The Experts below are selected from a list of 33327 Experts worldwide ranked by ideXlab platform
Daniel Lehmann - One of the best experts on this subject based on the ideXlab platform.
-
Generalized Qualitative Probability: Savage Revisited
arXiv: Artificial Intelligence, 2014Co-Authors: Daniel LehmannAbstract:Preferences among acts are analyzed in the style of L. Savage, but as partially ordered. The rationality postulates considered are weaker than Savage's on three counts. The Sure Thing Principle is derived in this setting. The postulates are shown to lead to a characterization of generalized Qualitative Probability that includes and blends both traditional Qualitative Probability and the ranked structures used in logical approaches.
-
Nonmonotonic Logics and Semantics
arXiv: Artificial Intelligence, 2002Co-Authors: Daniel LehmannAbstract:Tarski gave a general semantics for deductive reasoning: a formula a may be deduced from a set A of formulas iff a holds in all models in which each of the elements of A holds. A more liberal semantics has been considered: a formula a may be deduced from a set A of formulas iff a holds in all of the "preferred" models in which all the elements of A hold. Shoham proposed that the notion of "preferred" models be defined by a partial ordering on the models of the underlying language. A more general semantics is described in this paper, based on a set of natural properties of choice functions. This semantics is here shown to be equivalent to a semantics based on comparing the relative "importance" of sets of models, by what amounts to a Qualitative Probability measure. The consequence operations defined by the equivalent semantics are then characterized by a weakening of Tarski's properties in which the monotonicity requirement is replaced by three weaker conditions. Classical propositional connectives are characterized by natural introduction-elimination rules in a nonmonotonic setting. Even in the nonmonotonic setting, one obtains classical propositional logic, thus showing that monotonicity is not required to justify classical propositional connectives.
-
UAI - Generalized Qualitative Probability: savage revisited
1996Co-Authors: Daniel LehmannAbstract:Preferences among acts are analyzed in the style of L. Savage, but as partially ordered. The rationality postulates considered are weaker than Savage's on three counts. The Sure Thing Principle is derived in this setting. The postulates are shown to lead to a characterization of generalized Qualitative Probability that includes and blends both traditional Qualitative Probability and the ranked structures used in logical approaches.
Arkadii Slinko - One of the best experts on this subject based on the ideXlab platform.
-
Simplicial Complexes Obtained from Qualitative Probability Orders
SIAM Journal on Discrete Mathematics, 2013Co-Authors: Paul H. Edelman, Tatiana Gvozdeva, Arkadii SlinkoAbstract:The goal of this paper is to introduce a new class of simplicial complexes that naturally generalize the threshold complexes. These will be derived from Qualitative Probability orders on subsets of a finite set that generalize subset orders induced by Probability measures. We show that this new class strictly contains the threshold complexes and is strictly contained in the shifted complexes. We conjecture that this class of complexes is exactly the set of strongly acyclic complexes, a class that has previously appeared in the context of cooperative games. Beyond the results themselves, this new class of complexes allows us to refine our understanding of one-point extensions of a particular oriented matroid.
-
Simplicial Complexes Obtained from Qualitative Probability Orders
arXiv: Combinatorics, 2011Co-Authors: Paul H. Edelman, Tatiana Gvozdeva, Arkadii SlinkoAbstract:In this paper we inititate the study of abstract simplicial complexes which are initial segments of Qualitative Probability orders. This is a natural class that contains the threshold complexes and is contained in the shifted complexes, but is equal to neither. In particular we construct a Qualitative Probability order on 26 atoms that has an initial segment which is not a threshold simplicial complex. Although 26 is probably not the minimal number for which such example exists we provide some evidence that it cannot be much smaller. We prove some necessary conditions for this class and make a conjecture as to a characterization of them. The conjectured characterization relies on some ideas from cooperative game theory.
-
A counterexample to Fishburn's conjecture on finite linear Qualitative Probability
Journal of Mathematical Psychology, 2004Co-Authors: Marston Conder, Arkadii SlinkoAbstract:Kraft, Pratt and Seidenberg (1959) provided an infinite set of axioms which, when taken together with de Finetti’s axiom, gives a necessary and sufficient set of “cancellation” conditions for representability of an ordering relation on subsets of a set by an order-preserving Probability measure. Fishburn (1996) defined f(n )t o be the smallest positive integer k such that every comparative Probability ordering on an n-element set which satisfies the cancellation conditions C4 ,... , Ck is representable. By the work of Kraft et al. (1959) and Fishburn (1996, 1997), it is known that n − 1 ≤ f(n) ≤ n +1 for all n ≥ 5. Also Fishburn proved that f(5) = 4, and conjectured that f(n )= n − 1 for all n ≥ 5. In this paper we confirm that f(6) = 5, but give counter-examples to Fishburn’s conjecture for n =7 ,showing that f(7) ≥ 7. We summarise, correct and extend many of the known results on this topic, including the notion of “almost representability”, and offer an amended version of Fishburn’s conjecture.
Giulianella Coletti - One of the best experts on this subject based on the ideXlab platform.
-
experimental evaluation of the understanding of Qualitative Probability and probabilistic reasoning in young children
International Conference Industrial Engineering & Other Applications Applied Intelligent Systems, 2017Co-Authors: Jean Baratgin, Giulianella Coletti, Frank Jamet, Davide PetturitiAbstract:De Finetti’s approach of an event of two levels of knowledge was recently proposed as the model of reference for psychology studies. We show that de Finetti’s Qualitative Probability framework seems to be “natural” to children aged from 3 to 4 as well as to account for children’s heuristic approach to probabilistic reasoning.
-
IEA/AIE (2) - Experimental Evaluation of the Understanding of Qualitative Probability and Probabilistic Reasoning in Young Children
Advances in Artificial Intelligence: From Theory to Practice, 2017Co-Authors: Jean Baratgin, Giulianella Coletti, Frank Jamet, Davide PetturitiAbstract:De Finetti’s approach of an event of two levels of knowledge was recently proposed as the model of reference for psychology studies. We show that de Finetti’s Qualitative Probability framework seems to be “natural” to children aged from 3 to 4 as well as to account for children’s heuristic approach to probabilistic reasoning.
-
Coherent Qualitative Probability
Journal of Mathematical Psychology, 1990Co-Authors: Giulianella ColettiAbstract:Abstract This note introduces the concepts of coherent, positive coherent, and strongly coherent Qualitative Probability. The first interesting result is that such a Qualitative Probability can be extended from a given domain (not necessarily an algebra) to an arbitrary larger one. The most important result of this paper consists in proving that coherent Qualitative probabilities can be represented by the Finetti's coherent previsions.
-
A coherent Qualitative Bayes' theorem and its application in artificial intelligence
1993 (2nd) International Symposium on Uncertainty Modeling and Analysis, 1Co-Authors: Giulianella Coletti, R. ScozzafavaAbstract:Qualitative Probability deals with properties of a binary relation to be read 'is no more probable than', or its strict companion 'is less probable than', on a set of conditional events, such as 'A given H'. From the point of view of applications, it is clearly very significant not assuming any specific structure for the set on which the Qualitative Probability is defined. This situation is typical for the conditional events representing uncertain statements in artificial intelligence, for example in expert systems. The intuitive meaning of the binary relation is simply 'A given H is no more probable than B given K', i.e., none of the usual axioms is a priori adopted. The authors introduce instead, for this binary relation, coherence conditions which are related to de Finetti's coherent systems of bets and study their implications with reference to the properties of Qualitative Probability and to the possibility of its numerical representation. A Qualitative Bayes' theorem is then derived. It allows the comparison of the conditional events 'H given E' and 'K given E' once the ordering between 'E given H' and 'E given K' and that between H and K are both given. Some applications are considered. >
-
IPMU - Conditional Events with Vague Information in Expert Systems
Uncertainty in Knowledge Bases, 1Co-Authors: Giulianella Coletti, Angelo Gilio, Romano ScozzafavaAbstract:Ad hoc techniques and inference methods used in expert systems are often logically inconsistent. On the other hand, among properties and assertions concerning handling of uncertainty, those which turns out to be well founded can be in general easily deduced from Probability laws. Relying on the general concept of event as a proposition and starting from a few conditional events of initial interest, a gradual and coherent assignment of conditional probabilities is possible by resorting to de Finetti's theory of coherent extension of subjective Probability. Moreover, even when numerical probabilities can be easily assessed, a more general approach is obtained introducing an ordering among conditional events by means of a coherent Qualitative Probability.
Jean Baratgin - One of the best experts on this subject based on the ideXlab platform.
-
experimental evaluation of the understanding of Qualitative Probability and probabilistic reasoning in young children
International Conference Industrial Engineering & Other Applications Applied Intelligent Systems, 2017Co-Authors: Jean Baratgin, Giulianella Coletti, Frank Jamet, Davide PetturitiAbstract:De Finetti’s approach of an event of two levels of knowledge was recently proposed as the model of reference for psychology studies. We show that de Finetti’s Qualitative Probability framework seems to be “natural” to children aged from 3 to 4 as well as to account for children’s heuristic approach to probabilistic reasoning.
-
IEA/AIE (2) - Experimental Evaluation of the Understanding of Qualitative Probability and Probabilistic Reasoning in Young Children
Advances in Artificial Intelligence: From Theory to Practice, 2017Co-Authors: Jean Baratgin, Giulianella Coletti, Frank Jamet, Davide PetturitiAbstract:De Finetti’s approach of an event of two levels of knowledge was recently proposed as the model of reference for psychology studies. We show that de Finetti’s Qualitative Probability framework seems to be “natural” to children aged from 3 to 4 as well as to account for children’s heuristic approach to probabilistic reasoning.
-
Deductive schemas with uncertain premises using Qualitative Probability expressions
Thinking & Reasoning, 2015Co-Authors: Guy Politzer, Jean BaratginAbstract:ABSTRACTThe new paradigm in the psychology of reasoning redirects the investigation of deduction conceptually and methodologically because the premises and the conclusion of the inferences are assumed to be uncertain. A probabilistic counterpart of the concept of logical validity and a method to assess whether individuals comply with it must be defined. Conceptually, we used de Finetti's coherence as a normative framework to assess individuals' performance. Methodologically, we presented inference schemas whose premises had various levels of Probability that contained non-numerical expressions (e.g., “the chances are high”) and, as a control, sure levels. Depending on the inference schemas, from 60% to 80% of the participants produced coherent conclusions when the premises were uncertain. The data also show that (1) except for schemas involving conjunction, performance was consistently lower with certain than uncertain premises, (2) the rate of conjunction fallacy was consistently low (not exceeding 20%, ...
Paul Snow - One of the best experts on this subject based on the ideXlab platform.
-
Intuitions about Ordered Beliefs Leading to Probabilistic Models
arXiv: Artificial Intelligence, 2013Co-Authors: Paul SnowAbstract:The general use of subjective probabilities to model belief has been justified using many axiomatic schemes. For example, ?consistent betting behavior' arguments are well-known. To those not already convinced of the unique fitness and generality of Probability models, such justifications are often unconvincing. The present paper explores another rationale for Probability models. ?Qualitative Probability,' which is known to provide stringent constraints on belief representation schemes, is derived from five simple assumptions about relationships among beliefs. While counterparts of familiar rationality concepts such as transitivity, dominance, and consistency are used, the betting context is avoided. The gap between Qualitative Probability and Probability proper can be bridged by any of several additional assumptions. The discussion here relies on results common in the recent AI literature, introducing a sixth simple assumption. The narrative emphasizes models based on unique complete orderings, but the rationale extends easily to motivate set-valued representations of partial orderings as well.
-
Ignorance and the Expressiveness of Single- and Set-Valued Probability Models of Belief
arXiv: Artificial Intelligence, 2013Co-Authors: Paul SnowAbstract:Over time, there have hen refinements in the way that Probability distributions are used for representing beliefs. Models which rely on single Probability distributions depict a complete ordering among the propositions of interest, yet human beliefs are sometimes not completely ordered. Non-singleton sets of Probability distributions can represent partially ordered beliefs. Convex sets are particularly convenient and expressive, but it is known that there are reasonable patterns of belief whose faithful representation require less restrictive sets. The present paper shows that prior ignorance about three or more exclusive alternatives and the emergence of partially ordered beliefs when evidence is obtained defy representation by any single set of distributions, but yield to a representation baud on several uts. The partial order is shown to be a partial Qualitative Probability which shares some intuitively appealing attributes with Probability distributions.
-
UAI - Ignorance and the expressiveness of single- andset-valued Probability models of belief
Uncertainty Proceedings 1994, 1994Co-Authors: Paul SnowAbstract:Over time, there have been refinements in the way that Probability distributions are used for representing beliefs. Models which rely on single Probability distributions depict a complete ordering among the propositions of interest, yet human beliefs are sometimes not completely ordered. Non-singleton sets of Probability distributions can represent partially ordered beliefs. Convex sets are particularly convenient and expressive, but it is known that there are reasonable patterns of belief whose faithful representation require less restrictive sets. The present paper shows that prior ignorance about three or more exclusive alternatives and the emergence of partially ordered beliefs when evidence is obtained defy representation by any single set of distributions, but yield to a representation based on several sets. The partial order is shown to be a partial Qualitative Probability which shares some intuitively appealing attributes with Probability distributions.
-
UAI - Intuitions about ordered beliefs leading to probabilistic models
Uncertainty in Artificial Intelligence, 1992Co-Authors: Paul SnowAbstract:The general use of subjective probabilities to model belief has been justified using many axiomatic schemes. For example, 'consistent betting behavior" arguments are well-known. To those not already convinced of the unique fitness and generality of Probability models, such justifications are often unconvincing. The present paper explores another rationale for Probability models. "Qualitative Probability,' which is known to provide stringent constraints on belief representation schemes, is derived from five simple assumptions about relationships among beliefs. While counterparts of familiar rationality concepts such as transitivity, dominance, and consistency are used, the betting context is avoided. The gap between Qualitative Probability and Probability proper can be bridged by any of several additional assumptions. The discussion here relies on results common in the recent AI literature, introducing a sixth simple assumption. The narrative emphasizes models based on unique complete orderings, but the rationale extends easily to motivate set-valued representations of partial orderings as well.
