Predicate Calculus as a Language for representing Knowledge
Conceptualizations
The steps of representing the knowledge are as follows,
- The initial step is to represent the knowledge known by conceptualizing it in the form of objects, functions and relation. We can imagine any kind of objects which depends up on person who imagines.
- The objects, functions and relations are next expressed in the form of predicate-calculus expressions.
- Next we develop wffs that are satisfied by our conceptualized world.
- The conceptualizations must be grounded, if the designed agents must communicate with actual world i.e., at least some of the truth values of atoms that are present in the knowledge base have to be evaluated from the noticeable mechanisms in the world. These act as primitive or perceptual atoms.
- The truth values of other atoms are derived from the primitive atoms.
- The overall structure must conclude a relevant result in the world in which the robot lives.
- Examples: Consider an example of delivering a courier in an office building.
- The courier may be some object denoted by courier(x). It is delivered by an agent.
- If it is in a room y, denoted by In(x, y).
- These courier(x) and In(x, y) are relation constants.
- To represent an object which is smaller than other we use Smaller(x, y) which is a relation constant.
- Now we use predicate calculus to express the statements about the world of the robot(agent),
- 1) "All of the couriers in room 2 are smaller in size than any of the couriers in room 20".
- (∀x, y) {[Courier(x) ∧ Courier(y) ∧ Inroom(x, 2) A Inroom(y, 20)] ⊃ Smaller (x, y)}.
- 2) "Every courier in room 2 is smaller than one of the packages in room 5".
- It is little ambiguous statement. It can be represented as,
- (∃y) (∀x) {[Courier(x) ∧ Courier(y) ∧ Inroom(x, 2) ∧ Inroom(y, 5)] ⊃ Smaller (x, .Y)}.
- (or)
- (∀x) (∃y) {[Courier(x) ∧ Courier(y) ∧ Inroom(x, 2) ∧ Inroom(y, 5)] ⊃ Smaller (x, y)}.
- The knowledge of time is required by the robot to know which courier has arrived first and which is next.
- So we use a relation constant Arrived(x, z) where the object is denoted by x and time is denoted by z.
- The predicate-calculus expression can be written as,
- (∃z1, z2) [Arrived(A, z1) ∧ Arrived(B, z2) ∧ Before(z1, z2)]
