A logic is a system for expressing statements that have truth values, or questions whose answers have truth values; and for deriving new such statements from sets of such statements.
See the entry on Inference for discussion of different types of reasoning that may be formalized using Logic.
Logic and AGI
It is controversial whether a logic should explicitly be part of the design of an AGI System, or whether logic should be thought of as emergent (Emergence) from lower-level aspects of an AGI System.
And, among those to believe logic should be part of an AGI design, there is not much agreement on what kind of logic it should be.
See also Predicate Logic, Term Logic, Crisp Logic, Uncertain Logic, Temporal Logic