Approximate anytime inference: Half an answer on time is better than a perfect answer too late

Many branches of computer science rely on logical formalisms as their foundations. Logic provides a very solid foundation on which to build new results: after 2500 years of research, logic provides us with a strong set of theoretical notions: model theory, proof theory, completeness, correctness; there exists a well established body of knowledge concerning properties such expressiveness, decidability, complexity results, etc; and, in particular since the very fruitful encounter with Computer Science in the last half century, we have at our disposal a rich battery of algorithms for implementing logical formalisms on a computer: resolution, tableau-reasoning, local-search methods, etc. However, these strong foundations also come with a disadvantage: Logic aims to mode perfect reasoners under ideal circumstances. Logic does not tell us how to deal with mistakes during the deduction process; logical formalisms assume unlimited resources and fully available and fully correct knowledge. Logic does not study what it means to have “half a proof”, or what it would mean for a theorem to be “almost true”. As a result of all this, the deduction models that logic provides us with are crisp, abrupt, inefficient: