lambda calculus

http://www.kyriakides.net/CBCL/references/Papers/barendregt94introduction.pdf

first order predicate logic : http://www.rbjones.com/rbjpub/logic/log019.htm
http://mathworld.wolfram.com/Predicate.html
http://mathworld.wolfram.com/Term.html
http://mathworld.wolfram.com/AtomicStatement.html
http://mathworld.wolfram.com/Sentence.html
http://mathworld.wolfram.com/SententialFormula.html
http://mathworld.wolfram.com/FreeVariable.html

http://mathworld.wolfram.com/PropositionalCalculus.html
http://mathworld.wolfram.com/PredicateCalculus.html
predicate calculus = functional caculus = predicate logic
http://mathworld.wolfram.com/First-OrderLogic.html