Logic: Science of
reasoning. Here is a fairly
rapid and clear  I hope  introduction to standard logic using lemmas in the
Philosophical Dictionary:
There is very much more to logic. One setback for those interested in it
qua
science of
reasoning  such as psychologists, lawyers,
philosophers  is that much of modern logic looks mathematical, and
considerable parts are quite technical. This mostly cannot be
helped, in as much as mathematical notations and/or mathematical methods are
extraordinarily helpful, if only to abbreviate in a clear way patterns and
schemas of reasoning that would be difficult to treat as clearly, precisely
and fully in other ways. And the basics of
Propositional Logic,
First Order Logic, and
Set Theory should be known to anyone with
a serious intererst in philosophy (or mathematics or indeed science). 
See also: Basic Logic,
Classical Propositional Logic,
Entailment,
Extended Propositional Logic,
First Order Logic, Inference, Higher
Order Logic,
Logic Notation,
Logical terms,
Mathematical Logic, Modal Logic,
Natural Deduction,
Propositional Logic, Rules of Inference
Literature: Logic Books
Adams, Beth, Bernays, Bochenski, Boole, Boolos, Boolos & Jeffrey, Benaceraff &
Putnam, Carnap, Cartwright, Curry, Gentzen, Hamilton, Hasenjäger, Hilbert & Bernays,
Gödel, Grize, Hodges, Hooker, Kneale, C.I. Lewis, D. Lewis, Mal'cev,
Montague, Naimark, Quine, Schütte, Shoenfield, Slupecki & Borkowski,
Smullyan, Sneed, Stegmüller, Stoll, Tarski, Tennant, Waerden, Wang,
Weinberg, Whitehead & Russell, Zinoviev
