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For a more in-depth book, see the wikibook Formal Logic. This chapter for AI Logic is aimed to be an introduction of specific elements of Logic that pertain to AI only.
What is logic? The philosophical definition is that logic is a description of how one should think. In the context of AI, logic is "formal," which means it resembles math in its clarity and lack of ambiguity.
There are lots of different kinds of logics out there (temporal logics, ethical logics, etc.). But when most people, particularly in AI, refer to logic, they are talking about propositional logic or the more complex predicate logic. So although you can make a logic with any kind of rules and symbols you want, what most people mean when they refer to logic are the widely-accepted rules and notations commonly taught in introductory logic courses.
Next we will discuss the basics of representation of propositions in logic.
Next: Representational perspectives