Erratum to: Conditional states and independence in D-posets

We continue our studies of the foundation of probability theory using elementary category theory. We propose a classification scheme of probability domains in terms of cogenerators and their algebraic and topological properties and use the scheme to describe the transition from classical to fuzzy probability. We show that Łukasiewicz tribes form a category of natural probability domains in which σ -fields of sets are "minimal" and measurable [0, 1]-valued functions are "maximal" objects. The maximal objects form an epireflective subcategory in which both the classical and fuzzy probability can be modelled. This leads to a better understanding of the transition.

show abstract

“…In view of [19,22], and [5], it might be interesting to study conditioning and conditional probability for ID-posets with products.…”

Section: Discussionmentioning

confidence: 99%

On Probability Domains II

Frič

Papčo

2011

Int J Theor Phys

View full text Add to dashboard Cite

show abstract

“…. ), an additional binary operation "product" has been studied primarily in connection with joint observables, stochastic independence, conditional expectation, and conditional probability, e.g., in [7], [8], [10], [25], [26], [28], [30], [31], [39], [40], [43]. It is known [31], [40] that in a full Lukasiewicz tribe the "product" reduces to the usual pointwise product of functions.…”

Section: P(a × B) P(a) P(b)mentioning

confidence: 99%

Real Functions in Stochastic Dependence

Babicová

Frič

2019

Tatra Mountains Mathematical Publications

View full text Add to dashboard Cite

In a fuzzified probability theory, random events are modeled by measurable functions into [0,1] and probability measures are replaced with probability integrals. The transition from Boolean two-valued logic to Lukasiewicz multivalued logic results in an upgraded probability theory in which we define and study asymmetrical stochastic dependence/independence and conditional probability based on stochastic channels and joint experiments so that the classical constructions follow as particular cases. Elementary categorical methods enable us to put the two theories into a perspective.

show abstract

Erratum to: Conditional states and independence in D-posets

Cited by 2 publications

References 0 publications

On Probability Domains II

On Probability Domains II

Real Functions in Stochastic Dependence

Contact Info

Product

Resources

About