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
Describe generic framework for electronic commerce Generic Framework for electronic commerce contains the Applications of EC   (like as banking, shopping in online stores and m

Write the HTML code to accomplish the web page to insert the frame extending 300 pixels across the page from left side. The HTML code to accomplish the web page is given below

Question 1: a. Give NINE general properties of an MIS b. Name and explain the THREE main Problems and Issues of EIS Question 2: a. What are information systems for?

What are the restrictions of traditional payment instruments? How are such restrictions overcome by electronic payment systems? The restrictions of traditional payment system a

Hardware Cost It refers to the cost involved in the execution of an interconnection network. It consists of the cost of switches, connectors, , arbiter unit, interface logic an

As per Nyquist criterion the sampling rate is (A) 2fs                                                  (B) (1/2)fs (C) (1/2fs)

what are the different techniques of biasing a transistor?

In this problem you are given a board in which some of the elements are placed as shown in diagram below. Each element represents a color. Fill the other elements in the board, suc

State about the multiple inheritance multiple inheritance is shown in Figure. In this, one class is inherited from more than one class.

Q. Illustrate Basic strategy used in RAID? Basic strategy used in RAID is to replace large capacity disk drive with multiple smaller capacity disks. Data on these disks is dist