Введение
Правило вывода в предикатной логике
In predicate logic, universal instantiation (UI; also called universal specification or universal elimination, and sometimes confused with dictum de omni) is a valid rule of inference from a truth about each member of a class of individuals to the truth about a particular individual of that class. It is generally given as a quantification rule for the universal quantifier but it can also be encoded in an axiom schema. It is one of the basic principles used in quantification theory. Example: "All dogs are mammals. Fido is a dog. Therefore Fido is a mammal." Formally, the rule as an axiom schema is given as
for every formula A and every term t, where is the result of substituting t for each free occurrence of x in A. is an instance of
And as a rule of inference it is
from infer
Irving Copi noted that universal instantiation " follows from variants of rules for 'natural deduction', which were devised independently by Gerhard Gentzen and Stanisław Jaśkowski in 1934."
В предикатной логике универсальное инстанцирование (UI; также называемое универсальной спецификацией или универсальным устранением, и иногда путают с dictum de omni) – это корректное правило вывода от истины о каждом элементе класса индивидов к истине об определенном индивиде этого класса. Оно обычно представляется как правило квантификации для универсального квантора, но также может быть закодировано в аксиоматической схеме. Это один из базовых принципов, используемых в теории квантификации. Пример: "Все собаки – млекопитающие. Фидо – собака. Следовательно, Фидо – млекопитающее". Формально правило как аксиоматическая схема задается следующим образом:
In predicate logic, universal instantiation (UI; also called universal specification or universal elimination, and sometimes confused with dictum de omni) is a valid rule of inference from a truth about each member of a class of individuals to the truth about a particular individual of that class. It is generally given as a quantification rule for the universal quantifier but it can also be encoded in an axiom schema. It is one of the basic principles used in quantification theory. Example: "All dogs are mammals. Fido is a dog. Therefore Fido is a mammal." Formally, the rule as an axiom schema is given as
for every formula A and every term t, where is the result of substituting t for each free occurrence of x in A. is an instance of
And as a rule of inference it is
from infer
Irving Copi noted that universal instantiation " follows from variants of rules for 'natural deduction', which were devised independently by Gerhard Gentzen and Stanisław Jaśkowski in 1934."
для любой формулы A и любого терма t, где – результат подстановки t вместо каждого свободного вхождения x в A. является инстанцией
In predicate logic, universal instantiation (UI; also called universal specification or universal elimination, and sometimes confused with dictum de omni) is a valid rule of inference from a truth about each member of a class of individuals to the truth about a particular individual of that class. It is generally given as a quantification rule for the universal quantifier but it can also be encoded in an axiom schema. It is one of the basic principles used in quantification theory. Example: "All dogs are mammals. Fido is a dog. Therefore Fido is a mammal." Formally, the rule as an axiom schema is given as
for every formula A and every term t, where is the result of substituting t for each free occurrence of x in A. is an instance of
And as a rule of inference it is
from infer
Irving Copi noted that universal instantiation " follows from variants of rules for 'natural deduction', which were devised independently by Gerhard Gentzen and Stanisław Jaśkowski in 1934."
А как правило вывода:
In predicate logic, universal instantiation (UI; also called universal specification or universal elimination, and sometimes confused with dictum de omni) is a valid rule of inference from a truth about each member of a class of individuals to the truth about a particular individual of that class. It is generally given as a quantification rule for the universal quantifier but it can also be encoded in an axiom schema. It is one of the basic principles used in quantification theory. Example: "All dogs are mammals. Fido is a dog. Therefore Fido is a mammal." Formally, the rule as an axiom schema is given as
for every formula A and every term t, where is the result of substituting t for each free occurrence of x in A. is an instance of
And as a rule of inference it is
from infer
Irving Copi noted that universal instantiation " follows from variants of rules for 'natural deduction', which were devised independently by Gerhard Gentzen and Stanisław Jaśkowski in 1934."
из следует
In predicate logic, universal instantiation (UI; also called universal specification or universal elimination, and sometimes confused with dictum de omni) is a valid rule of inference from a truth about each member of a class of individuals to the truth about a particular individual of that class. It is generally given as a quantification rule for the universal quantifier but it can also be encoded in an axiom schema. It is one of the basic principles used in quantification theory. Example: "All dogs are mammals. Fido is a dog. Therefore Fido is a mammal." Formally, the rule as an axiom schema is given as
for every formula A and every term t, where is the result of substituting t for each free occurrence of x in A. is an instance of
And as a rule of inference it is
from infer
Irving Copi noted that universal instantiation " follows from variants of rules for 'natural deduction', which were devised independently by Gerhard Gentzen and Stanisław Jaśkowski in 1934."
Ирвинг Копи отметил, что универсальное инстанцирование "вытекает из вариантов правил "естественного вывода", разработанных независимо друг от друга Герхардом Гентценом и Станиславом Яшковским в 1934 году".
In predicate logic, universal instantiation (UI; also called universal specification or universal elimination, and sometimes confused with dictum de omni) is a valid rule of inference from a truth about each member of a class of individuals to the truth about a particular individual of that class. It is generally given as a quantification rule for the universal quantifier but it can also be encoded in an axiom schema. It is one of the basic principles used in quantification theory. Example: "All dogs are mammals. Fido is a dog. Therefore Fido is a mammal." Formally, the rule as an axiom schema is given as
for every formula A and every term t, where is the result of substituting t for each free occurrence of x in A. is an instance of
And as a rule of inference it is
from infer
Irving Copi noted that universal instantiation " follows from variants of rules for 'natural deduction', which were devised independently by Gerhard Gentzen and Stanisław Jaśkowski in 1934."
Куин
Согласно Уилларду Ван Орман Куину, универсальная инстанциарность и экзистенциальная генерализация — это два аспекта единого принципа, поскольку вместо утверждения, что "∀x x = x" влечет "Сократ = Сократ", мы можем столь же корректно утверждать, что отрицание "Сократ ≠ Сократ" влечет "∃x x ≠ x". Принцип, лежащий в основе этих двух операций, представляет собой связь между квантификацией и сингулярными высказываниями, которые выступают в качестве их экземпляров. Однако это принцип лишь в переносном смысле. Он верен только в тех случаях, когда термин является именем и, кроме того, употребляется референциально.