FunctionalProgramming
* where the value of an expression is computed, usually close to the lambda calculus.
* or to put it differently: where the fundamental operation is reduction (of applicative terms).
ImperativeProgramming
* where cells in some sort of memory are filled and overwritten with values. Inspired by the TuringMachine and curiously never mentioned in the above table (or to put it differently: where the fundamental operation is assignment.)
* Actually, this generalizes to the fundamental operation being communication. The common case is simply communication to a cell maintained by some memory service (you send either a 'set' or a 'get', or possibly an 'apply-function' as needed for atomic ops or fast XOR processing). The more general case can consist of sends and receives on a fully networked, distributed model.
* * (different author replying) Actually, this "generalization" sound much more like the ActorsModel, which is no where near ImperativeProgramming, actually the actor model is much more similar to FunctionalProgramming than it is to imperative programming.
LogicProgramming (and ConstraintProgramming)
* where a solution to a set of logic formulas is sought; very declarative and incorporating some sort of search strategy like backtracking.
* or to put it differently: where the fundamental operation is satisfaction of a predicate.
* ConstraintProgramming envelopes LogicProgramming, since any logic domain can be expressed in terms of a constraint system, but the inverse is not often easy to express (due to the more strictly typed variables in LogicProgramming). However, the fields are disparate enough to have been split into LogicProgramming, ConstraintProgramming, and ConstraintLogicProgramming. (ConstraintAndLogicProgramming). This sort of programming is also called 'DeclarativeProgramming', but the word 'declarative' is somewhat overloaded.
That's it! Everything else is built on one of these three paradigms (Functional, Imperative and Logic), while sometimes incorporating elements of the others.