A Characterization of Probability-based Dichotomous Belief Revision

This article investigates the properties of multistate top revision, a dichotomous (AGM-style) model of belief revision that is based on an underlying model of probability revision. A proposition is included in the belief set if and only if its probability is either 1 or infinitesimally close to 1. Infinitesimal probabilities are used to keep track of propositions that are currently considered to have negligible probability, so that they are available if future information makes them more plausible. Multistate top revision satisfies a slightly modified version of the set of basic and supplementary AGM postulates, except the inclusion and success postulates. This result shows that hyperreal probabilities can provide us with efficient tools for overcoming the well known difficulties in combining dichotomous and probabilistic models of belief change.

Bottom-up populism: How relative deprivation and populist attitudes mobilize leaderless anti-government protest

The present research focuses on populism as a bottom-up phenomenon that emerges from shared perceptions of relative deprivation. We predict that by serving as a shared ideological basis, populist attitudes can mobilize leaderless anti-government protest across ideological boundaries. We test this prediction in the context of the French Yellow Vests movement. Using a sample of French citizens (N = 562), we compare the effects of different indicators of relative deprivation on Yellow Vest protest participation and the extent to which populist attitudes account for these relationships. Results indicate that protests were fuelled by indicators of relative deprivation at the individual and group levels. Populist attitudes were best predicted by vertical comparisons between “the people” and “the elite” and fully accounted for the relationship between this type of group relative deprivation and protesting. Conversely, populist attitudes only partially accounted for the relationships between protesting and traditional measures of relative deprivation that either contrast natives with immigrants or individuals with fellow citizens. The findings strengthen the understanding of populism as a “thin centred” belief set that can unite and mobilize those who feel unfairly disadvantaged compared to a socio-political elite.

TWO LEVEL CREDIBILITY-LIMITED REVISIONS

In this paper, we propose a new kind of nonprioritized operator which we call two level credibility-limited revision. When revising through a two level credibility-limited revision there are two levels of credibility and one of incredibility. When revising by a sentence at the highest level of credibility, the operator behaves as a standard revision, if the sentence is at the second level of credibility, then the outcome of the revision process coincides with a standard contraction by the negation of that sentence. If the sentence is not credible, then the original belief set remains unchanged. In this article, we axiomatically characterize several classes of two level credibility-limited revision operators.

Revising Probabilities and Full Beliefs

A new formal model of belief dynamics is proposed, in which the epistemic agent has both probabilistic beliefs and full beliefs. The agent has full belief in a proposition if and only if she considers the probability that it is false to be so close to zero that she chooses to disregard that probability. She treats such a proposition as having the probability 1, but, importantly, she is still willing and able to revise that probability assignment if she receives information that gives her sufficient reasons to do so. Such a proposition is (presently) undoubted, but not undoubtable (incorrigible). In the formal model it is assigned a probability 1 − δ, where δ is an infinitesimal number. The proposed model employs probabilistic belief states that contain several underlying probability functions representing alternative probabilistic states of the world. Furthermore, a distinction is made between update and revision, in the same way as in the literature on (dichotomous) belief change. The formal properties of the model are investigated, including properties relevant for learning from experience. The set of propositions whose probabilities are infinitesimally close to 1 forms a (logically closed) belief set. Operations that change the probabilistic belief state give rise to changes in this belief set, which have much in common with traditional operations of belief change.

Kernel Contraction and Base Dependence

The AGM paradigm of belief change studies the dynamics of belief states in light of new information. Finding, or even approximating, those beliefs that are dependent on or relevant to a change is valuable because, for example, it can narrow the set of beliefs considered during belief change operations. A strong intuition in this area is captured by Gärdenfors’s preservation criterion (GPC), which suggests that formulas independent of a belief change should remain intact. GPC thus allows one to build dependence relations that are linked with belief change. Such dependence relations can in turn be used as a theoretical benchmark against which to evaluate other approximate dependence or relevance relations. Fariñas and Herzig axiomatize a dependence relation with respect to a belief set, and, based on GPC, they characterize the correspondence between AGM contraction functions and dependence relations. In this paper, we introduce base dependence as a relation between formulas with respect to a belief base, and prove a more general characterization that shows the correspondence between kernel contraction and base dependence. At this level of generalization, different types of base dependence emerge, which we show to be a result of possible redundancy in the belief base. We further show that one of these relations that emerge, strong base dependence, is parallel to saturated kernel contraction. We then prove that our latter characterization is a reversible generalization of Fariñas and Herzig’s characterization. That is, in the special case when the underlying belief base is deductively closed (i.e., it is a belief set), strong base dependence reduces to dependence, and so do their respective characterizations. Finally, an intriguing feature of Fariñas and Herzig’s formalism is that it meets other criteria for dependence, namely, Keynes’s conjunction criterion for dependence (CCD) and Gärdenfors’s conjunction criterion for independence (CCI). We prove that our base dependence formalism also meets these criteria. Even more interestingly, we offer a more specific criterion that implies both CCD and CCI, and show our base dependence formalism also meets this new criterion.

Epistemic-entrenchment Characterization of Parikh’s Axiom

In this article, we provide the epistemic-entrenchment characterization of the weak version of Parikh’s relevance-sensitive axiom for belief revision — known as axiom (P) — for the general case of incomplete theories. Loosely speaking, axiom (P) states that, if a belief set K can be divided into two disjoint compartments, and the new information φ relates only to the first compartment, then the second compartment should not be affected by the revision of K by φ. The above-mentioned characterization, essentially, constitutes additional constraints on epistemic-entrenchment preorders, that induce AGM revision functions, satisfying the weak version of Parikh’s axiom (P).

At the Forefront of Innovation, 1962–1963

In chapter 3, Frank discusses three important Nueva Figuración exhibitions. In one of these, a drawing show, the group focused on the governmental crisis that was then erupting. The military had divided into two factions in a disagreement over how to manage the Peronist movement: these factions, the Azules and Colorados, actually battled in the streets of Buenos Aires. Ernesto Deira created an important work based on Julio Cortázar’s 1960 novel Los premios (The Winners), an allegory of political chaos in Argentina of the time. Jorge de la Vega began a series of works depicting monsters of various kinds, one of them a critical commentary on developmentalism—the dominant belief set of the country's leaders. Luis Felipe Noé created Introduction to Hope, an important work that engaged many then-current issues, including Peronism, elections, and political passion.