Infinitary Belief Revision

This paper extends the AGM theory of belief revision to accommodate infinitary belief change. We generalize both axiomatization and modeling of the AGM theory. We show that most properties of the AGM belief change operations are preserved by the generalized operations whereas the infinitary belief change operations have their special properties. We prove that the extended axiomatic system for the generalized belief change operators with a Limit Postulate properly specifies infinite belief change. This framework provides a basis for first-order belief revision and the theory of revising a belief state by a belief state.     

My beliefs about your beliefs: a case study in theory of mind and epistemic logic

We model three examples of beliefs that agents may have about other agents’ beliefs, and provide motivation for this conceptualization from the theory of mind literature. We assume a modal logical framework for modelling degrees of belief by partially ordered preference relations. In this setting, we describe that agents believe that other agents do not distinguish among their beliefs (‘no preferences’), that agents believe that the beliefs of other agents are in part as their own (‘my preferences’), and the special case that agents believe that the beliefs of other agents are exactly as their own (‘preference refinement’). This multi-agent belief interaction is frame characterizable. We provide examples for introspective agents. We investigate which of these forms of belief interaction are preserved under three common forms of belief revision.     

What Makes People Revise Their Beliefs Following Contradictory Anecdotal Evidence?: The Role of Systemic Variability and Direct Experience

The extent to which belief revision is affected by systematic variability and direct experience of a conditional (if A then B) relation was examined in two studies. The first used a computer generated apparatus. This presented two rows of 5 objects. Pressing one of the top objects resulted in one of the bottom objects being lit up. The 139 adult participants were given one of two levels of experience (5 or 15 trials) and one of two types of apparatus. One of these was completely uniform, while the other had an element that randomly alternated in its result. Following the testing of the apparatus, participants were asked to rate their certainty of the action of the middle element, which was always uniform (the AB belief). Then they were told of an observation inconsistent with this belief. Participants were then asked whether they considered the AB belief or the anecdotal observation to be more believable. Results showed that increased experience decreased the tendency to reject the AB belief, when the apparatus did not have any randomness. However, the presence of a single element showing random variation in the system strongly increased rejection of this belief. A second study looked at the effect of a single random element on a mechanical system as well as an electronic system using graphical representations. This confirmed the generality of the effect of randomness on belief revision, and provided support for the effects of embedding a belief into a system of relations. These results provide some insight into the complex factors that determine belief revision.     

Detecting and predicting changes

When required to predict sequential events, such as random coin tosses or basketball free throws, people reliably use inappropriate strategies, such as inferring temporal structure when none is present. We investigate the ability of observers to predict sequential events in dynamically changing environments, where there is an opportunity to detect true temporal structure. In two experiments we demonstrate that participants often make correct statistical decisions when asked to infer the hidden state of the data generating process. However, when asked to make predictions about future outcomes, accuracy decreased even though normatively correct responses in the two tasks were identical. A particle filter model accounts for all data, describing performance in terms of a plausible psychological process. By varying the number of particles, and the prior belief about the probability of a change occurring in the data generating process, we were able to model most of the observed individual differences.     

自省主体对Moore-型信息的处理与融合

The main task is to discuss the issue in belief dynamics in which philosophical beliefs and rational introspective agents incorporate Moorean type new information. First, a brief survey is conducted on Moore’s Paradox, and one of its solutions is introduced with the help of Update Semantics. Then, we present a Dynamic Doxastic Logic (DDL) which revises the belief of introspective agents put forward by Lindström &; Rabinowicz. Next, we attempt to incorporate Moorean type new information within the DEL (DDL) framework, as advised by van Benthem, Segerberg et al. Though we maintain the principle of “the primacy of new information” from the literature on traditional belief revision theory, several unsuccessful ways are also presented. We then conclude that some special kind of success (weak success) can still be found in those revision processes although absolute success does not hold. At last, the relevant problem of “learnability” is re-considered through weak success.     

Replacement—A Sheffer Stroke for Belief Change

By replacement is meant an operation that replaces one sentence by another in a belief set. Replacement can be used as a kind of Sheffer stroke for belief change, since contraction, revision, and expansion can all be defined in terms of it. Replacement can also be defined either in terms of contraction or in terms of revision. Close connections are shown to hold between axioms for replacement and axioms for contraction and revision. Partial meet replacement is axiomatically characterized. It is shown that this operation can have outcomes that are not obtainable through either partial meet contraction or partial meet revision.     

Usage-based account of the acquisition of liaison: evidence from sensitivity to the singular/plural orientation of nouns

This study investigates whether children’s production and recognition of obligatory liaison sequences in French depend on the singular/plural orientation of nouns. Certain nouns occur more frequently in the plural (e.g., arbre “tree”), whereas others are found more often in the singular (e.g., arc-en-ciel “rainbow”). In the input, children more frequently encounter these plural-oriented nouns after determiners that indicate plurality (e.g., les,des “the”, deux “two”) and that are often associated with a /z/ liaison (e.g., deux arbres [døzarbr] “two trees”). In Experiment 1, 122 children (3 years 2 months to 6 years 3 months of age) were asked to produce nominal phrases with either /z/ liaisons (i.e., in plural contexts such as deux ours [døzurs] “two bears”) or /n/ liaisons (i.e., in singular contexts such as un ours [nurs] “one bear”). We found correlations between the plural orientation of the nouns and (a) the probability that they will be preceded by an incorrect /z/ liaison in the singular context and (b) the probability that they will be preceded by a correct /z/ liaison in the plural context. This result was, however, restricted to the younger children. In Experiment 2, 20 children (5 years 5 months to 6 years 3 months of age) were asked to monitor target words in auditorily presented sentences. The results showed shorter reaction times for singular-oriented nouns when preceded by a singular determiner than when preceded by a plural determiner. Conversely, plural-oriented nouns were responded to faster when preceded by a plural determiner than when preceded by a singular determiner. Results are discussed within the framework of a two-stage model of liaison acquisition recently proposed by Chevrot, Chabanal, and Dugua (Journal of French Language Studies,17 [2007] 103-128) as well as by Chevrot, Dugua, and Fayol (Journal of Child Language [in press]).     

Bridging learning theory and dynamic epistemic logic

This paper discusses the possibility of modelling inductive inference (Gold 1967) in dynamic epistemic logic (see e.g. van Ditmarsch et al. 2007). The general purpose is to propose a semantic basis for designing a modal logic for learning in the limit. First, we analyze a variety of epistemological notions involved in identification in the limit and match it with traditional epistemic and doxastic logic approaches. Then, we provide a comparison of learning by erasing (Lange et al. 1996) and iterated epistemic update (Baltag and Moss 2004) as analyzed in dynamic epistemic logic. We show that finite identification can be modelled in dynamic epistemic logic, and that the elimination process of learning by erasing can be seen as iterated belief-revision modelled in dynamic doxastic logic. Finally, we propose viewing hypothesis spaces as temporal frames and discuss possible advantages of that perspective.