Stratification (mathematics)
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Stratification has several usages in mathematics. In mathematical logic, stratification is any consistent assignment of numbers to predicate symbols guaranteeing that a unique formal interpretation of a logical theory exists. Specifically, for Horn clause theories, we say that such a theory is stratified if and only if there is a stratification assignment S that fulfills the following conditions: 1. If a predicate P is positively derived from a predicate Q, then the stratification number of P must be greater than or equal to the stratification number of Q, in short S(P) geq S(Q). 2. If a predi...
Stratification has several usages in mathematics. In mathematical logic, stratification is any consistent assignment of numbers to predicate symbols guaranteeing that a unique formal interpretation of a logical theory exists. Specifically, for Horn clause theories, we say that such a theory is stratified if and only if there is a stratification assignment S that fulfills the following conditions: 1. If a predicate P is positively derived from a predicate Q, then the stratification number of P must be greater than or equal to the stratification number of Q, in short S(P) geq S(Q). 2. If a predicate P is derived from a negated predicate Q, then the stratification number of P must be greater than the stratification number of Q, in short S(P) S(Q).
