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Probability of real-valued events: a logico-algebraic investigation

Projektbeschreibung

Neue algebraische Ansätze zur Beschreibung der Wahrscheinlichkeit von unscharfen Aussagen

In der Wahrscheinlichkeitstheorie unterscheiden sich reale Ereignisse von mathematischen Ereignissen – ihnen kann nur ein Wert von 0 oder 1 zugewiesen werden, je nachdem, ob sie zu einem bestimmten Zeitpunkt verifiziert werden oder nicht. Logisch gesehen sind sie entweder wahr oder falsch. Das EU-finanzierte Projekt PROREAL will algebraische Semantik-Werkzeuge zur Untersuchung der unscharfen Logik einsetzen. Anstelle der üblichen Kategorien „wahr oder falsch“ ordnet letztere „Wahrheitsgrade“ zu, um reelle deklarative, jedoch vage Anweisungen zu behandeln. Der Wahrheitswert dieser Anweisungen kann irgendwo im Bereich zwischen vollständig wahr und vollständig falsch liegen. Besonderes Augenmerk wird auf die Untersuchung von unscharfen Verknüpfungen gelegt, die auf T-Normen basieren.

Ziel

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.

Koordinator

AGENCIA ESTATAL CONSEJO SUPERIOR DE INVESTIGACIONES CIENTIFICAS
Netto-EU-Beitrag
€ 160 932,48
Adresse
CALLE SERRANO 117
28006 Madrid
Spanien

Auf der Karte ansehen

Region
Comunidad de Madrid Comunidad de Madrid Madrid
Aktivitätstyp
Research Organisations
Links
Gesamtkosten
€ 160 932,48