When an agent undergoes fission, how should the beliefs of the fission results relate to the pre-fission beliefs? This question is important for the Everett interpretation of quantum mechanics, but it is of independent philosophical interest. Among other things, fission scenarios demonstrate that ‘self-locating’ information can affect the probability of uncentred propositions even if an agent has no essentially self-locating uncertainty. I present a general update rule for centred beliefs that gives sensible verdicts in cases of fission, without relying on (...) controversial metaphysical or linguistic assumptions. The rule is supported by the same considerations that support standard conditioning in the traditional framework of uncentred propositions. (shrink)

This paper discusses simultaneous belief updates. I argue here that modeling such belief updates using the Principle of Minimum Information can be regarded as applying Jeffrey conditionalization successively, and so that, contrary to what many probabilists have thought, the simultaneous belief updates can be successfully modeled by means of Jeffrey conditionalization.

The purpose of this paper is to introduce a form of update based on the minimization of the geodesic distance on a graph. We provide a characterization of this class using set- theoretic operators and show that such operators bijectively correspond to geodesic metrics. As distance is generated by distinguishability, our framework is appropriate in contexts where distance is generated by threshold, and therefore, when measurement is erroneous.

We tackle two open questions from Leitgeb and Pettigrew (2010b) regarding what the belief update framework described in that paper mandates as correct responses to two problems. One of them concerns credences in overlapping propositions and is known in the literature as the “simultaneous update problem”. The other is the well known “Judy Benjamin” problem concerning conditional credences. We argue that our results concerning the problems point to deficiencies of the framework. More generally, we observe that the method of (...) minimizing inverse relative entropy seems to work better than (or at least equally well as) its competitors in many situations. (shrink)

Moral psychologists have shown that people’s past moral experiences can affect their subsequent moral decisions. One prominent finding in this line of research is that when people make a judgment about the Trolley dilemma after considering the Footbridge dilemma, they are significantly less likely to decide it is acceptable to redirect a train to save five people. Additionally, this ordering effect is asymmetrical, as making a judgment about the Trolley dilemma has little to no effect on people’s judgments about the (...) Footbridge dilemma. We argue that this asymmetry is the result of a difference in how each dilemma affects people’s beliefs about the importance of saving lives. In two experiments, we show that considering the Footbridge dilemma disconfirms these beliefs, while considering the Trolley dilemma does not significantly affect them. Consistent with predictions of sequential learning models, our findings offer a clear and parsimonious account of the asymmetry in the ordering effect. (shrink)

In this paper we explore a class of belief update operators, in which the definition of the operator is compositional with respect to the sentence to be added. The goal is to provide an update operator that is intuitive, in that its definition is based on a recursive decomposition of the update sentence’s structure, and that may be reasonably implemented. In addressing update, we first provide a definition phrased in terms of the models of a knowledge base. While this (...) operator satisfies a core group of the benchmark Katsuno Mendelzon update postulates, not all of the postulates are satisfied. Other Katsuno Mendelzon postulates can be obtained by suitably restricting the syntactic form of the sentence for update, as we show. In restricting the syntactic form of the sentence for update, we also obtain a hierarchy of update operators with Winslett’s standard semantics as the most basic interesting approach captured. We subsequently give an algorithm which captures this approach; in the general case the algorithm is exponential, but with some not unreasonable assumptions we obtain an algorithm that is linear in the size of the knowledge base. Hence the resulting approach has much better complexity characteristics than other operators in some situations. We also explore other compositional belief change operators: erasure is developed as a dual operator to update; we show that a forget operator is definable in terms of update; and we give a definition of the compositional revision operator. We obtain that compositional revision, under the most natural definition, yields the Satoh revision operator. (shrink)

This doctoral dissertation investigates what influence indicative conditionals have on belief updating and how learning from conditionals may be modelled in a probabilistic framework. Because the problem is related to the interpretation of conditionals, we first assess different semantics of indicative conditionals. We propose that conditionals should be taken as primary concepts. This allows us to defend a claim that learning a conditional is equivalent to learning that the relevant conditional probability is 1. This implies that learning a (...) conditional can be modelled as learning a material conditional. We then turn to a few competing approaches to the problem of learning from a conditional -- an approach that models these situations with regards to changes in the explanatory status of the antecedent, as minimising probability distances between the prior and posterior probability distributions, and, particularly, an approach based on epistemic entrenchment. It is argued that although all approaches are important for their pioneering contributions, none of them ultimately provides a fully satisfactory solution. We then formulate a proposal according to which learning a conditional may be modelled as learning a material conditional in conjunction with other contextually inferred or observed information. We show that the view has an intuitive appeal on the grounds of pragmatics and empirical research in psychology of reasoning. We also show that the proposed approach successfully resolves all standard cases from the literature. The proposal is then extended to left-nested conditionals. To do so, we first inspect some preliminary empirical data about actual reasoning with nested conditionals and then show that the proposed approach also successfully models these cases. We then investigate how the approach may be extended to the so-called imperative conditionals. We introduce a tripartite typology of imperative conditionals and argue that although imperatives cannot be probabilistically modelled in any straight-forward way, at least some general insights of the proposed method help us understand the influence that the three different types of imperative conditionals have on listeners’ beliefs. We conclude with a summary and some open questions that should be addressed in future work (e.g. the influence of counterfactuals on belief updating). (shrink)

In recent decades much literature has been produced on disagreement; the puzzling conclusion being that epistemic disagreement is, for the most part, either impossible (e.g. Aumann (Ann Stat 4(6):1236–1239, 1976)), or at least easily resolvable (e.g. Elga (Noûs 41(3):478–502, 2007)). In this paper I show that, under certain conditions, an equally puzzling result arises: that is, disagreement cannot be rationally resolved by belief updating. I suggest a solution to the puzzle which makes use of some of the principles (...) of Hintikka’s Socratic epistemology. (shrink)

Jeffrey updating is a natural extension of Bayesian updating to cases where the evidence is uncertain. But, the resulting degrees of belief appear to be sensitive to the order in which the uncertain evidence is acquired, a rather un-Bayesian looking effect. This order dependence results from the way in which basic Jeffrey updating is usually extended to sequences of updates. The usual extension seems very natural, but there are other plausible ways to extend Bayesian updating (...) that maintain order-independence. I will explore three models of sequential updating, the usual extension and two alternatives. I will show that the alternative updating schemes derive from extensions of the usual rigidity requirement, which is at the heart of Jeffrey updating. Finally, I will establish necessary and sufficient conditions for order-independent updating, and show that extended rigidity is closely related to these conditions. (shrink)

We present an approach to database update as a form of non monotonic temporal reasoning, the main idea of which is the (circumscriptive) minimization of changes with respect to a set of facts declared “persistent by default”. The focus of the paper is on the relation between this approach and the update semantics recently proposed by Katsuno and Mendelzon. Our contribution in this regard is twofold:We prove a representation theorem for KM semantics in terms of a restricted subfamily of the (...) operators defined by our construction.We show how the KM semantics can be generalized by relaxing our construction in a number of ways, each justified in certain intuitive circumstances and each corresponding to one specific postulate. It follows that there are reasonable update operators outside the KM family.Our approach is not dependent for its plausibility on this connection with KM semantics. Rather, it provides a relatively rich and flexible framework in which the frame and ramification problems can be solved in a systematic way by reasoning about default persistence of facts. (shrink)

There are some candidates that have been thought to measure the degree to which evidence incrementally confirms a hypothesis. This paper provides an argument for one candidate—the log-likelihood ratio measure. For this purpose, I will suggest a plausible requirement that I call the Requirement of Collaboration. And then, it will be shown that, of various candidates, only the log-likelihood ratio measure \(l\) satisfies this requirement. Using this result, Jeffrey conditionalization will be reformulated so as to disclose explicitly what determines new (...) credences after experience. (shrink)

Beliefs like the Gambler's Fallacy and the Hot Hand have interested cognitive scientists, economists, and philosophers for centuries. We propose that these judgment patterns arise from the observer's mental models of the sequence-generating mechanism, moderated by the strength of belief in an a priori base rate. In six behavioral experiments, participants observed one of three mechanisms generating sequences of eight binary events: a random mechanical device, an intentional goal-directed actor, and a financial market. We systematically manipulated participants’ beliefs about (...) the base rate probabilities at which different outcomes were generated by each mechanism. Participants judged 18 sequences of outcomes produced by a mechanism with either an unknown base rate, a specified distribution of three equiprobable base rates, or a precise, fixed base rate. Six target sequences ended in streaks of between two and seven identical outcomes. The most common predictions for subsequent events were best described as pragmatic belief updating, expressed as an increasingly strong expectation that a streak of identical signals would repeat as the length of that streak increased. The exception to this pattern was for sequences generated by a random mechanical device with a fixed base rate of.50. Under this specific condition, participants exhibited a bias toward reversal of streaks, and this bias was larger when participants were asked to make a dichotomous choice versus a numerical probability rating. We review alternate accounts for the anomalous judgments of sequences and conclude with our favored interpretation that is based on Rabin's version of Tversky & Kahneman's Law of Small Numbers. (shrink)

We present an approach to database update as a form of non monotonic temporal reasoning, the main idea of which is the (circumscriptive) minimization of changes with respect to a set of facts declared persistent by default. The focus of the paper is on the relation between this approach and the update semantics recently proposed by Katsuno and Mendelzon. Our contribution in this regard is twofold: • We prove a representation theorem for KM semantics in terms of a restricted subfamily (...) of the operators defined by our construction. • We show how the KM semantics can be generalized by relaxing our construction in a number of ways, each justified in certain intuitive circumstances and each corresponding to one specific postulate. It follows that there are reasonable update operators outside the KM family. • Our approach is not dependent for its plausibility on this connection with KM semantics. Rather, it provides a relatively rich and flexible framework in which the frame and ramification problems can be solved in a systematic way by reasoning about default persistence of facts. (shrink)

In updating our beliefs on the basis of our background attitudes and evidence we frequently employ objects in our environment to represent pertinent information. For example, we may write our premises and lemmas on a whiteboard to aid in a proof or move the beads of an abacus to assist in a calculation. In both cases, we generate extramental (that is, occurring outside of the mind) representational states, and, at least in the case of the abacus, we operate over (...) these states in light of their contents (e.g., the integers represented by the beads) to generate new representations. In this paper, I argue that our belief updating processes and the grounds of their rational evaluation are partly constituted by extramental representations and operations. In other words, we don’t merely update our attitudes through an internal process of reasoning on the basis of available evidence. If we are to accurately understand and rationally evaluate our belief updating processes and resultant attitudes, we need to examine how we representationally appropriate our extramental environment in the updating process. (shrink)

Jeffrey (1983) proposed a generalization of conditioning as a means of updating probability distributions when new evidence drives no event to certainty. His rule requires the stability of certain conditional probabilities through time. We tested this assumption (“invariance”) from the psychological point of view. In Experiment 1 participants offered probability estimates for events in Jeffrey’s candlelight example. Two further scenarios were investigated in Experiment 2, one in which invariance seems justified, the other in which it does not. Results were (...) in rough conformity to Jeffrey (1983)’s principle. (shrink)

Choquet expected utility substitutes capacities for subjective probabilities to explain uncertainty aversion and related phenomena. This paper studies capacities as models of belief. The notions of inner and outer acceptance context are defined. These are shown to be the natural acceptance contexts when belief expansion is described by naïve Bayesian and Dempster–Shafer updating of capacities respectively. We also show that Eichberger and Kelsey's use of Dempster–Shafer updating as a model of belief revision may lead to (...) violations of the AGM axioms for rational belief change. (shrink)

Self-locating beliefs cause a problem for conditionalization. Miriam Schoenfield offers a solution: that on learning E, agents should update on the fact that they learned E. However, Schoenfield is not explicit about whether the fact that they learned E is self-locating. I will argue that if the fact that they learned E is self-locating then the original problem has not been addressed, and if the fact that they learned E is not self-locating then the theory generates implausible verdicts which Schoenfield (...) explicitly rejects. (shrink)

SUGGESTED COURSES Introductory level A (Requires very little background in logic .): 4: -9 - - -7 -2 Introductory level B: -9,:+-+ -,2:+,2: -,3:20+-22+ -7 -2 ...

When preferences are such that there is no unique additive prior, the issue of which updating rule to use is of extreme importance. This paper presents an axiomatization of the rule which requires updating of all the priors by Bayes rule. The decision maker has conditional preferences over acts. It is assumed that preferences over acts conditional on event E happening, do not depend on lotteries received on Ec, obey axioms which lead to maxmin expected utility representation with (...) multiple priors, and have common induced preferences over lotteries. The paper shows that when all priors give positive probability to an event E, a certain coherence property between conditional and unconditional preferences is satisfied if and only if the set of subjective probability measures considered by the agent given E is obtained by updating all subjective prior probability measures using Bayes rule. (shrink)

In this study, we examine the problem of belief revision, defined as deciding whic h of several initially-accepted sentences to disbelieve, when new information presents a l ogical inconsistency with the initial set. In the first three experiments, the initial sentence set included a conditional sentence, a non-conditional sentence, and an inferred conclusi on drawn from the first two. The new information contradicted the inferred conclusion. Results indicated that the conditional sentences were more readily abandoned than non-c onditional sentences, (...) even when either choice would lead to a consistent belief state, and that this preference was more pronounced when problems used natural language cover sto ries rather than symbols. The pattern of belief revision choices differed depending on whe ther the contradicted conclusion from the initial belief set had been a modus ponens or m odus tollens inference. Two additional experiments examined alternative model-theoretic definitions of minimal change to a belief state, using problems that contained multiple mo dels of the initial belief state and of the new information that provided the contradiction. The results indicated that people did not follow any of four formal definitions of minimal change on these problems. The new information and the contradiction it offered was not, for example, used to select a particular model of the initial belief state as a way of reconci ling the contradiction. The preferred revision was to retain only those initial sentences th at had the same, unambiguous truth value within and across both the initial and new info rmation sets. The study and results are presented in the context of certain logic-based for malizations of belief revision, syntactic and model-theoretic representations of belief stat es, and performance models of human deduction. Principles by which some types of sent ences might be more "entrenched" than others in the face of contradiction are also discuss ed from the perspective of induction and theory revision. (shrink)

In this paper, I argue that some plausible principles concerning which credences are rationally permissible for agents given information about one another’s epistemic and credal states have some surprising consequences for which credences an agent ought to have in light of self-locating information. I provide a framework that allows us to state these constraints and draw out these consequences precisely. I then consider and assess the prospects for rejecting these prima facie plausible principles.

The Bayesian model has been used in psychology as the standard reference for the study of probability revision. In the first part of this paper we show that this traditional choice restricts the scope of the experimental investigation of revision to a stable universe. This is the case of a situation that, technically, is known as focusing. We argue that it is essential for a better understanding of human probability revision to consider another situation called updating (Katsuno & Mendelzon, (...) 1992), in which the universe is evolving. In that case the structure of the universe has definitely been transformed and the revision message conveys information on the resulting universe. The second part of the paper presents four experiments based on the Monty Hall puzzle that aim to show that updating is a natural frame for individuals to revise their beliefs. (shrink)

Sometimes you are unreliable at fulfilling your doxastic plans: for example, if you plan to be fully confident in all truths, probably you will end up being fully confident in some falsehoods by mistake. In some cases, there is information that plays the classical role of evidence—your beliefs are perfectly discriminating with respect to some possible facts about the world—and there is a standard expected‐accuracy‐based justification for planning to conditionalize on this evidence. This planning‐oriented justification extends to some cases where (...) you do not have transparent evidence, in the sense that your beliefs are not perfectly discriminating with respect to any non‐trivial facts. In other cases, accuracy considerations do not tell you to plan to conditionalize on any information at all, but rather to plan to follow a different updating rule. Even in the absence of evidence, accuracy considerations can guide your doxastic plan. (shrink)

Traditional procedures for rational updating fail when it comes to self-locating opinions, such as your credences about where you are and what time it is. This paper develops an updating procedure for rational agents with self-locating beliefs. In short, I argue that rational updating can be factored into two steps. The first step uses information you recall from your previous self to form a hypothetical credence distribution, and the second step changes this hypothetical distribution to reflect information (...) you have genuinely learned as time has passed. While the second step resembles traditional procedures of updating by conditionalization, the first is best understood by analogy to traditional models of how agents transmit self-locating opinions through ordinary interpersonal communication. (shrink)

The technique of minimizing information (infomin) has been commonly employed as a general method for both choosing and updating a subjective probability function. We argue that, in a wide class of cases, the use of infomin methods fails to cohere with our standard conception of rational degrees of belief. We introduce the notion of a deceptive updating method and argue that non-deceptiveness is a necessary condition for rational coherence. Infomin has been criticized on the grounds that there (...) are no higher order probabilities that ‘support’ it, but the appeal to higher order probabilities is a substantial assumption that some might reject. Our elementary arguments from deceptiveness do not rely on this assumption. While deceptiveness implies lack of higher order support, the converse does not, in general, hold, which indicates that deceptiveness is a more objectionable property. We offer a new proof of the claim that infomin updating of any strictly-positive prior with respect to conditional-probability constraints is deceptive. In the case of expected-value constraints, infomin updating of the uniform prior is deceptive for some random variables but not for others. We establish both a necessary condition and a sufficient condition (which extends the scope of the phenomenon beyond cases previously considered) for deceptiveness in this setting. Along the way, we clarify the relation which obtains between the strong notion of higher order support, in which the higher order probability is defined over the full space of first order probabilities, and the apparently weaker notion, in which it is defined over some smaller parameter space. We show that under certain natural assumptions, the two are equivalent. Finally, we offer an interpretation of Jaynes, according to which his own appeal to infomin methods avoids the incoherencies discussed in this paper. (shrink)