The following are the main points you should have learned from this chapter:

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  In domains characterized by individuals and relations, constants denoting individuals and predicate symbols denoting relations can be reasoned with to determine what is true in the domain.

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  Datalog is a logical language with constants, universally quantified variables, relations, and rules.

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  Substitutions are used to make instances of atoms and rules. Unification makes atoms identical for use in proofs.

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  Function symbols are used to denote a possibly infinite set of individuals described in terms of other individuals. Function symbols can be used to build data structures.

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  It is possible to use definite clauses to represent natural language grammars.

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  Equality between terms means that the terms denote the same individual.

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  Clark’s completion can be used to define the semantics of negation as failure under the complete knowledge assumption.