Implicative normal form, Computer Engineering

Assignment Help:

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


Related Discussions:- Implicative normal form

Functionality of hypethread processor, Hyper-threading works by duplicating...

Hyper-threading works by duplicating those parts of processor which store architectural state but not duplicating main execution resources. This permits a Hyper-threading equipped

Compare single bus structure and multiple bus structure, Compare single bus...

Compare single bus structure and multiple bus structure? A system that having only one bus(i.e only one transfer at a time) is known as a single bus structure. A system is know

Explain the storage class static, Explain the Storage Class Static Th...

Explain the Storage Class Static The Storage Class Static : Static declarations have two important and distinct uses. The more elementary use is to allow a local variable to

What is virtual memory, What is virtual memory? Virtual memory is a met...

What is virtual memory? Virtual memory is a method used in some large computer systems that allow the user to construct program as by a large memory space were available, equal

Responsibilities of objects, The Transaction object is responsible for read...

The Transaction object is responsible for reading the transaction file, finding the relevant account in the array of customers and applying the transaction. To find the relevant ac

What is relational database, What is relational database? Relational da...

What is relational database? Relational database has data that is perceived as tables. A relational DBMS manages tables of data and associated structures that enhances the func

What is home banking, Home Banking: E-commerce is used in Home Banking ...

Home Banking: E-commerce is used in Home Banking as single call or single click. Online banking (Internet banking) is a term used for performing transactions, payments etc. ove

How transmission bridges help in satisfying the connectivity, How do tra...

How do transmission bridges help in satisfying the connectivity? A usual transmission bridge is demonstrated in figure. The series capacitance and the shunt inductances of

What are the major systems of a telecommunication network, What are the maj...

What are the major systems of a telecommunication network? The main systems of any telecommunication network may contain the following main systems: a. Subscriber end instr

Introduction to the sorted arraylist, Consider  a  collection  class  that ...

Consider  a  collection  class  that  is  similar  to  the ArrayList  class,  except  that  elements  are sorted in a certain order. We will call this class SortedArrayList. This c

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd