Project description
New algebraic approaches to describe the probability of fuzzy statements
In probability theory, real events differ from mathematical events – they can only be assigned a value of 0 or 1 depending on whether they are verified at some point in time or not. In logical terms, they are either true or false. The EU-funded PROREAL project plans to use algebraic semantics tools to study fuzzy logic, which assigns 'degrees of truth' rather than the usual 'true or false' to treat real declarative statements that are vague. The truth value of these statements may range between completely true and completely false. Special focus will be placed on studying fuzzy connectives based on t-norms.
Objective
The goal of this project is to develop logico-algebraic and measure theoretical techniques to study the probability theory of real-valued events. The classical approach to probability only allows the study of events that at some moment will either be verified or not. In more logical terms, they will become either true or false. In order to be able to treat the intrinsic vagueness of real-life declarative statements, we will study events whose truth-value can be intermediate, varying in the real unit interval (where 0 represents absolute falseness and 1 absolute truth). Our focus will be on the state theory, i.e. probability theory, of continuous (or more generally left-continuous) t-norm based fuzzy logics. The study will be carried out by the point of view of the algebraic semantics of such logics, which has proven to be extremely fruitful in recent years, showing interesting connections to measure theory. Indeed, in different fuzzy logics it is possible to introduce a notion of probability map on the algebras of formulas in such a way that it axiomatizes the Lebesgue integral of the formulas (which, thanks to universal algebraic results, can be seen as real-valued functions). As a most challenging goal, we will investigate the minimal properties for a logic to allow the axiomatization of a probability theory axiomatizing the Lebesgue integral of formulas. Moreover, as in recent years the artificial intelligence perspective is emerging, we will develop logical frameworks for many-valued probabilistic reasoning, and study the satisfiability of the probabilistic assertions for such logics. The study will strongly ground on preliminary work of research the fellow has conducted in recent years. Moreover, it will benefit from the broad experience of the supervisor as a leading researcher in the field, and of the high level, multidisciplinary environment of the hosting institute.
Fields of science
Keywords
Programme(s)
Funding Scheme
MSCA-IF - Marie Skłodowska-Curie Individual Fellowships (IF)Coordinator
28006 Madrid
Spain