Translating this into a matrix gives the following tensor for P: To compute the truth value of 'John is a mathematician', we perform predicate-argument application as tensor contraction (matrix-vector multiplication, in this case): Likewise for 'Tom is a mathematician': Model theory for predicate calculus represents any n-ary relation R, such as a verb, as the set M R of n-tuples of elements from D for which R holds.
such relations can be viewed as functions f R : D n → B where: We can represent the boolean function for such a relation R as a tensor As was the case for predicates, the weights for relational tensors are defined in terms of the set modelling the relation: c T R 1α 1 ...α n is 1 if the tuple (x, .