Conjunctive normal form -artificial intelligence , Computer Engineering

Conjunctive Normal Form -artificial intelligence :

For the resolution law to determine two sentences, they should both be in a normalized format known as conjunctive normal form, which is generally cut to CNF. This is an unlucky name because the sentences themselves are made up of orders of disjunctions. It is implicitly understood that the whole knowledge base is a huge conjunction of the sentences, which is where conjunctive normal form haveits name. So, CNF is basically a conjunction of disjunctions. The disjunctions are made up of literals which may either be a predicate or the negation of a predicate (for propositional read a proposition or the negation of a proposition):

So, CNF sentences are of the form:

(p1p2 ∨      ...  ∨ pm)  (q1 ∨ q2 ∨ ...∨qn)∧  etc.

Where each pi and qj  is a truthful. Note that we call the disjunction of such truthful a Clause. As a concrete example,

Likes (George, X) ∨ likes (tony, George)∨¬ is mad(Maggie)

Is in conjunctive normal form, but:

Likes (George, X) ∨ likes (tony, George) -> ¬ is mad (Maggie) ∧ is mad (tony) is not in CNF.

The following eight-stage method converts any sentence into CNF:

1. remove arrow connectives by rewriting with

P <-> Q  => (P ->Q) ∧(Q ->P)

P<-> Q  =>   ¬P ∨ Q

2.   Move ¬ inwards using De Morgan's laws (inc. quantifier versions) and double negation:

¬ (P ∨ Q)   =>   ¬P ∧ Q

¬ (P ∧ Q)   =>   ¬P ∨  Q

¬ ∀X. P => X. ¬P

¬∃X. P        =>        X. ¬P

¬¬P              =>   P

3. Rename variables distant: the similar variable name may be reused a lot of time for different variables, within one sentence or among several. To ignore uncertainty later rename every dissimilar variable with a exclusive name.

4. Move quantifiers outwards:  the sentence is now in a form where all the quantifiers may be moved strongly to the outside without disturbing the semantics, provided they are reserved in the similar order.

5. Solemnize existential variables by replacing them with Solemn constants and methods. This is similar to the existential removal law from the last  format we  just  replace a word  for  each  existential  variable  so as to  represents  the 'something' for which it handles. If there are no preceding unique quantifiers the 'something' is immediately a new constant. However, if there are then we use a method that may have all these preceding unique variables as arguments. When we are done we immediately drop all the general quantifiers. This leaves a quantifier-free statement . For example:

 X. ∃Y. person(X)-> has(X, Y) heart(Y) is Solemnized like

person (X) ->has(X, f(X)) ∧heart(f(X))

6. Distribut ∧ over  to get a conjunction of disjunctions. This includes rewriting with:

P ∧(Q ∨R)   =>   (P ∧Q) ∨(P ∧R)

(P∨Q)∧ R => (P∧R)   (Q ∧ R)

7. Flatten binary connectives: swap nested ∧ and ∨ with flat lists of conjuncts and disjoints:

P ∧(Q∧ R)   =>   P∧ Q ∧ R

(P∧ Q)∧ R   =>   P ∧ Q∧ R

P ∨ (Q ∨ R)   =>   P∨Q∨R 

(P ∨ Q) ∨ R   =>   P ∨ Q ∨ R

8. The sentence is now in CNF. more simplification may take place by avoiding duplicate literals and sinking any clause which contains both A and ¬A (one will be right, so the clause is always right. In the conjunction of clauses we need everything to be exact, so  we can drop it.) There is an another possible final step that takes it to Kowalski normal form, also famous as implicative normal form (INF):

9. Reintroduce implication  by collecting up all the negative literals (the negated ones)  and  making  their  conjunction  N,  then  taking  the  disjunction  P  of  the affirmative literals, and forming the logically equivalent clause N-> P.

Posted Date: 10/2/2012 9:25:25 AM | Location : United States







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

Write discussion on Conjunctive normal form -artificial intelligence
Your posts are moderated
Related Questions
How to clear a datagrid on a button click? You require to Clear the DataSource of the dataGrid. So try this: dataSet1.Clear(); dataGrid1.DataSource = dataSet1.TableNam

How does bus arbitration typically work? i.  A bus master waiting to use the bus asserts by  the bus request. ii.  A bus master cannot be the bus until it's request is grant

Q. Explain working of D Flip -Flop? D (data) flip-flop is modification of RS flip-flop. Problem of undefined output in SR flip-flop when both R and S become 1 gets avoided in D

PRAM is one among the models which are used for designing the parallel algorithm as shown in Figure. The PRAM model comprises the following components: i)  A group of identical

The 68HC11F1 has two types of serial ports namely asynchronous (SCI) and synchronous (SPI). The most common form of communication device used in control is the SCI as this provides

Explain the use of structures with pointers C permits a pointer to a structure variable. In fact a pointer to a structure is same to a pointer to any other variable. The pointe

Q. What is Unordered Lists? First, we will build an unordered list. Many times, these lists are also termed as bulleted lists. These lists are characterized by list items which

write a program to copt values of object without using copy constructor or = operator

Q. Describe short note on Information system for strategic advantage? Ans. Strategic role of information systems engage using information technology to develop products or serv

Q. Illustrate Domain Names and Address Resolution? But what if you don't know IP address of the computer you want to connect to? What happens if you need to access a web server