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PRODID:-//Grails iCalendar plugin//NONSGML Grails iCalendar plugin//EN
VERSION:2.0
CALSCALE:GREGORIAN
METHOD:PUBLISH
BEGIN:VEVENT
DTSTAMP:20260416T180343Z
DTSTART;TZID=America/New_York:20221201T140000
DTEND;TZID=America/New_York:20221201T143000
SUMMARY:Probability Spaces for First-Order Logic
UID:20260421T210027Z-iCalPlugin-Grails@philevents-web-f5d4878dd-x5n6c
TZID:America/New_York
LOCATION:Online\, Athens\, United States
DESCRIPTION:<p>Abstract: Probability for first-order languages has previously been studied from the perspective of Bayesian subjective probability (Hailperin) or abstract measure functions on sentences (Gaifman).&nbsp\; This paper defines standard probability spaces in the Kolmogorov style as a measure space (*O\, *F\, mu )\, where *O will be defined as a product space and mu() as a product of measures.. We show how to interpret 1^o formulas as extensions which are measurable sets. Modern probability spaces have been typically used with&nbsp\; propositional (Boolean) or set-theoretic expressions denoting events as elements of the sigma-field *F\, ie measurable subsets of the domain set *O. For 1^o expressions we define the domain as a product space of two sample types\, combining the two basic modes of sampling from a population\, viz\, sampling with replacement and without replacement. These spaces are an extension of cylindrical algebra (Monk) or polyadic algebra (Halmos). The constructed probability space is interpreted into first-order model theory\, by showing events in the probability space to be extensions of expressions in the 1^o language. Probability calculations are demonstrated for a variety of expressions\, some basic and some from contemporary research. One interesting conclusion is that Ramsey&rsquo\;s conjecture on conditional probability can be proved for quantified conditionals\, P[(x)(Ax&rarr\;Bx)] = P[(x)Bx | (x)Ax].</p>
ORGANIZER;CN=Aaron Meskin;CN=L. Brooke Rudow;CN=Lauren Bunch:
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