How to use boolean logic without using native booleans in Java

BooleanLogic.java

interface Conditional {
    
    Boolean implies(Boolean b);
    
}

interface BiConditional {
    
    Boolean equalTo(Boolean b);
    
}

interface Disjunction {
    
    Boolean or(Boolean b);
    
}

interface Conjunction {
    
    Boolean and(Boolean b);
    
}

interface Negation {
    
    Boolean not();
    
}

public abstract class Boolean implements Conditional, BiConditional, Disjunction, Conjunction, Negation {
    
    public abstract Boolean implies(Boolean b);
    
    public abstract Boolean equalTo(Boolean b);
    
    public abstract Boolean or(Boolean b);
    
    public abstract Boolean and(Boolean b);
    
    public abstract Boolean not();
    
    public abstract String toString();
}

public class True extends Boolean {
    
    private static True instance;
    
    private True() {
        //
    }
    
    public static Boolean getInstance() {
		if (instance == null) {
			// Thread Safe. Might be costly operation in some case
			synchronized (True.class) {
				if (instance == null) {
					instance = new True();
				}
			}
		}
		
		return instance;
    }
    
    public Boolean implies(Boolean b) {
        return b;
    }
    
    public Boolean equalTo(Boolean b) {
        return b;
    }
    
    public Boolean or(Boolean b) {
        return this;   
    }
    
    public Boolean not() {
        return False.getInstance(); 
    }
    
    public Boolean and(Boolean b) {
        return b;
    }
    
    public String toString() {
        return "true";
    }
    
}

public class False extends Boolean {
    
    private static False instance;
    
    private False() {
        //
    }
    
    public static Boolean getInstance() {
		if (instance == null) {
			// Thread Safe. Might be costly operation in some case
			synchronized (False.class) {
				if (instance == null) {
					instance = new False();
				}
			}
		}
		
		return instance;
    }
    
    public Boolean implies(Boolean b) {
        return True.getInstance();
    }
    
    public Boolean equalTo(Boolean b) {
        return b.not();
    }
    
    public Boolean or(Boolean b) {
        return b;   
    }
    
    public Boolean not() {
        return True.getInstance();
    }
    
    public Boolean and(Boolean b) {
        return this;
    }
    
    public String toString() {
        return "false";
    }
    
}

public class Demo {
    
    public static void main(String[] args) {
        Boolean _false = False.getInstance();
        Boolean _true = True.getInstance();
        
        System.out.println("toString");
        System.out.println(_false.toString()); // "false"
        System.out.println(_true.toString()); // "true"
        
        System.out.println("Implication");
        System.out.println(_false.implies(_false).toString()); // "true"
        System.out.println(_false.implies(_true).toString()); // "true"
        System.out.println(_true.implies(_false).toString()); // "false"
        System.out.println(_true.implies(_true).toString()); // "true"
        
        System.out.println("Bi-Implication");
        System.out.println(_false.equalTo(_false).toString()); // "true"
        System.out.println(_false.equalTo(_true).toString()); // "false"
        System.out.println(_true.equalTo(_false).toString()); // "false"
        System.out.println(_true.equalTo(_true).toString()); // "true"
        
        System.out.println("Negation");
        System.out.println(_false.not().toString()); // "true" 
        System.out.println(_true.not().toString()); // "false"
        
        System.out.println("Disjunction");
        System.out.println(_false.or(_false).toString()); // "false"
        System.out.println(_false.or(_true).toString()); // "true"
        System.out.println(_true.or(_false).toString()); // "true"
        System.out.println(_true.or(_true).toString()); // "true"
        
        System.out.println("Conjunction");
        System.out.println(_false.and(_false).toString()); // "false"
        System.out.println(_false.and(_true).toString()); // "false"
        System.out.println(_true.and(_false).toString()); // "false"
        System.out.println(_true.and(_true).toString()); // "true"
        
    }
    
}