Deductive Logic

The most prominent form of deductive logic is “classical” or “standard” or “Frege–Russell” logic (Wikipedia). Classical logic is very influential and has been extensively studied, but is often dissatisfying on an intuitive level:

• Principle of explosion: Any conclusion can be derived if you have contradictory premises
  
• Raven paradox:Observing that an apple is both green and not a raven constitutes some evidence that all ravens are black.
  

Alternative logics aim to address these kinds of shortcomings, e.g. relevance logic.