6533b831fe1ef96bd12983cc

RESEARCH PRODUCT

Probabilistic Interpretations of Predicates

Janusz Czelakowski

subject

Discrete mathematicsUnary operationComputer Science::Logic in Computer ScienceCumulative distribution functionClassical logicProbabilistic logicRandom variableŁukasiewicz logicDe Morgan algebraMathematicsProbability measure

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 \(\mathbb {R}^m\). The paper is mainly concerned with probabilistic interpretations of unary predicates in the algebra of cumulative distribution functions defined on \(\mathbb {R}\). 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
https://doi.org/10.1007/978-3-319-29300-4_13