Artificial Intelligence - Knowledge Engineering in FOL

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Knowledge engineering is the process of building a knowledge base. It creates a logical structure, facts, relationships, and rules that computers can grasp and think about.

What is Knowledge-Engineering?

Knowledge Engineering in First-Order Logic (FOL) involves encoding knowledge that is represented through objects, predicates, functions, and logical rules to enable AI systems to reason. It provides facts, axioms, and inference rules used to model complex relationships so machines can learn and make logical choices.

In this chapter, we will analyze how the knowledge engineering approach is applied in electronic circuits. This strategy works very well to develop custom-built knowledge bases for specific functions.

Steps of Knowledge Engineering in FOL

To build systems that can reason and make decisions, knowledge engineering in AI entails collecting, organizing, and processing knowledge. These processes, which result in the creation of intelligent applications, usually involve knowledge gathering, representation, and inference. Following is the diagram which represents steps in the knowledge engineering −

Identify the task

The first stage in the procedure is to define the task; in the case of a digital circuit, various reasoning tasks can be accomplished.

• Identify the task similar to PEAS (Performance measure, Environment, Actuators, Sensors) design.

• Knowledge engineer must describe the range of the question that the knowledge base will support.

• There are many reasoning tasks associated with digital circuits. At the highest level, we will examine the functionality circuit.

• For example, does the circuit in actually add properly? (circuit verification)

• What are the expected outputs for given inputs?

• At the second level we will examine circuit's structure.

• For example, what are all the gates connected to the first input terminal?

• Does the circuit contain feedback loops?

Gather Relevant Knowledge

We need to understand how gates interpret input signals.

• The circuit is made up of AND, OR, XOR, and NOT gates. AND, OR, and XOR have two inputs, while NOT only has one. Each gate has only one output, and circuits, like gates, have distinct input and output terminals.

• Irrelevant knowledge: Our study is unaffected by component characteristics such as size, shape, color, or cost.

Choose a Vocabulary

To accurately represent the digital circuit in First-Order Logic (FOL), we establish a structured language that includes gates, terminals, connections, and signal states. The key components are as follows −

• Gates and Types: Each gate is designated as an object (e.g., Gate(X1)) and given a type (Type(X1) = XOR). Circuits are similarly labeled (Circuit(1)).

• Terminals and connections: Terminals are defined using Terminal(x), with In(i, X1) and Out(i, X1) representing inputs and outputs, respectively. Connections are represented as Connected(Out(1, X1), In(1, X2).

• Signals and Values: Signals at terminals are represented by Signal(t), where 1 (ON) and 0 (OFF) indicate active or inactive states.

Encode general knowledge about the domain

These are all the axioms we need −

If two terminals are connected, then they have the same signal −

 t1, t2 Terminal (t1)  Terminal (t2)  Connect (t1, t2) → Signal (t1) = Signal (2)

The signal at every terminal is either 1 or 0 −

 t Terminal (t) → Signal (t) = 1 Signal (t) = 0.

Connect is commutative −

 t1, t2 Connect(t1, t2) → Connect (t2, t1).

They are four types of gates and represented as below −

g Gate(g)  r = Type(g) → r = OR r = AND r = XOR r = NOT.

AND gate's output is 0 if and only if any of its input is 0 −

g Gate(g)  Type(g) = AND → Signal (Out(1, g))= 0  n Signal (In(n, g))= 0.

An OR gate's output is 1 if and only if any of its input is 1 −

 g Gate(g)  Type(g) = OR → Signal (Out(1, g))= 1  n Signal (In(n, g))= 1

An XOR gate's output is 1 if and only if its inputs are different −

 g Gate(g)  Type(g) = XOR → Signal (Out(1, g)) = 1  Signal (In(1, g))  Signal (In(2, g)).

A NOT gate's output is different from it's input (negation) −

 g Gate(g)  Type(g) = NOT → Signal (In(1, g))  Signal (Out(1, g)).

The gates (except for NOT) have two inputs and one output.

 g Gate(g)  Type(g) = NOT → Arity(g, 1, 1) 
	 g Gate(g)  r =Type(g)  (r= AND r= OR r= XOR) → Arity(g, 2, 1).

All gates are logic circuits −

 g Gate(g) → Circuit (g).

Encode a description of the problem instance

To define Circuit C1, we classify its components and generate linkages between them. This means that we describe the circuit and its gates as atomic sentences in First Order Logic (FOL).

First, we categorize the circuit and its component gates.

Circuit (C1) Arity(C1, 3, 2)
Gate(X1) A Type(X1) = XOR
Gate(X2) A Type(X2) = XOR
Gate(A1) A Type(A1) = AND
Gate(A2) A Type(A2) = AND
Gate(01) A Type(01) = OR

Second, we represent the connections between gates −

For example, Connect(Out(1, X1), In(1, X2)) represents X1s output going into X2s input.

Pose queries to the inference procedure and get answers

In this phase, we will find all possible input combinations for all terminals in the adder circuit.

What input combinations make C1's first output to be 0 and its second output to be 1.This is a simple example of verification of circuits.

  i1, i2, i3 Signal (In(1, C1))=i1    Signal (In(2, C1)) = i2   Signal (In(3, C1))= i3  
 Signal (Out(1, C1)) = 0  Signal (Out(2, C1))=1 

This is a simple example of verification of circuits.

Debug the knowledge base

We can test the knowledge base with small faults and see improper behavior.

• For example, Failure to assert 1 0 may lead to wrong answers for any input save for particular ones like 000 and 110. Debugging through observing each gate's output helps pinpoint such faults.

To build a First-Order Logic (FOL) knowledge base, needs careful domain analysis, vocabulary choice, and axiom encoding to ensure that the logical results are correct.