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Belief revision theory studies how an ideal doxastic agent should revise her beliefs when she receives new information. In part I, I have first presented the AGM theory of belief revision. Then I have focused on the problem of iterated belief revisions. In part II, I will first present ranking theory (Spohn 1988). Then I will show how it solves the problem of iterated belief revisions. I will conclude by sketching two areas of future research. |
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Recent accounts of actual causation are stated in terms of extended causal models. These extended causal models contain two elements representing two seemingly distinct modalities. The first element are structural equations which represent the or mechanisms of the model, just as ordinary causal models do. The second element are ranking functions which represent normality or typicality. The aim of this paper is to show that these two modalities can be unified. I do so by formulating two constraints under which extended (...) |
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Epistemology is the study of knowledge and justified belief. Belief is thus central to epistemology. It comes in a qualitative form, as when Sophia believes that Vienna is the capital of Austria, and a quantitative form, as when Sophia's degree of belief that Vienna is the capital of Austria is at least twice her degree of belief that tomorrow it will be sunny in Vienna. Formal epistemology, as opposed to mainstream epistemology (Hendricks 2006), is epistemology done in a formal way, (...) |
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Various theories try to give accounts of how measures of this confidence do or ought to behave, both as far as the internal mental consistency of the agent as ... |
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And this paper is an attempt to say precisely how, thus addressing a philosophical problem which is commonly taken to be a serious one. It does so, however, in quite an idiosyncratic way. It is based on the account of inductive schemes I have given in (1988) and (1990a) and on the conception of causation I have presented in (1980), (1983), and (1990b), and it intends to fill one of many gaps which have been left by these papers. Still, I (...) |
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Ranking functions have been introduced under the name of ordinal conditional functions in Spohn (1988; 1990). They are representations of epistemic states and their dynamics. The most comprehensive and up to date presentation is Spohn (manuscript). |
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Degrees of belief are familiar to all of us. Our confidence in the truth of some propositions is higher than our confidence in the truth of other propositions. We are pretty confident that our computers will boot when we push their power button, but we are much more confident that the sun will rise tomorrow. Degrees of belief formally represent the strength with which we believe the truth of various propositions. The higher an agent’s degree of belief for a particular (...) |
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The paper provides an argument for the thesis that an agent’s degrees of disbelief should obey the ranking calculus. This Consistency Argument is based on the Consistency Theorem. The latter says that an agent’s belief set is and will always be consistent and deductively closed iff her degrees of entrenchment satisfy the ranking axioms and are updated according to the ranktheoretic update rules. |
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– We offer a new motivation for imprecise probabilities. We argue that there are propositions to which precise probability cannot be assigned, but to which imprecise probability can be assigned. In such cases the alternative to imprecise probability is not precise probability, but no probability at all. And an imprecise probability is substantially better than no probability at all. Our argument is based on the mathematical phenomenon of non-measurable sets. Non-measurable propositions cannot receive precise probabilities, but there is a natural (...) |
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Ranking theory is one of the salient formal representations of doxastic states. It differs from others in being able to represent belief in a proposition (= taking it to be true), to also represent degrees of belief (i.e. beliefs as more or less firm), and thus to generally account for the dynamics of these beliefs. It does so on the basis of fundamental and compelling rationality postulates and is hence one way of explicating the rational structure of doxastic states. Thereby (...) |
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This note is a sequel to Huber. It is shown that obeying a normative principle relating counterfactual conditionals and conditional beliefs, viz. the royal rule, is a necessary and sufficient means to attaining a cognitive end that relates true beliefs in purely factual, non-modal propositions and true beliefs in purely modal propositions. Along the way I will sketch my idealism about alethic or metaphysical modality. |
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I want to look at recent developments of representing AGM-style belief revision in dynamic epistemic logics and the options for doing something similar for ranking theory. Formally, my aim will be modest: I will define a version of basic dynamic doxastic logic using ranking functions as the semantics. I will show why formalizing ranking theory this way is useful for the ranking theorist first by showing how it enables one to compare ranking theory more easily with other approaches to belief (...) |
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As the paper explains, it is crucial to epistemology in general and to the theory of causation in particular to investigate the properties of conditional independence as completely as possible. The paper summarizes the most important results concerning conditional independence with respect to two important representations of epistemic states, namely (strictly positive) probability measures and natural conditional (or disbelief or ranking) functions. It finally adds some new observations. |
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First, ranking functions are argued to be superior to AGM belief revision theory in two crucial respects. Second, it is shown how ranking functions are uniquely reflected in iterated belief change. More precisely, conditions on threefold contractions are specified which suffice for representing contractions by a ranking function uniquely up to multiplication by a positive integer. Thus, an important advantage AGM theory seemed to have over ranking functions proves to be spurious. |
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"A Survey of Ranking Theory": The paper gives an up-to-date survey of ranking theory. It carefully explains the basics. It elaborates on the ranking theoretic explication of reasons and their balance. It explains the dynamics of belief statable in ranking terms and indicates how the ranks can thereby be measured. It suggests how the theory of Bayesian nets can be carried over to ranking theory. It indicates what it might mean to objectify ranks. It discusses the formal and the philosophical (...) |
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Modern belief revision theory is based to a large extent on partial meet contraction that was introduced in the seminal article by Carlos Alchourrón, Peter Gärdenfors, and David Makinson that appeared in 1985. In the same year, Alchourrón and Makinson published a significantly different approach to the same problem, called safe contraction. Since then, safe contraction has received much less attention than partial meet contraction. The present paper summarizes the current state of knowledge on safe contraction, provides some new results (...) |
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The volume analyses and develops David Makinson’s efforts to make classical logic useful outside its most obvious application areas. The book contains chapters that analyse, appraise, or reshape Makinson’s work and chapters that develop themes emerging from his contributions. These are grouped into major areas to which Makinsons has made highly influential contributions and the volume in its entirety is divided into four sections, each devoted to a particular area of logic: belief change, uncertain reasoning, normative systems and the resources (...) |
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In this brief note I show how to model conceptual change, logical learning, and revision of one's beliefs in response to conditional information such as indicative conditionals that do not express propositions. |
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