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First Order Predicate Logic

First Order Logic in AI​

  • Also known as Predicate Logic or First order predicate logic
  • First order logic is a powerful language that develops information about the objects in a more easy way and can also express the relationship between those objects
  • First order logic is an extension to propositional logic
  • First order logic is sufficiently expressive to represent the natural language statements in a concise way
  • Like natural language, it doesn't only assume that the world contains facts like propositional logic but also assumes objects, relations, function
  • As a natural language, it also has two main parts syntax & semantics

Inference Rules​

1. Universal Generalisation​

  • It is a valid inference rule which states that if premise P(c) is true for any arbitrary element c in the universe of discourse, then we can have a conclusion as ∀ x P(x)
  • This rule can be used if we want to show that every element has a similar property
  • Representation:
    P(c)
= ----------
   ∀ x P(x)

2. Universal Instantiation​

  • Also called universal elimination or UI is a valid inference rule. It can be applied multiple times to add new sentences
  • As per UI, we can infer any sentence obtained by substituting a ground term for the variable
  • It states that we can infer any sentence P(c) by substituting a ground term c (a constant within domain x) from ∀ x P(x) for any object in the universe of discourse
  • Representation:
   ∀ x P(x)
= ----------
     P(c)