Illustrate in detail about First-Order Logic andKnowledge Engineering in First-Order Logicwith suitable examples?

First-Order Logic (FOL):

First-Order Logic, also known as Predicate Logic or First-Order Predicate Calculus, is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. It goes beyond propositional logic by allowing quantified variables over non-logical objects and using them in the predicate position.

In FOL, sentences are made up of terms and predicates. Terms represent objects in the domain of discourse, while predicates represent relationships between these objects. For example, in the sentence "Socrates is a man", "Socrates" is a term and "is a man" is a predicate.

Quantifiers are also a key part of FOL. The two most common quantifiers are "for all" (∀) and "there exists" (∃). For example, the sentence "All men are mortal" can be represented in FOL as "∀x (Man(x) → Mortal(x))", where "x" is a variable representing an arbitrary object, "Man(x)" is a predicate representing the property of being a man, and "Mortal(x)" is a predicate representing the property of being mortal.

Knowledge Engineering in First-Order Logic:

Knowledge engineering in FOL involves representing knowledge in a formal, logical manner that can be used by automated reasoning systems. This involves defining the domain of discourse, the objects in that domain, the predicates that describe relationships between those objects, and the rules that govern those relationships.

For example, consider a simple domain involving people and their ages. We might define objects like "Alice" and "Bob", predicates like "is older than", and rules like "If person A is older than person B, and person B is older than person C, then person A is older than person C". This could be represented in FOL as follows:

1. Older(Alice, Bob).
2. Older(Bob, Charlie).
3. ∀x ∀y ∀z ((Older(x, y) ∧ Older(y, z)) → Older(x, z)).

This knowledge base can then be used by an automated reasoning system to infer new facts. For example, given the facts and rules above, the system could infer that "Alice is older than Charlie".