In particular we prove a completeness result showing that the modal system that Schotch and Jennings derive from a form of non-adjunctive inference in (Schotch and Jennings, 1980) is a classical system strictly stronger than EMN and weaker than K (following the notation for classical modalities presented in Chellas, 1980). The unified (...) semantical characterization in terms of neighborhoods permits comparisons between different forms of non-adjunctive inference. For example, we show that the non-adjunctive logic proposed in (Schotch and Jennings, 1980) is not adequate in general for representing the logic of high probability operators. An alternative interpretation of the forcing relation of Schotch and Jennings is derived from the proposed unified semantics and utilized in order to propose a more fine-grained measure of epistemic coherence than the one presented in (Schotch and Jennings, 1980). Finally we propose a syntactic translation of the purely implicative part of Jaśkowski's system D₂ into a classical system preserving all the theorems (and non-theorems) explicilty mentioned in (Jaśkowski, 1969). The translation method can be used in order to develop epistemic semantics for a larger class of non-adjunctive (discursive) logics than the ones historically investigated by Jaśkowski. (shrink)

An important trend in contemporary epistemology centers on elaborating an old idea of pragmatist pedigree: theory selection (and in general the process of changing view and fixing beliefs) presupposes epistemic values. This article focuses on analyzing the case where epistemic values are indeterminate or when the sources of valuation are multiple (epistemic values like coherence and simplicity need not order options in compatible ways). According to the theory that thus arises epistemic alternatives need not be fully ordered by an underlying (...) notion of information-value and therefore the usual economic techniques of optimization cannot be applied in order to compute optimal contractions. But in cases of this sort it is still rational to maximize, i.e. to deem an option as choosable when it is not known to be worse that any other. We present here basic results about a notion of liberal contraction based on maximizing quasi-orderings. This requires the previous solution of some open problems in the theory of rational choice functions, namely a full characterization of choice functions rationalizable in terms of maximization of quasi-transitive relations. We conclude by discussing the problem of what is the adequate feasible set for calculating maximizing solutions for contraction problems and by considering the epistemological roots of some counterexamples against the most fundamental axioms on choice functions (like α). While the first part of the paper shows how economic insights can be used to improve our understanding of the principles of belief formation and change, this final section reverses this strategy by showing the utility of epistemological insights and techniques for providing invariance conditions capable of regulating the applicability of the pure principles of choice. (shrink)

Sven-Ove Hansson and Erik Olsson studied in Hansson and Olsson, 103–119 1995) the logical properties of an operation of contraction first proposed by Isaac Levi in Levi. They provided a completeness result for the simplest version of contraction that they call Levi-contraction but left open the problem of characterizing axiomatically the more complex operation of value-based contraction or saturatable contraction. In this paper we propose an axiomatization for this operation and prove a completeness result for it. We argue that the (...) resulting operation is better behaved than various rival operations of contraction defined in recent years. (shrink)

The recent literature offers several models of the notion of matter of fact supposition1 revealed in the acceptance of the so-called indicative conditionals. Some of those models are qualitative [Collins 90], [Levi 96], [Stalnaker 84]. Other probabilistic models appeal either to infinitesimal probability or two place probability functions. Recent work has made possible to understand which is the exact qualitative counterpart of the latter probabilistic models. In this article we show that the qualitative notion of change that thus arises is (...) hypothetical revision, a notion previously axiomatized in [Arló-Costa 97] and [Arló-Costa & Thomason 96]. This notion is incompatible with AGM as well as with other standard methods of theory change. The way in which matter-of-fact supposition is modeled by hypothetical revision is illustrated via examples. The model is compared with other qualitative accounts of the notion of supposition encoded in two-place probability functions, with models of subjunctive supposition, as well as with some of the well know models of learning. Applications in knowledge representation and in the theory of games and decisions are summarized. (shrink)