Universal instantiation and substitution

Universal Instantiation (UI) This rule says that any substitution instance of a proposition function can be validly deduced from a universal proposition. A universal proposition is true only when it has only true substitution instances.

What is universal instantiation give an example?

For example, the following argument can be proven correct using the Universal Instantiation:“No humans can fly. John Doe is human. Therefore John Doe can not fly.”

Example:

1. x [H(x) F(x)] Hypothesis
3. H(d) F(d) Universal instantiation on 1.
4. F(d) Modus ponens on 2 and 3.

What is universal instantiation rule?

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.

What is the difference between that universal instantiation and existential instantiation?

Universal instantiation takes note of the fact that if something is true of everything, then it must also be true of whatever particular thing is named by the constant c. Existential generalization takes note of the fact that if something is true of a particular constant c, then it’s at least true of something.

What is existential instantiation in AI?

In predicate logic, existential instantiation (also called existential elimination) is a rule of inference which says that, given a formula of the form , one may infer for a new constant symbol c.

What is universal generalization in philosophy?

A proposition generalizing over all things of a kind. In first-order logic, one with a universal quantifier having the rest of the formula within its scope. From: universal generalization in The Oxford Dictionary of Philosophy »

How do you prove universal quantifiers?

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What is universal elimination in artificial intelligence?

Universal instantiation is also called as universal elimination or UI is a valid inference rule. It can be applied multiple times to add new sentences. The new KB is logically equivalent to the previous KB. As per UI, we can infer any sentence obtained by substituting a ground term for the variable.

What is universal quantifier in math?

In mathematical logic, a universal quantification is a type of quantifier, a logical constant which is interpreted as “given any” or “for all”. It expresses that a predicate can be satisfied by every member of a domain of discourse.

What is first order logic in AI?

FOL is a mode of representation in Artificial Intelligence. It is an extension of PL. FOL represents natural language statements in a concise way. FOL is also called predicate logic. It is a powerful language used to develop information about an object and express the relationship between objects.