Search results for " Conjunction and disjunction of conditionals"

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Canonical Extensions of Conditional Probabilities and Compound Conditionals

2022

In this paper we show that the probability of conjunctions and disjunctions of conditionals in a recently introduced framework of Boolean algebras of conditionals are in full agreement with the corresponding operations of conditionals as defined in the approach developed by two of the authors to conditionals as three-valued objects, with betting-based semantics, and specified as suitable random quantities. We do this by first proving that the canonical extension of a full conditional probability on a finite algebra of events to the corresponding algebra of conditionals is compatible with taking subalgebras of events.

Settore MAT/06 - Probabilita' E Statistica MatematicaBoolean algebras of conditionals Conditional probability Conjunction and disjunction of conditionals
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Algebraic aspects and coherence conditions for conjoined and disjoined conditionals

2019

We deepen the study of conjoined and disjoined conditional events in the setting of coherence. These objects, differently from other approaches, are defined in the framework of conditional random quantities. We show that some well known properties, valid in the case of unconditional events, still hold in our approach to logical operations among conditional events. In particular we prove a decomposition formula and a related additive property. Then, we introduce the set of conditional constituents generated by $n$ conditional events and we show that they satisfy the basic properties valid in the case of unconditional events. We obtain a generalized inclusion-exclusion formula and we prove a …

Pure mathematicsProperty (philosophy)Settore MAT/06 - Probabilita' E Statistica MatematicaDistributivityApplied MathematicsProbability (math.PR)02 engineering and technologyCoherence (statistics)Characterization (mathematics)Settore MAT/01 - Logica Matematica60Axx 03B48Theoretical Computer ScienceCoherenceConditional random quantities Conjunction and disjunction of conditionals Decomposition formula Conditional constituents Inclusion-exclusion formulaSet (abstract data type)Artificial Intelligence020204 information systemsFOS: Mathematics0202 electrical engineering electronic engineering information engineering020201 artificial intelligence & image processingInclusion–exclusion principleAlgebraic numberMathematics - ProbabilitySoftwareCounterexampleMathematics
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