Barbara Vantaggi

Locally Strong Coherence in Inference Processes

In this paper we deal with probabilistic inference in the most general form of coherent conditional probability assessments. In particular, our aim is to reduce computational difficulties that could arise with a direct application of the main characterization results. We reach our goal by introducing the notion of locally strong coherence and characterizing it by logical conditions. Hence, some of the numerical constraints are replaced by Boolean satisfiability conditions. An automatic procedure is proposed and its efficiency is proved. Some examples are reported to make easier the understanding of the machinery and to show its effectiveness.

T-conditional possibilities: Coherence and inference

In this paper we refer to an axiomatic definition of T-conditional possibility, where T is any t-norm. We characterize a full T-conditional possibility in terms of a suitable set of unconditional possibilities. Starting from this characterization we are able to manage coherent conditional possibility assessments and their enlargements. To compare T-conditional possibility related to different t-norm T, we study binary relations locally representable by a T-conditional possibility.

Statistical matching of multiple sources: A look through coherence

In several applications there is the need to consider different data sources and to integrate information: a specific case is the so-called statistical matching, where data sources have just a set of common variables and inference is required on the other variables. The traditional way to cope with such situations is to combine the available data with assumptions strong enough to identify pointwise the joint probability. Such assumptions cannot always be justified and inference should take into account all the set of compatible probabilities. In this paper, we show how statistical matching problems can be managed by means of coherent conditional probability: coherence allows us to combine the knowledge coming from different multiple sources, included those given from field experts, without necessarily assuming further hypothesis. Moreover, inferences and decisions can be dealt with by taking in consideration also logical constraints among the variables, which arise naturally in the applications. An example showing advantages and drawbacks of the proposed method is given.

Inferential processes leading to possibility and necessity

This paper deals with the upper and lower bounds of a class of uncertainty measures endowed with particular characteristics (decomposability, monotonicity, partial additivity and so on). We consider an initial partial assessment consistent with either probability or possibility or necessity, then we study the upper and lower envelopes of all possible extensions. By resorting to a notion of weak logical independence we get as lower or upper envelope a possibility or a necessity, respectively, starting either from a probability or from a possibility or from a necessity.

Conditional Independence in A Coherent Finite Setting

A definition of stochastic independence which avoids the inconsistencies (related to events of probability 0 or 1) of the classic one has been proposed by Coletti and Scozzafava for two events. We extend it to conditional independence among finite sets of events. In particular, the case of (finite) discrete random variables is studied. We check which of the relevant properties connected with graphical structures hold. Hence, an axiomatic characterization of these independence models is given and it is compared to the classic ones.

The L-separation criterion for description of cs-independence models

Different conditional independence models have been proposed in literature; in this paper we consider models induced by conditional probabilities based on the definition of conditional cs-independence. These models need not comply with the symmetry property, so that they have not the graphoid structure. Hence, the well-known d-separation criterion for directed acyclic graphs may not be able to represent such independence models. Therefore, we introduce a new separation criterion called L-separation. We study its main properties and show how it allows to represent the above-mentioned independence models through directed acyclic graphs.

Fuzzy inclusion and similarity through coherent conditional probability

Our aim is to study some specific fuzzy relations (inclusion and similarity) in the framework of the interpretation of fuzzy theory in terms of coherent conditional probability.

Independence and conditional possibility for strictly monotone triangular norms

In the literature there are different definitions of conditional possibility. Starting from a general axiomatic definition, we propose a definition of independence for ⊙‐conditional possibility, in the case that ⊙ is a strictly monotone triangular norm. We study its main properties to compare it to other definitions introduced in possibility theory. Then, we show that the controversial aspects related to logical dependencies (structural zeros) can be circumvented. Moreover, a set of properties (the well‐known graphoid properties) has been considered to be tested, allowing us to compare the proposed definition to the independence notions given in the context of other uncertainty formalisms.

Simplification Rules for the Coherent Probability Assessment Problem

In this paper we develop a procedure for checking the consistency (coherence) of a partial probability assessment. The general problem (called CPA) is NP-complete, hence, to have a reasonable application some heuristic is needed. Our proposal differs from others because it is based on a skilful use of the logical relations present among the events. In other approaches the consistency problem is reduced directly to the satisfiability of a system of linear constraints. Here, thanks to the characterization of particular configurations and to the elimination of variables, an instance of the problem is reduced to smaller instances. To obtain such results, we introduce a procedure based on rules resembling those given by Davis–Putnam for the satisfiability of Boolean formulas. At the end a particularized description of an actual implementation is given.

Conditional independence structure and its closure: Inferential rules and algorithms

In this paper, we deal with conditional independence models closed with respect to graphoid properties. Such models come from different uncertainty measures, in particular in a probabilistic setting. We study some inferential rules and describe methods and algorithms to compute efficiently the closure of a set of conditional independence statements.