Non-monotonic Reasoning and the Reversibility of Belief Change

Traditional approaches to nonmonotonic reasoning fail to satisfy a number of plausible axioms for belief revision and suffer from conceptual difficulties as well. Recent work on ranked preferential models (RPMs) promises to overcome some of these difficulties. Here we show that RPMs are not adequate to handle iterated belief change. Specifically, we show that RPMs do not always allow for the reversibility of belief change. This result indicates the need for numerical strengths of belief.

Belief change with noisy sensing in the situation calculus

Situation calculus has been applied widely in arti?cial intelligence to model and reason about actions and changes in dynamic systems. Since actions carried out by agents will cause constant changes of the agents’ beliefs, how to manage
these changes is a very important issue. Shapiro et al. [22] is one of the studies that considered this issue. However, in this framework, the problem of noisy sensing, which often presents in real-world applications, is not considered. As a
consequence, noisy sensing actions in this framework will lead to an agent facing inconsistent situation and subsequently the agent cannot proceed further. In this paper, we investigate how noisy sensing actions can be handled in iterated
belief change within the situation calculus formalism. We extend the framework proposed in [22] with the capability of managing noisy sensings. We demonstrate that an agent can still detect the actual situation when the ratio of noisy sensing actions vs. accurate sensing actions is limited. We prove that our framework subsumes the iterated belief change strategy in [22] when all sensing actions are accurate. Furthermore, we prove that our framework can adequately handle belief introspection, mistaken beliefs, belief revision and belief update even with noisy sensing, as done in [22] with accurate sensing actions only.

Justified Belief Change

Justification Logic is a framework for reasoning about evidence and justification. Public Announcement Logic is a framework for reasoning about belief changes caused by public announcements. This paper develops JPAL, a dynamic justification logic of public announcements that corresponds to the modal theory of public announcements due to Gerbrandy and Groeneveld. JPAL allows us to reason about evidence brought about by and changed by Gerbrandy--Groeneveld-style public announcements.

A belief revision framework for revising epistemic states with partial epistemic states

Belief revision performs belief change on an agent’s beliefs when new evidence (either of the form of a propositional formula or of the form of a total pre-order on a set of interpretations) is received. Jeffrey’s rule is commonly used for revising probabilistic epistemic states when new information is probabilistically uncertain. In this paper, we propose a general epistemic revision framework where new evidence is of the form of a partial epistemic state. Our framework extends Jeffrey’s rule with uncertain inputs and covers well-known existing frameworks such as ordinal conditional function (OCF) or possibility theory. We then define a set of postulates that such revision operators shall satisfy and establish representation theorems to characterize those postulates. We show that these postulates reveal common characteristics of various existing revision strategies and are satisfied by OCF conditionalization, Jeffrey’s rule of conditioning and possibility conditionalization. Furthermore, when reducing to the belief revision situation, our postulates can induce Darwiche and Pearl’s postulates C1 and C2.

Randomized controlled trial of an intervention to change cardiac misconceptions in myocardial infarction patients

There is converging evidence that changing beliefs about an illness leads to positive recovery outcomes. However, cardiac misconceptions interventions have been investigated mainly in Angina or Coronary Heart Disease patients, and less in patients following Myocardial Infarction (MI). In these patients, cardiac misconceptions may play a role in the adjustment or lifestyle changes. This article reports a randomized controlled trial of an intervention designed to reduce the strength of misconceptions in patients after a first MI. The primary outcome was the degree of change in misconceptions and the secondary outcomes were: exercise, smoking status, return to work and mood (anxiety and depression). Patients in the intervention condition (n = 60) were compared with a control group (n = 67) receiving usual care. Both groups were evaluated at baseline and 4, 8 and 12 months after hospital discharge. There was a significant time-by-group interaction for the total score of cardiac misconceptions. Patients in the intervention group significantly decreased their total score of cardiac misconceptions at 4 months compared with the control group and this difference was sustained over time. Patients in the intervention group were also more likely to exercise at the follow-up period after MI than the control group. This intervention was effective in reducing the strength of cardiac misconceptions in MI patients and had a positive impact on health behaviour outcomes. These results support the importance of misconceptions in health behaviours and the utility of belief change interventions in promoting health in patients with Myocardial Infarction.

A framework for managing uncertain inputs: An axiomization of rewarding

The success postulate in belief revision ensures that new evidence (input) is always trusted. However, admitting uncertain input has been questioned by many researchers. Darwiche and Pearl argued that strengths of evidence should be introduced to determine the outcome of belief change, and provided a preliminary definition towards this thought. In this paper, we start with Darwiche and Pearl’s idea aiming to develop a framework that can capture the influence of the strengths of inputs with some rational assumptions. To achieve this, we first define epistemic states to represent beliefs attached with strength, and then present a set of postulates to describe the change process on epistemic states that is determined by the strengths of input and establish representation theorems to characterize these postulates. As a result, we obtain a unique rewarding operator which is proved to be a merging operator that is in line with many other works. We also investigate existing postulates on belief merging and compare them with our postulates. In addition, we show that from an epistemic state, a corresponding ordinal conditional function by Spohn can be derived and the result of combining two epistemic states is thus reduced to the result of combining two corresponding ordinal conditional functions proposed by Laverny and Lang. Furthermore, when reduced to the belief revision situation, we prove that our results induce all the Darwiche and Pearl’s postulates as well as the Recalcitrance postulate and the Independence postulate.

The Relevance Framework for Category-Based Induction: Evidence From Garden-Path Arguments

Relevance theory (Sperber & Wilson. 1995) suggests that people expend cognitive effort when processing information in proportion to the cognitive effects to be gained from doing so. This theory has been used to explain how people apply their knowledge appropriately when evaluating category-based inductive arguments (Medin, Coley, Storms, & Hayes, 2003). In such arguments, people are told that a property is true of premise categories and are asked to evaluate the likelihood that it is also true of conclusion categories. According to the relevance framework, reasoners generate hypotheses about the relevant relation between the categories in the argument. We reasoned that premises inconsistent with early hypotheses about the relevant relation would have greater effects than consistent premises. We designed three premise garden-path arguments where the same 3rd premise was either consistent or inconsistent with likely hypotheses about the relevant relation. In Experiments 1 and 2, we showed that effort expended processing consistent premises (measured via reading times) was significantly less than effort expended on inconsistent premises. In Experiment 2 and 3, we demonstrated a direct relation between cognitive effect and cognitive effort. For garden-path arguments, belief change given inconsistent 3rd premises was significantly correlated with Premise 3 (Experiment 3) and conclusion (Experiments 2 and 3) reading times. For consistent arguments, the correlation between belief change and reading times did not approach significance. These results support the relevance framework for induction but are difficult to accommodate under other approaches.

A Syntactic Approach to Revising Epistemic States with Uncertain Inputs

Revising its beliefs when receiving new information is an important ability of any intelligent system. However, in realistic settings the new input is not always certain. A compelling way of dealing with uncertain input in an agent-based setting is to treat it as unreliable input, which may strengthen or weaken the beliefs of the agent. Recent work focused on the postulates associated with this form of belief change and on finding semantical operators that satisfy these postulates. In this paper we propose a new syntactic approach for this form of belief change and show that it agrees with the semantical definition. This makes it feasible to develop complex agent systems capable of efficiently dealing with unreliable input in a semantically meaningful way. Additionally, we show that imposing restrictions on the input and the beliefs that are entailed allows us to devise a tractable approach suitable for resource-bounded agents or agents where reactiveness is of paramount importance.

On the iteration of Katsuno and Mendelzon update

In this dissertation we present a model for iteration of Katsuno and Mendelzon’s Update, inspired in the developments for iteration in AGM belief revision. We adapt Darwiche and Pearls’ postulates of iterated belief revision to update (as well as the independence postulate proposed in [BM06, JT07]) and show two families of such operators, based in natural [Bou96] and lexicographic revision [Nay94a, NPP03]. In all cases, we provide a possible worlds semantics of the models.

On AGM for Non-Classical Logics

The AGM theory of belief revision provides a formal framework to represent the dynamics of epistemic states. In this framework, the beliefs of the agent are usually represented as logical formulas while the change operations are constrained by rationality postulates. In the original proposal, the logic underlying the reasoning was supposed to be supraclassical, among other properties. In this paper, we present some of the existing work in adapting the AGM theory for non-classical logics and discuss their interconnections and what is still missing for each approach.

On theory multiple contraction

The one which is considered the standard model of theory change was presented in [AGM85] and is known as the AGM model. In particular, that paper introduced the class of partial meet contractions. In subsequent works several alternative constructive models for that same class of functions were presented, e.g.: safe/kernel contractions ([AM85, Han94]), system of spheres-based contractions ([Gro88]) and epistemic entrenchment-based contractions ([G ar88, GM88]). Besides, several generalizations of such model were investigated. In that regard we emphasise the presentation of models which accounted for contractions by sets of sentences rather than only by a single sentence, i.e. multiple contractions. However, until now, only two of the above mentioned models have been generalized in the sense of addressing the case of contractions by sets of sentences: The partial meet multiple contractions were presented in [Han89, FH94], while the kernel multiple contractions were introduced in [FSS03]. In this thesis we propose two new constructive models of multiple contraction functions, namely the system of spheres-based and the epistemic entrenchment-based multiple contractions which generalize the models of system of spheres-based and of epistemic entrenchment-based contractions, respectively, to the case of contractions (of theories) by sets of sentences. Furthermore, analogously to what is the case in what concerns the corresponding classes of contraction functions by one single sentence, those two classes are identical and constitute a subclass of the class of partial meet multiple contractions. Additionally, and as the rst step of the procedure that is here followed to obtain an adequate de nition for the system of spheres-based multiple contractions, we present a possible worlds semantics for the partial meet multiple contractions analogous to the one proposed in [Gro88] for the partial meet contractions (by one single sentence). Finally, we present yet an axiomatic characterization for the new class(es) of multiple contraction functions that are here introduced.

On the iteration of Katsuno and Mendelzon update

In this dissertation we present a model for iteration of Katsuno and Mendelzon’s Update, inspired in the developments for iteration in AGM belief revision. We adapt Darwiche and Pearls’ postulates of iterated belief revision to update (as well as the independence postulate proposed in [BM06, JT07]) and show two families of such operators, based in natural [Bou96] and lexicographic revision [Nay94a, NPP03]. In all cases, we provide a possible worlds semantics of the models.