Implicative normal form, Computer Engineering

Implicative normal form:

Thus the sentence is now in CNF. In Fact for simplification can take place by removing duplicate literals and dropping any clause that contains both A and ¬A where one will be true because the clause is always true. However in the conjunction of clauses we want everything to be true than we can drop it. Furthermore there is an optional final step that takes it to Kowalski normal form called as implicative normal form (INF) too aS: 

Although by reintroduce implication by gathering up all the negative literals in the negated ones and forming them in their conjunction N thus taking the disjunction P of the positive literals so forming the logically equivalent clause N  →P. 

There is example for understand: just Converting to CNF. Here we will work through a simple propositional example like: 

(B ? (A ^ C)) → (B?  ¬ A) 

So there is this first thing to do is remove the implication sign as: 

¬ (B?  (A ^ C)) ? (B ? ¬ A)  

Now we use De Morgan's laws just to move our negation sign from the outside to the inside of brackets as: 

(¬ B  ^ ¬ (A^  C)) ? (B ? ¬ A) 

So now we can use De Morgan's law again just to move a negation sign inwards as: 

(¬ B^  ( ¬ A?  ¬ C)) ? (B  ?¬ A) 

And now next we distribute  over  as follows: 

(¬ B ? (B ? ¬ A))  (( ¬ A ? ¬ C) ? (B ? ¬ A)) 

There if we flatten our disjunctions so than we get our sentence into CNF form. Notice here the conjunction of disjunctions: 

(¬ B?  B ? ¬ A)^  ( ¬ A ? ¬ C ?  B ? ¬ A) 

Now the finally first conjunction has ¬B and B, then the whole conjunction must be true that we can remove the duplicate ¬A in the second conjunction also as: 

True ^  (¬ A ? ¬ C ? B) 

So however the truth of this sentence is only dependent on the second conjunct. Then if it is false, the complete thing is false hence it is true for the whole thing is true. Thus we can remove the True through giving us a single clause into its final conjunctive normal form as: 

¬ A ? ¬ C ?B 

There if we want Kowalski normal form we take one more step to get as: 

(A ^ C) → B

Posted Date: 1/11/2013 6:19:18 AM | Location : United States

Related Discussions:- Implicative normal form, Assignment Help, Ask Question on Implicative normal form, Get Answer, Expert's Help, Implicative normal form Discussions

Write discussion on Implicative normal form
Your posts are moderated
Related Questions
What are the types of data warehouses? Various types of data warehouses are illustrated below: a) Financial Data Warehouses b) Insurance Data Warehouses c) Human Resou

Dynamic partitioning: To rise above from difficulties with fixed partitioning, partitioning can be done dynamically, which called dynamic partitioning. Having it, the primary

Real time clock A real-time clock keeps the time in real time - i.e. in hours and minutes. Software for the real-time clock comprises an interrupt service procedure which is c

Q. Logic diagrams for same Boolean expression? The expression F can be simplified using Boolean algebra. The logic diagram of simplified expression is drawn in fig (b)

State in brief about the proxy server A proxy server also helps a lot since it hides the real IP addresses of users requesting resources outside the firewall. Finally, the

Define register file. All general purpose registers are combined into a one block called the register file.

Which loader is executed when a system is first turned on or restarted? Ans. Bootstrap loader executed while a system is first turned on or restarted.

What is the significance of XML in EDI and electronic commerce?   XML has been defined as lightweight SGML XML shows great promise for its inherent ability to permit a " doc

Q. Rank the list elements in terms of distance? Rank the list elements in terms of distance from each to last element in given linear linked list. A parallel algorithm for t

A doubly linked list is like a linked list except that each node has a pointer both to the next node in the list and to the previous node in the list. There are also pointers to th