Predicates can have calculus {predicate calculus, logic} {calculus of relations}.
laws
Predicate calculus uses contradiction law, excluded-middle law, detachment rule, tautology, addition, association, permutation, and summation. AND, NOT, OR, ALL, SOME, and EQUIVALENT have meaning.
variables
Predicates can have variables. Predicate can have more than one variable {n-place predicate}.
first-order
Variable can be terms {first-order predicate}. For first-order predicates, constants are proper nouns, and variables are pronouns or common nouns {term, predicate}.
First-order predicate calculus is complete.
first-order: quantifiers
First-order predicate calculus {functional calculus} {first-order logic} {restricted predicate calculus} can have quantifiers. Quantifiers can affect variables {bound variable} or not {free variable}.
If A implies B, if A and B have bound variables, and if B, then every A value has a B value {generalization rule} {rule of generalization}. If A implies B, if A and B have bound variables, and if B implies A, then an A value exists {specification rule} {rule of specification}.
second-order
Variables can be predicates {second-order predicate}.
second-order: recursion
Predicates can contain themselves {recursive predicate}. Recursive predicates can assume existence of a set that does not actually exist and so have contradiction.
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Date Modified: 2022.0224