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

What is multiprogramming, Multiprogramming is a rapid switching of the CPU ...

Multiprogramming is a rapid switching of the CPU back and forth among processes.

Which things should microprocessor validate, Q. Which things should micropr...

Q. Which things should microprocessor validate? A microprocessor should validate: Powerful addressing modes More addressing capability More throughput Po

Device drivers in unix, Device Drivers in UNIX, MS-DOS and Windows System ...

Device Drivers in UNIX, MS-DOS and Windows System Though device drivers are in effect add-on modules they are however considered to be part of system because they are closely i

What are micrographics, What are micrographics? A micrographic is an im...

What are micrographics? A micrographic is an image or photographic reproduction of an object which is then changed to film. Micrographics are frequently used for permanent reco

Which scheduling in cpu is allocate for least cpu-burst time, The schedulin...

The scheduling in which CPU is allocated to the process with least CPU-burst time is called? Ans. Shortest job first Scheduling wherein CPU is allocated to the process with lea

Define the edge-triggered flip-flops, Define the Edge-Triggered Flip-flops?...

Define the Edge-Triggered Flip-flops? An edge-triggered flip-flop changes states either at the negative edge (falling edge) or at the positive edge (rising edge) of the clock p

Why pointer variable to a function as an argument, Why pointer variable som...

Why pointer variable sometimes desirable to pass a pointer to a function as an argument? Frequently, a called function needs to make changes to objects declared in the calling

What is the cih, CIH, also known  as Chernobyl or Spacefiller, is a Microso...

CIH, also known  as Chernobyl or Spacefiller, is a Microsoft Windows computer virus which first emerged in 1998. It is one of the most damaging viruses, overwriting critical inform

Explain about threads model - programming model, Q. Explain about Threads M...

Q. Explain about Threads Model - programming model? In this model a single process can have many as well as concurrent execution paths. The main program is planned to run by na

State some of the uses of ms access, MS Access provides a vast range of fun...

MS Access provides a vast range of functions some of them are ? It is used by small business, departments of large corporations, and by amateurs to make applications on their d

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