Coherence checking and propagation of lower probability bounds

Gilio, Angelo; Biazzo, Veronica; Sanfilippo, Giuseppe

doi:10.1007/s00500-002-0218-2

Cited by 14 publications

(11 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We observe that Σ J is solvable if and only if P J ∈ I J , where I J is the convex hull associated with the pair (F J , P J ). Then, we have ([20, Thm 3.2]; see also [3,21]) Theorem 2. Given a probability assessment P n on the family F n , if the system Σ associated with (F n , P n ) is solvable, then for every J ⊂ J n , such that J \ I 0 = ∅, the system Σ J associated with (F J , P J ) is solvable too.…”

Section: Coherence Checkingmentioning

confidence: 99%

Conditional Random Quantities and Compounds of Conditionals

2013

View full text Add to dashboard Cite

Abstract.In this paper we consider finite conditional random quantities and conditional previsions assessments in the setting of coherence. We use a suitable representation for conditional random quantities; in particular the indicator of a conditional event E|H is looked at as a three-valued quantity with values 1, or 0, or p, where p is the probability of E|H. We introduce a notion of iterated conditional random quantity of the form (X|H)|K defined as a suitable conditional random quantity, which coincides with X|HK when H ⊆ K. Based on a recent paper by S. Kaufmann, we introduce a notion of conjunction of two conditional events and then we analyze it in the setting of coherence. We give a representation of the conjoined conditional and we show that this new object is a conditional random quantity. We examine some cases of logical dependencies, by also showing that the conjunction may be a conditional event; moreover, we introduce the negation of the conjunction and by De Morgan's Law the operation of disjunction. Finally, we give the lower and upper bounds for the conjunction and the disjunction of two conditional events, by showing that the usual probabilistic properties continue to hold.

show abstract

Section: Coherence Checkingmentioning

confidence: 99%

Conditional Random Quantities and Compounds of Conditionals

2013

View full text Add to dashboard Cite

show abstract

“…In particular, it has been shown in [4,7] that further variables can be removed in coherence-based probabilistic reasoning by a refined characterization based on random gain. We expect that this result carries over to model-theoretic probabilistic reasoning.…”

Section: Discussionmentioning

confidence: 99%

“…Direct methods to check consistency and to propagate conditional probability assessments, which do not involve sequences of linear programming problems (with unknowns the probabilities of the constituents), are given in Walley et al [58]. The problem of reducing or eliminating the computational difficulties of checking consistency and of the propagation of probabilistic assessments has been recently investigated by Biazzo et al [7,8], Capotorti and Vantaggi [11], Capotorti et al [10], and Coletti and Scozzafava [16].…”

Section: Introductionmentioning

confidence: 99%

Probabilistic logic under coherence: complexity and algorithms

Biazzo

Gilio

Lukasiewicz

et al. 2005

Ann Math Artif Intell

View full text Add to dashboard Cite

In previous work [V. Biazzo, A. Gilio, T. Lukasiewicz and G. Sanfilippo, Probabilistic logic under coherence, model-theoretic probabilistic logic, and default reasoning in System P, Journal of Applied Non-Classical Logics 12(2) (2002) 189-213.], we have explored the relationship between probabilistic reasoning under coherence and model-theoretic probabilistic reasoning. In particular, we have shown that the notions of g-coherence and of g-coherent entailment in probabilistic reasoning under coherence can be expressed by combining notions in model-theoretic probabilistic reasoning with concepts from default reasoning. In this paper, we continue this line of research. Based on the above semantic results, we draw a precise picture of the computational complexity of probabilistic reasoning under coherence. Moreover, we introduce transformations for probabilistic reasoning under coherence, which reduce an instance of deciding g-coherence or of computing tight intervals under g-coherent entailment to a smaller problem instance, and which can be done very efficiently. Furthermore, we present new algorithms for deciding g-coherence and for computing tight intervals under g-coherent entailment, which reformulate previous algorithms using terminology from default reasoning. They are based on reductions to standard problems in model-theoretic probabilistic reasoning, which in turn can be reduced to linear optimization problems. Hence, efficient techniques for model-theoretic probabilistic reasoning can immediately be applied for probabilistic reasoning under coherence (for example, column generation techniques). We describe several such techniques, which transform problem instances in model-theoretic probabilistic reasoning into smaller problem instances. We also describe a technique for obtaining a reduced set of variables for the associated linear optimization problems in the conjunctive case, and give new characterizations of this reduced set as a set of non-decomposable variables, and using the concept of random gain

show abstract

“…Probabilistic relational databases [2,3,4] have been studied from the late 80"s until today. But today Application Need to manage imprecision"s in data.…”

Section: Database Is Deterministic and Query Answers Are Probabilistimentioning

confidence: 99%

A Method of Computing with Words to Answer Queries in Relational Database

Rajpal¹

2010

IJCA

View full text Add to dashboard Cite

In this paper we are proposing a new method of intelligent search based on the concept of computing with words introduced by Prof. Zadeh [1] in 1996 to find the most suitable match for the predicates to answer any imprecise query made by the database users. The method is based on the theory of Computing with Words (CW). It is also to be mentioned that the proposed method could be easily incorporated in the existing commercial query languages of DBMS to serve the lay users better. So in this Paper Author is suggesting a new method called as α-CWequality Search to answer the queries of Relational database based on ranks.

show abstract

Coherence checking and propagation of lower probability bounds

Cited by 14 publications

References 23 publications

Conditional Random Quantities and Compounds of Conditionals

Conditional Random Quantities and Compounds of Conditionals

Probabilistic logic under coherence: complexity and algorithms

A Method of Computing with Words to Answer Queries in Relational Database

Contact Info

Product

Resources

About