Logic

Logic is the systematic study of valid inference, reasoning, and the principles that determine when a conclusion follows necessarily from given premises.  Logic arguments are analyzed not by their empirical content but by their form or structure.  An inference is considered valid if, by virtue of its logical form alone, it is impossible for the premises to be true while the conclusion is false.  This distinguishes logic from empirical sciences, as its truths are established through formal proof rather than observation or experimentation.

Overall, logic as a formal science is characterized by its concern with abstract structures of reasoning, its reliance on formal symbolic methods, and its aim to establish universally valid principles of inference independent of specific subject matter.

Logic Branches 

Formal Logic  -  The study of valid inference using abstract symbols, axioms, and rules, independent of specific content, it includes sub-areas such as propositional logic (dealing with statements and connectives like and, or, not) and predicate logic (incorporating quantifiers and relations).
Informal Logic  -  The analysis of arguments in natural language, focusing on everyday reasoning, rhetoric, fallacies, and practical evaluation rather than strict symbolic form.
Deductive Logic  -  Concerned with arguments where the conclusion necessarily follows from the premises if they are true, emphasizing validity and soundness.
Inductive Logic  -  Study of arguments where premises provide probable but not certain support for the conclusion, often used in scientific reasoning and generalization from evidence.
Mathematical Logic  -  Including subfields such as proof theory, model theory, set theory, and recursion theory, it overlaps heavily with formal logic and mathematics.
Modal Logic  -  Dealing with notions of necessity, possibility, and other modalities (e.g., "must" or "can").
Non-Classical Logics  -  Various systems that deviate from classical assumptions, including intuitionistic logic, fuzzy logic, paraconsistent logic, and many-valued logics.