Term Algebra - Herbrand Base

The signature σ of a language is a triple consisting of the alphabet of constants O, the function symbols F, and the predicates P. The Herbrand base of a signature σ consists of all ground atoms of σ: of all formulas of the form R(t1, …, tn), where t1, …, tn are terms containing no variables (i.e. elements of the Herbrand universe) and R is an n-ary relation symbol (i.e. predicate). In the case of logic with equality, it also contains all equations of the form t1=t2, where t1 and t2 contain no variables.

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