Formal logic is a means of expressing declarative knowledge.
Deduction is the mechanism used to infer more facts from such knowledge. Theorem provers are systems that automate this process to various degrees. Deduction is also part of several AI systems and database systems, amongst others. Decision procedures, on the other hand, are specialized theorem proving methods designed for subclass of formulas from a particular domain. These are faster, predictable and more efficient than general purpose deduction systems.