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R. B. Jones: First Order Predicate Logic
Great introduction to basic ideas in predicate logic. Conveys fundamental ideas without using technical notation. A good place to start.
Stanford University
Stanford Ency. Of Philosophy: Logical Construction
This site from the Stanford Encyclopedia of Philosophy discusses Bertrand Russell's notion of "logical construction" and its influence in the development of logical positivism. Mostly historical in orientation and is accessible to those...