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
With respect to security, which one is the better choice? .Net or J2EE? Explain? As per majority programmers .NET is the best one which have single vendor compare to, the

Q. Illustration of cache size of a system? Cache Size: Cache memory is very costly as compared to main memory and therefore its size is generally kept very small.  It has bee

A data structure in which an element is added and detached only from one end, is known as Stack

mod12 counter connection diagram

Approach to reasoning - first-order logic: The formal approach to reasoning has bigger return and disadvantages. In generally we notice, if a computer program has proved somet

Q. Explain about Merge sort circuit? First split the given sequence of n numbers in two parts every part comprising of n/2 numbers. Afterwards recursively divide the sequence i

Q. What is Charge-coupled Devices? CCDs are employed for storing information. They have arrays of cells that can hold charge packets of electron. A word is signified by a set o

PROCEDURE TO CREATE PROJECT IN COLLABORATION SYSTEM

The aim of this project is for you to construct a fully working compiler for a small simple programming language, SPL. The compiler will read in SPL source code and produce ANSI C

Digital switch It is a device that handles digital signals formed at or passed by a telephone company's central office and sends them across the company's backbone network.