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
Q. Multithreaded Architecture? It is clear at the moment if we provide a lot of contexts to multiple threads then processors with numerous contexts are known as multithreaded s

Q. Explain the Memory Transfer process? Memory Transfer Transfer of information from memory to outside world which implies I/O Interface is known as a read operation. Tra

Cheques vs Credit Cards       E-cheques:  E-cheques are used for business dealing in e-commerce.  Transactions of these cheques take place on Internet. In this system the elect

Solve the following 8-department problem using the MIP method.  What is the resulting layout and flow-distance score?  Note that the aspect ratio of each department should be 2.

List the allowed register pairs of 8085. B-C register pair D-E register pair H-L register pair

Question: a) Evary cell in a cellular network is assigned a band of frequencies. The allocated frequencies are divided into two types of channels. Indentify and describe each t

What are advantages and benefits to businesses by e-commerce over extranets? The advantages and benefits to businesses comprise: Less Paperwork: along with documents and bus

A Choice is displayed in a compact form that needs you to pull it down to see the list of available choices and only one item may be selected from a choice. A List may be shown in

Serial Execution Execution of a program serially, one statement at one instance of time. In the simplest case, that's what takes place on a one processor machine. But even mo

Differentiate between AT and XT computer system? Ans    XT -> Extended and AT->Advanced Technology Some differences between PC and XT include the type of power supply initia