A logic for reasoning about the probability of fuzzy events

Authors:
Tommaso Flaminio;Lluís Godo
Affiliations:
Dip. di Matematica e Scienze Informatiche, University of Siena, 53100 Siena, Italy;Artificial Intelligence Research Institute (IIIA), CSIC, 089193 Bellaterra, Spain
Venue:
Fuzzy Sets and Systems
Year:
2007

Citing 2
Cited 18

An Algebraic Approach to Propositional Fuzzy Logic

Journal of Logic, Language and Information
A zero-layer based fuzzy probabilistic logic for conditional probability

ECSQARU'05 Proceedings of the 8th European conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty

Complexity of fuzzy probability logics II

Fuzzy Sets and Systems
A complete fuzzy logical system to deal with trust management systems

Fuzzy Sets and Systems
Description Logic Programs Under Probabilistic Uncertainty and Fuzzy Vagueness

ECSQARU '07 Proceedings of the 9th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Fuzzy system models (FSMs) for analysis of rock mass displacement caused by underground mining in soft rock strata

Expert Systems with Applications: An International Journal
MV-algebras with internal states and probabilistic fuzzy logics

International Journal of Approximate Reasoning
Description logic programs under probabilistic uncertainty and fuzzy vagueness

International Journal of Approximate Reasoning
Exploring Extensions of Possibilistic Logic over Gödel Logic

ECSQARU '09 Proceedings of the 10th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Uncertainty modelling for vague concepts: A prototype theory approach

Artificial Intelligence
Fuzzy logics with an additional involutive negation

Fuzzy Sets and Systems
The coherence of Łukasiewicz assessments is NP-complete

International Journal of Approximate Reasoning
Notes on strong completeness in łukasiewicz, product and BL logics and in their first-order extensions

Algebraic and proof-theoretic aspects of non-classical logics
Extending possibilistic logic over Gödel logic

International Journal of Approximate Reasoning
Belief functions on MV-algebras of fuzzy events based on fuzzy evidence

ECSQARU'11 Proceedings of the 11th European conference on Symbolic and quantitative approaches to reasoning with uncertainty
State operators on generalizations of fuzzy structures

Fuzzy Sets and Systems
A logic with imprecise probabilities and an application to automated reasoning using rewriting techniques

Fuzzy Sets and Systems
Logics for belief functions on MV-algebras

International Journal of Approximate Reasoning
Characterization of continuous t-norms compatible with Zadeh's probability of fuzzy events

Fuzzy Sets and Systems
Generalized Bosbach states: Part II

Archive for Mathematical Logic

Quantified Score

Hi-index	0.21

Visualization

Abstract

In this paper we present the logic FP(L"n,L) which allows to reason about the probability of fuzzy events formalized by means of the notion of state in a MV-algebra. This logic is defined starting from a basic idea exposed by Hajek [Metamathematics of Fuzzy Logic, Kluwer, Dordrecht, 1998]. Two kinds of semantics have been introduced, namely the class of weak and strong probabilistic models. The main result of this paper is a completeness theorem for the logic FP(L"n,L) w.r.t. both weak and strong models. We also present two extensions of FP(L"n,L): the first one is the logic FP(L"n,RPL), obtained by expanding the FP(L"n,L)-language with truth-constants for the rationals in [0,1], while the second extension is the logic FCP(L"n,L@P12) allowing to reason about conditional states.