About: Fréchet inequalities     Goto   Sponge   NotDistinct   Permalink

An Entity of Type : yago:WikicatProbabilisticInequalities, within Data Space : dbpedia.demo.openlinksw.com associated with source document(s)
QRcode icon
http://dbpedia.demo.openlinksw.com/describe/?url=http%3A%2F%2Fdbpedia.org%2Fresource%2FFréchet_inequalities&invfp=IFP_OFF&sas=SAME_AS_OFF

In probabilistic logic, the Fréchet inequalities, also known as the Boole–Fréchet inequalities, are rules implicit in the work of George Boole and explicitly derived by Maurice Fréchet that govern the combination of probabilities about logical propositions or events logically linked together in conjunctions (AND operations) or disjunctions (OR operations) as in Boolean expressions or fault or event trees common in risk assessments, engineering design and artificial intelligence. These inequalities can be considered rules about how to bound calculations involving probabilities without assuming independence or, indeed, without making any dependence assumptions whatsoever. The Fréchet inequalities are closely related to the Boole–Bonferroni–Fréchet inequalities, and to Fréchet bounds.

AttributesValues
rdf:type
rdfs:label
  • Fréchet inequalities (en)
rdfs:comment
  • In probabilistic logic, the Fréchet inequalities, also known as the Boole–Fréchet inequalities, are rules implicit in the work of George Boole and explicitly derived by Maurice Fréchet that govern the combination of probabilities about logical propositions or events logically linked together in conjunctions (AND operations) or disjunctions (OR operations) as in Boolean expressions or fault or event trees common in risk assessments, engineering design and artificial intelligence. These inequalities can be considered rules about how to bound calculations involving probabilities without assuming independence or, indeed, without making any dependence assumptions whatsoever. The Fréchet inequalities are closely related to the Boole–Bonferroni–Fréchet inequalities, and to Fréchet bounds. (en)
dcterms:subject
Wikipage page ID
Wikipage revision ID
Link from a Wikipage to another Wikipage
sameAs
dbp:wikiPageUsesTemplate
has abstract
  • In probabilistic logic, the Fréchet inequalities, also known as the Boole–Fréchet inequalities, are rules implicit in the work of George Boole and explicitly derived by Maurice Fréchet that govern the combination of probabilities about logical propositions or events logically linked together in conjunctions (AND operations) or disjunctions (OR operations) as in Boolean expressions or fault or event trees common in risk assessments, engineering design and artificial intelligence. These inequalities can be considered rules about how to bound calculations involving probabilities without assuming independence or, indeed, without making any dependence assumptions whatsoever. The Fréchet inequalities are closely related to the Boole–Bonferroni–Fréchet inequalities, and to Fréchet bounds. If Ai are logical propositions or events, the Fréchet inequalities are * Probability of a logical conjunction * Probability of a logical disjunction where P denotes the probability of an event or proposition. In the case where there are only two events, say A and B, the inequalities reduce to * Probability of a logical conjunction * Probability of a logical disjunction The inequalities bound the probabilities of the two kinds of joint events given the probabilities of the individual events. For example, if A is "has lung cancer", and B is "has mesothelioma", then A & B is "has both lung cancer and mesothelioma", and A ∨ B is "has lung cancer or mesothelioma or both diseases", and the inequalities relate the risks of these events. Note that logical conjunctions are denoted in various ways in different fields, including AND, &, ∧ and graphical AND-gates. Logical disjunctions are likewise denoted in various ways, including OR, |, ∨, and graphical OR-gates. If events are taken to be sets rather than logical propositions, the set-theoretic versions of the Fréchet inequalities are * Probability of an intersection of events * Probability of a union of events (en)
gold:hypernym
prov:wasDerivedFrom
page length (characters) of wiki page
foaf:isPrimaryTopicOf
is Link from a Wikipage to another Wikipage of
is Wikipage redirect of
is notable ideas of
is notableIdea of
is foaf:primaryTopic of
Faceted Search & Find service v1.17_git139 as of Feb 29 2024


Alternative Linked Data Documents: ODE     Content Formats:   [cxml] [csv]     RDF   [text] [turtle] [ld+json] [rdf+json] [rdf+xml]     ODATA   [atom+xml] [odata+json]     Microdata   [microdata+json] [html]    About   
This material is Open Knowledge   W3C Semantic Web Technology [RDF Data] Valid XHTML + RDFa
OpenLink Virtuoso version 08.03.3330 as of Mar 19 2024, on Linux (x86_64-generic-linux-glibc212), Single-Server Edition (378 GB total memory, 67 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2024 OpenLink Software