>>509998297>practical ability to use logic.No, not really.
IQ is a rough estimate of fluid-g, which is a statistical residual discovered when comparing aggregate batteries of general cognitive assessment, i.e. matrix reasoning, working memory, digit span, symbolic input (symbols and the estimate of their meaning, important for understanding the rules of syntax), processing speed, and a few others.
These different facets of "intelligence" have a correlation between each other, and when that correlate is isolated (as a residual) then a new factor appears, dubbed fluid-g.
IQ tests have a ratio of correlation with fluid-g, just as nearly every other task which requires multitasking, translating, pattern recognition, or memory does. For example, the SAT (standard US high school benchmark for college readiness) has a correlation with fluid-g of approximately 0.77. Different sub components of IQ (POI, WMI, VCI) all have different correlate values as well, but they're typically as high as psychometricians can ensure (WMI is a 0.9, for example, and POI is ~0.95).
Logic is more like a skill than the measure of a persons fluid-g. It could safely be assumed that most people who are skilled in logic probably have fairly high IQ, but it's feasible that a person with average IQ could learn how to apply syllogisms and other systems of logic sufficiently to be considered "highly logical". Not every coder has a sky-high IQ, but nearly all of them have learned a skill (programming) which requires routine use of logic.
The estimates I listed above assume that eminent politicians likely exist in a cognitively competitive environment similarly to academics. There are winners and losers, and winners usually are capable of analyzing the playing field and determining "good plays" in their respective fields, avoiding "bad plays" and formalizing a system of "plays" as a comprehensive meta-game sufficiently to "win" political power with regularity over large spans of time.
