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24
The cognitive structure of surprise: looking for basic principles
 International Review of Philosophy
, 2007
"... We develop a conceptual and formal clarification of the notion of surprise as a beliefbased phenomenon by exploring a rich typology. Each kind of surprise is associated with a particular phase of the cognitive processing and involves particular kinds of epistemic representations (representations an ..."
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We develop a conceptual and formal clarification of the notion of surprise as a beliefbased phenomenon by exploring a rich typology. Each kind of surprise is associated with a particular phase of the cognitive processing and involves particular kinds of epistemic representations (representations and expectations under scrutiny, implicit beliefs, presuppositions). We define two main kinds of surprise: mismatchbased surprise and astonishment. In the central part of the paper we suggest how a formal model of surprise can be integrated with a formal model of belief change. We investigate the role of surprise in triggering the process of belief reconsideration. There are a number of models of surprise developed in psychology of emotion. We provide several comparisons of our approach with those models.
From conditional probability to the logic of doxastic actions
 In TARK ’07: Proceedings of the 11th
, 2007
"... We investigate the discrete (finite) case of the PopperRenyi theory of conditional probability, introducing discrete conditional probabilistic models for knowledge and conditional belief, and comparing them with the more standard plausibility models. We also consider a related notion, that of safe ..."
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We investigate the discrete (finite) case of the PopperRenyi theory of conditional probability, introducing discrete conditional probabilistic models for knowledge and conditional belief, and comparing them with the more standard plausibility models. We also consider a related notion, that of safe belief, which is a weak (nonnegatively introspective) type of “knowledge”. We develop a probabilistic version of this concept (“degree of safety”) and we analyze its role in games. We completely axiomatize the logic of conditional belief, knowledge and safe belief over conditional probabilistic models. We develop a theory of probabilistic dynamic belief revision, introducing “action models ” and a notion of probabilistic update product, that comes together with appropriate reduction laws. 1
NPContainment for the Coherence Tests of Assessment of Conditional Probability: a FuzzyLogical Approach, Archive for Mathematical Logic
"... In this paper we investigate the problem of testing the coherence of an assessment of conditional probability following a purely logical setting. In particular we will prove that the coherence of an assessment of conditional probability χ can be characterized by means of the logical consistency of a ..."
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In this paper we investigate the problem of testing the coherence of an assessment of conditional probability following a purely logical setting. In particular we will prove that the coherence of an assessment of conditional probability χ can be characterized by means of the logical consistency of a suitable theory Tχ defined on the modalfuzzy logic FPk(R L∆) built up over the manyvalued logic R L∆. Such modalfuzzy logic was previously introduced in [11] in order to treat conditional probability by means of a list of simple probabilities following the well known (smart) ideas exposed in [18] by Halpern and in [7] by Coletti and Scozzafava. Roughly speaking, such logic is obtained by adding to the language of R L ∆ a list of k modalities for “probably ” and axioms reflecting the properties of simple probability measures. Moreover we proved that the satisfiability problem for modal formulas of FPk(R L∆) is NPcomplete. Finally, as main result of this paper, we used FPk(R L∆) in order to prove that the problem of establishing the coherence of rational assessments of conditional probability is NPcomplete. 1
A Nonstandard Characterization of Sequential Equilibrium, Perfect Equilibrium, and Proper Equilibrium
, 2008
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Conditional Probability and Defeasible Inference
 Journal of Philosophical Logic 34 (1):97–119, 2005. H. ArlóCosta and E. Pacuit
"... Abstract. We offer a probabilistic model of rational consequence relations (Lehmann and Magidor, 1990) by appealing to the extension of the classical RamseyAdams test proposed by Vann McGee in (McGee, 1994). Previous and influential models of nonmonotonic consequence relations have been produced i ..."
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Abstract. We offer a probabilistic model of rational consequence relations (Lehmann and Magidor, 1990) by appealing to the extension of the classical RamseyAdams test proposed by Vann McGee in (McGee, 1994). Previous and influential models of nonmonotonic consequence relations have been produced in terms of the dynamics of expectations (Gärdenfors and Makinson, 1994), (Gärdenfors, 1993). ‘Expectation’ is a term of art in these models, which should not be confused with the notion of expected utility. The expectations of an agent are some form of belief weaker than absolute certainty. Our model offers a modified and extended version of an account of qualitative belief in terms of conditional probability, first presented in (van Fraassen, 1995). We use this model to relate probabilistic and qualitative models of nonmonotonic relations in terms of expectations. In doing so we propose a probabilistic model of the notion of expectation. We provide characterization results both for logically finite languages and for logically infinite, but countable, languages. The latter case shows the relevance of the axiom of countable additivity for our probability functions. We show that a rational logic defined over a logically infinite language can only be fully characterized in terms of finitely additive conditional probability.
Preferencebased belief operators
, 2005
"... We show how different kinds of belief operators derived from preferences can be defined in terms an accessibility relation of epistemic priority, and characterized by means of a vector of nested accessibility relations. The semantic structure enables us to compare and reconcile certain nonstandard n ..."
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We show how different kinds of belief operators derived from preferences can be defined in terms an accessibility relation of epistemic priority, and characterized by means of a vector of nested accessibility relations. The semantic structure enables us to compare and reconcile certain nonstandard notions of belief that have recently been used in epistemic analyses of games.
Conditional belief types
, 2013
"... We study type spaces where a player’s type at a state is a conditional probability on the space. We axiomatize these type spaces using conditional belief operators, and examine three additional axioms of increasing strength. First, introspection, which requires the agent to be unconditionally certai ..."
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We study type spaces where a player’s type at a state is a conditional probability on the space. We axiomatize these type spaces using conditional belief operators, and examine three additional axioms of increasing strength. First, introspection, which requires the agent to be unconditionally certain of her beliefs. Second, echo, according to which the unconditional beliefs implied by the condition must be held given the condition. Third, determination, which says that the conditional beliefs are the unconditional beliefs that are conditionally certain. The echo axiom implies that conditioning on an event is the same as conditioning on the event being certain, which formalizes the standard informal interpretation of conditioning in probability theory. The echo axiom also implies that the conditional probability given an event is a prior of the unconditional probability. The gametheoretic application of our model, which we treat in the context of an example, sheds light on a number of basic issues in the analysis of extensive form games. Type spaces are closely related to the sphere models of counterfactual conditionals and to models of hypothetical knowledge, and we discuss these relationships in detail.
BELIEF AND PROBABILITY: A GENERAL THEORY OF PROBABILITY CORES
"... This paper considers varieties of probabilism capable of distilling paradoxfree qualitative doxastic notions (e.g., full belief, expectation, and plain belief) from a notion of probability taken as a primitive. We show that core systems, collections of nested propositions expressible in the underl ..."
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This paper considers varieties of probabilism capable of distilling paradoxfree qualitative doxastic notions (e.g., full belief, expectation, and plain belief) from a notion of probability taken as a primitive. We show that core systems, collections of nested propositions expressible in the underlying algebra, can play a crucial role in these derivations. We demonstrate how the notion of a probability core can be naturally generalized to high probability, giving rise to what we call a high probability core, a notion that when formulated in terms of classical monadic probability coincides with the notion of stability proposed by Hannes Leitgeb [2010]. Our work continues work done by one of us in collaboration with Rohit Parikh [ArlóCosta and Parikh, 2005]. In turn, the latter work was inspired by the seminal work of Bas van Fraassen [1995]. We argue that the adoption of dyadic probability as a primitive (as articulated by van Fraassen [1995]) admits a smoother connection with the standard theory of probability cores as well as a better model in which to situate doxastic notions like full belief. We also illustrate how the the basic structure underlying a system of cores
Belief hierarchies in standard state space models and epistemic equivalence of belief spaces
, 2010
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Independence for Sets of Full Conditional Probabilities, Sets of Lexicographic Probabilities, and Sets of Desirable Gambles
, 2013
"... Abstract In this paper we examine concepts of independence for sets of full conditional probabilities; that is, for sets of setfunctions where conditional probability is the primitive concept, and where conditioning can be considered on events of probability zero. We also discuss the related issue ..."
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Abstract In this paper we examine concepts of independence for sets of full conditional probabilities; that is, for sets of setfunctions where conditional probability is the primitive concept, and where conditioning can be considered on events of probability zero. We also discuss the related issue of independence for (sets of) lexicographic probabilities and for sets of desirable gambles.