Default Logic in a Coherent Setting

In this talk - based on the results of a forthcoming paper (Coletti, Scozzafava and Vantaggi 2002), presented also by one of us at the Conference on "Non Classical Logic, Approximate Reasoning and Soft-Computing" (Anacapri, Italy, 2001) - we discuss the problem of representing default rules by means of a suitable coherent conditional probability, defined on a family of conditional events. An event is singled-out (in our approach) by a proposition, that is a statement that can be either true or false; a conditional event is consequently defined by means of two propositions and is a 3-valued entity, the third value being (in this context) a conditional probability

Conditionally coherent qualitative probabilities

Si introduce il concetto di probabilità qualitativa (debole) condizionatamente coerente. Si dimostra che una tale probabilità qualitativa può essere estesa da un dato dominio (che non è necessariamente un'algebra) ad un qualunque insieme che lo contenga. Si dimostra infine che le probabilità qualitative condizionatamente coerenti sono tutte e sole quelle quasi realizzabili con una probabilità condizionata coerente nel senso di de Finetti

Coherence principles for handling qualitative and quantitative partial probabilistic assessments

In this paper we present an overview of mathematical models for handling partial entailments and their extensions in a probabilistic frame

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. © 2008 Elsevier B.V. All rights reserved

Inference with fuzzy and probabilistic information

In the paper we deal with fuzzy sets under the interpretation given in a coherent probabilistic setting. We provide a general Bayesian inference process involving fuzzy and partial probabilistic information by showing its peculiarities. © 2010 Springer-Verlag Berlin Heidelberg

Managing uncertainty and fuzziness trough a generalized conditional plausibility model

The paper deals with a model for handling fuzziness and uncertainty simultaneously. The framework of reference is that of generalized conditional plausibility, in the sense of Dempster conditioning rule, which contains as particular cases both conditional probability and conditional possibility. Particular focus is placed on the interpretation of the interval fuzzy sets by means of this model

Hybrid models: Probabilistic and fuzzy information

Under the interpretation of fuzzy set as coherent conditional probability, we study inferential processes starting from a probability distribution (on a random variable) and a coherent conditional probability on "fuzzy conditional events". We characterize the coherent extensions and we analyze an example proposed by Zadeh. © 2013 Springer-Verlag

From Comparative Degrees of Belief to Conditional Measures

Aim of this paper is to give a contribute to the discussion about the "best" definition of conditional model for plausibilty functions and its subclass of the possibility functions. We propose to use the framework of the theory of measurements: by studying the comparative structure underling different conditional models. This approach gives an estimate of the "goodness" and "effectiveness" of the model, by pointing out the rules necessarily accepted by the user. Moreover, the results related to the characterization of comparative degree of belief by means conditional uncertainty measures can be used in decision theory. They are in fact necessary when we need a model for a decision maker interested in choosing by taking into account, at the same moment, different scenarios

Knowledge processing in decisions under fuzziness and uncertainty

Uncertainty cannot always be' managed by probability measures, the uncertainty non-additive measures are considered. We discuss the interpretation of fuzzy sets and the main mathematical properties. In order to update the information we propose fuzzy Bayes facto