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RESEARCH PRODUCT

On probabilistic interpretations of predicates

subject

random variableDe Morgan algebrapredicateconsequence operationcumulative distribution functionprobability space

description

In classical logic, any m-ary predicate is interpreted as an m-argument two-valued relation defined on a non-empty universe. In probability theory, m-ary predicates are interpreted as probability measures on the mth power of a probability space. m-ary probabilistic predicates are equivalently semantically characterized as m-dimensional cumulative distribution functions defined on Rm. The paper is mainly concerned with probabilistic interpretations of unary predicates in the algebra of cumulative distribution functions defined on R. This algebra, enriched with two constants, forms a bounded De Morgan algebra. Two logical systems based on the algebra of cumulative distributions are defined and their basic properties are isolated. Comparisons with the infinitely-valued Łukasiewicz logic and open problems are also discussed.

yearjournalcountryeditionlanguage
2016-01-01
10.1007/978-3-319-29300-4_13https://doi.org/10.1007/978-3-319-29300-4_13