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**Topic under **Control Engineering

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__Short Desciption__:

Handbook of Logic in AI and Logic
Programming
Volume I: Logical Foundations
Chapter 4:
Deduction Systems Based on
Resolution

__Summary__:

A general theory of deduction systems is presented. The theory is
illustrated with deduction systems based on the resolution calculus,
in particular with clause graphs.
This theory distinguishes four constituents of a deduction system:
• the logic, which establishes a notion of semantic entailment;
• the calculus, whose rules of inference provide the syntactic
counterpart of entailment;
• the logical state transition system, which determines the rep-
resentation of formulae or sets of formulae together with their
interrelationships, and also may allow additional operations re-
ducing the search space;
• the control, which comprises the criteria used to choose the
most promising from among all applicable inference steps.
Much of the standard material on resolution is presented in this
framework. For the last two levels many alternatives are discussed.
Appropriately adjusted notions of soundness, completeness, conflu-
ence, and Noetherianness are introduced in order to characterize the
properties of particular deduction systems. For more complex deduc-
tion systems, where logical and topological phenomena interleave,
such properties can be far from obvious

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