This article provides a discussion of the principle of transmission of evidential support across entailment from the perspective of belief revision theory in the AGM tradition. After outlining and briefly defending a small number of basic principles of belief change, which include a number of belief contraction analogues of the Darwiche-Pearl postulates for iterated revision, a proposal is then made concerning the connection between evidential beliefs and belief change policies in rational agents. This proposal is found to be suffcient to (...) establish the truth of a much-discussed intuition regarding transmission failure. (shrink)

Frank Ramsey (1931) wrote: If two people are arguing 'if p will q?' and both are in doubt as to p, they are adding p hypothetically to their stock of knowledge and arguing on that basis about q. We can say that they are fixing their degrees of belief in q given p. Let us take the first sentence the way it is often taken, as proposing the following test for the acceptability of an indicative conditional: ‘If p then q’ (...) is acceptable to a subject S iff, were S to accept p and consider q, S would accept q. Now consider an indicative conditional of the form (1) If p, then I believe p. Suppose that you accept p and consider ‘I believe p’. To accept p while rejecting ‘I believe p’ is tantamount to accepting the Moore-paradoxical sentence ‘p and I do not believe p’, and so is irrational. To accept p while suspending judgment about ‘I believe p’ is irrational for similar reasons. So rationality requires that if you accept p and consider ‘I believe p’, you accept ‘I believe p’. (shrink)

The problems that surround iterated contractions and expansions of beliefs are approached by studying hypertheories, a generalisation of Adam Grove's notion of systems of spheres. By using a language with dynamic and doxastic operators different ideas about the basic nature of belief change are axiomatised. It is shown that by imposing quite natural constraints on how hypertheories may change, the basic logics for belief change can be strengthened considerably to bring one closer to a theory of iterated belief change. It (...) is then argued that the logic of expansion, in particular, cannot without loss of generality be strengthened any further to allow for a full logic of iterated belief change. To remedy this situation a notion of directed expansion is introduced that allows for a full logic of iterated belief change. The new operation is given an axiomatisation that is complete for linear hypertheories. (shrink)

According to the Ramsey Test hypothesis the conditional claim that if A then B is credible just in case it is credible that B, on the supposition that A. If true the hypothesis helps explain the way in which we evaluate and use ordinary language conditionals. But impossibility results for the Ramsey Test hypothesis in its various forms suggest that it is untenable. In this paper, I argue that these results do not in fact have this implication, on the grounds (...) that similar results can be proved without recourse to the Ramsey test hypothesis. Instead they show that a number of well entrenched principles of rational belief and belief revision do not apply to conditionals. (shrink)

We describe a model of iterated belief revision that extends the AGM theory of revision to account for the effect of a revision on the conditional beliefs of an agent. In particular, this model ensures that an agent makes as few changes as possible to the conditional component of its belief set. Adopting the Ramsey test, minimal conditional revision provides acceptance conditions for arbitrary right-nested conditionals. We show that problem of determining acceptance of any such nested conditional can be reduced (...) to acceptance tests for unnested conditionals. Thus, iterated revision can be accomplished in a "virtual" manner, using uniterated revision. (shrink)

This paper extends earlier work by its authors on formal aspects of the processes of contracting a theory to eliminate a proposition and revising a theory to introduce a proposition. In the course of the earlier work, Gardenfors developed general postulates of a more or less equational nature for such processes, whilst Alchourron and Makinson studied the particular case of contraction functions that are maximal, in the sense of yielding a maximal subset of the theory (or alternatively, of one of (...) its axiomatic bases), that fails to imply the proposition being eliminated. In the present paper, the authors study a broader class, including contraction functions that may be less than maximal. Specifically, they investigate "partial meet contraction functions", which are defined to yield the intersection of some nonempty family of maximal subsets of the theory that fail to imply the proposition being eliminated. Basic properties of these functions are established: it is shown in particular that they satisfy the Gardenfors postulates, and moreover that they are sufficiently general to provide a representation theorem for those postulates. Some special classes of partial meet contraction functions, notably those that are "relational" and "transitively relational", are studied in detail, and their connections with certain "supplementary postulates" of Gardenfors investigated, with a further representation theorem established. (shrink)

The paper proposes a unified analysis of the natural language connectives 'if', 'if … might', 'even if' (all of them with indicative and subjunctive mood), 'because' and 'though'. They are all interpreted as instances of universal (pro)conditionals, unconditionals, or counterconditionals. The paper imports the notion of relevance into the meaning of conditionals, viewing conditionals as close in meaning to explanations and statements about causal relations. The antecedent of a conditional is interpreted as being relevant for its consequent, thus avoiding the (...) general inference from A and B to 'If A, B'. The analysis is based on different variants of the Ramsey test (among them the 'Strong Ramsey Test') together with a fragment of the belief revision theory of Alchourrón, Gärdenfors and Makinson. (shrink)

In this paper it is argued that, in order to solve the problem of iterated belief change, both the belief state and its input should be represented as epistemic entrenchment (EE) relations. A belief revision operation is constructed that updates a given EE relation to a new one in light of an evidential EE relation. It is shown that the operation in question satisfies generalized versions of the Gärdenfors revision postulates. The account offered is motivated by Spohn's ordinal conditionalization functions, (...) and can be seen as the Jeffrization of a proposal considered by Rott. (shrink)

Famously, Frank P. Ramsey suggested a test for the acceptability of conditionals. Recently, David Chalmers and Alan Hájek (2007) have criticized a qualitative variant of the Ramsey test for indicative conditionals. In this paper we argue for the following three claims: (i) Chalmers and Hájek are right that the variant of the Ramsey test that they attack is not the correct way of spelling out an acceptability test for indicative conditionals. But there is a suppositional variant of the Ramsey test (...) which is still stated in purely qualitative terms, which avoids the problems, and which looks correct. (ii) While the variant of the Ramsey test that Chalmers and Hájek criticize is not correct, it is still a good approximation of a correct formulation of the Ramsey test which may be usefully employed in various contexts. (iii) The variant of the Ramsey test that Chalmers and Hájek suggest as a substitute for the deficient version of the Ramsey test is itself subject to worries similar to those raised by Chalmers and Hájek, if it is given a non-suppositional interpretation. (shrink)

I defend a formulation of the Ramsey Test with a condition for accepting negations of conditionals. It is implicit in the assumptions of the triviality theorems of Gärdenfors, Harper, and Lewis; and it allows for a unified proof of those theorems, from weaker assumptions about belief revision. This leads to a proof of McGee’s thesis that iterated conditionals do not obey modus ponens. †To contact the author, please write to: Institute of Philosophy, University of Leuven, Kardinaal Mercierplein 2, B‐3000 Leuven, (...) Belgium; e‐mail: [email protected]. (shrink)