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Table 2 Modified Gödel number representation.

From: An ontology-based search engine for protein-protein interactions

Term Prime number Relation Modified Gödel Number
Term1 2   
Term2 3 R1: Term2 is a Term1 relation(is a) = 3 × 2 = 6
Term3 5 R2: Term3 is part of Term2 relation(part of) = 5 × 3 × 2 = 30
Term4 7 R3: Term4 is a Term2 relation(is a) = 7 × 3 × 2 = 42
  1. Each term is assigned a prime number instead of natural number, and each relation is denoted by a modified Gödel number, which is a multiplication of prime numbers representing the term and its ancestors in the ontology hierarchy. For example, relation R3 is denoted by 42, which has prime factors 2 (Term1, root node in the hierarchy), 3 (Term2), and 7 (Term3). Using this representation, relation R3 can be easily inferred by unique factorization of it into primes (Term1, Term2, and Term3).