More generally, a logic is any set of '''rules for forming sentences (the logic's syntax)''' together with '''rules for assigning truth values to them (the logic's semantics)'''. Normally it includes a (possibly empty) set of '''types  (also called sorts)''', which represent the different kinds of objects that the theory discusses (typical examples might be sets, numbers, or sets of numbers). In addition it specifies particular quantifiers, connectives, and variables. Particular theories in the logic can then add relations and functions to fully specify a logical language.

http://planetmath.org/encyclopedia/Logic.html