
	Where results make sense

Topic: Conjunctive normal form

Related Topics

Disjunctive normal form

List of topics in logic

Conjunction introduction

Principia Mathematica

Resolution

BITS Pilani

Currency

In the News (Tue 10 Nov 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	Encyclopedia article: Conjunctive normal form (Site not responding. Last check: 2007-10-20)
		As a normal form (additional info and facts about normal form), it is useful in automated theorem proving (additional info and facts about automated theorem proving).
		As in Disjunctive Normal Form (additional info and facts about Disjunctive Normal Form), the only propositional operators in CNF are and (additional info and facts about and), or (A room in a hospital equipped for the performance of surgical operations), and not (additional info and facts about not).
		Conjunctive normal form can be taken further to yield the clausal normal form (additional info and facts about clausal normal form) of a logical formula, that is used to preform first-order resolution (additional info and facts about first-order resolution).
	www.absoluteastronomy.com /encyclopedia/C/Co/Conjunctive_normal_form.htm (496 words)

	PlanetMath: CNF
		A propositional formula is a CNF formula, meaning Conjunctive Normal Form, if it is a conjunction of disjunction of literals (a literal is a propositional variable or its negation).
		Hence, a CNF is a formula of the form:
		This is version 4 of CNF, born on 2003-10-16, modified 2004-03-09.
	planetmath.org /encyclopedia/ConjunctiveNormalForm.html (68 words)

	Automatic Generation of Normal Forms (Site not responding. Last check: 2007-10-20)
		To generate new normal forms automatically, for a class of formulae, from a set of axioms and lemmas.
		For instance, both conjunctive normal form and polynomial normal form consist of: reducing the number of symbols; stratifying the remaining ones into layers; and organising each layer.
		Normal forms are important in automated reasoning for simplifying formulae and as constituents of decision procedures.
	homepages.inf.ed.ac.uk /bundy/projects/96-97/normal.html (312 words)

	Normal Forms and Skolem Functions
		Normal forms are based on the expressing formulas in terms of negation, conjunction, disjunction, and the quantifiers, {¬, /\, \/, /\x, \/x}.
		The procedure to convert a formula to negation normal form is to recursively replace formulas appearing on the left with formulas appearing on the right.
		A formula is placed in prenix normal form by recursively moving quantifiers outward so that all quantifiers appear at the beginning of the formula.
	cs.wwc.edu /~aabyan/Logic/normal.html (671 words)

	Formal Logic/Sentential Logic/Expressibility - Wikibooks, collection of open-content textbooks
		A normal form provides a standardized rule of expression where any any formula is equivalent to one which conforms to the rule.
		Conjunctive normal form is a conjunction of a disjunctions of literals.
		The conjunctive normal form expression of an arbitrary truth function is the conjunction of all such disjunctions matching the interpretations for which the turh function evaluates to false.
	en.wikibooks.org /wiki/Introduction_to_Philosophy:Logic:Expressibility_in_Sentential_Logic (785 words)

	CS 540 - Introduction to Artificial Intelligence (Site not responding. Last check: 2007-10-20)
		Note the use of alternate terminology: conjunction refers to &and;, disjunction refers to ∨, and when you have a conditional expression such as p → q, then p is called the antecedent and q is called the consequent.
		Conjunctive Normal Form expressions can be thought of a list of constraints, each of which must be met in one of several possible ways.
		Using some equivalence laws we can then rewrite these horn clauses in the form of a conditional where the antecedent is a conjunction of unnegated variables and the consequent is either a single unnegated variable or it is empty.
	www.cs.wisc.edu /~mschultz/cs540/propositionallogic.html (1911 words)

	Clause Normal Form (Site not responding. Last check: 2007-10-20)
		A clause is an expression of the form
		Computationally, CNF is easier to work with, and is the form used by the resolution inference rule.
		Kowalski form forms the antecedent of an implication by conjoining the atoms of the negative literals in a clause, and forms the consequent from the disjunction of the positive literals.
	www.cs.miami.edu /~geoff/Courses/CSC648-F02/Content/FOFToCNF.shtml (980 words)

	Exponential blowup from conjunctive to disjunctive normal form
		Exponential blowup from conjunctive to disjunctive normal form
		The resulting disjunctive normal form is exponentially blown up compared to the size of the original conjunctive normal form.
		Since disjunctive normal forms are unique modulo permutations of the disjuncts and modulo the order of the literals in the disjuncts, the given disjunctive normal form cannot be reduced in size and the exponential blowup is unavoidable.
	www.dbai.tuwien.ac.at /proj/pf2html/proofs/445/445/445.html (778 words)

	Chris Taylor : Optimizing Database Queries (Site not responding. Last check: 2007-10-20)
		To explain disjunctive and conjunctive normal form is beyond the scope of this post, but in very basic terms, the OR operator would be the root of the expression tree for an expression in disjunctive normal form, while the AND operator is at the root of the expression tree in conjunctive normal form.
		To convert this to conjunctive normal form there is a law called DeMorgan’s law, which can be applied to convert the expression from disjunctive to conjunctive normal form.
		In this case the original query was completing in 180ms, the conjunctive normal form optimization in 650ms and the UNION optimization 600ms.
	dotnetjunkies.com /WebLog/chris.taylor/archive/2004/02/15/7268.aspx (980 words)

	Resolution Method. Normal Forms. Skolem. Mathematical Logic. Part 5.
		Note that a formula and its Skolem normal form are not equivalent (even in the classical logic!), they are only a kind of "semi-equivalent": a set of formulas is inconsistent, iff so is the set of their Skolem normal forms.
		Let us continue the "normalization" process that we started in Section 5.1 by reducing formulas to their prenex normal forms, where all quantifiers are gathered in front of a formula that does not contain quantifiers.
		Since, in general, Skolem normal form is not equivalent to the initial formula, we cannot use reduction to Skolem normal forms in the usual ("positive", or affirmative) proofs.
	www.ltn.lv /~podnieks/mlog/ml5.htm (5348 words)

	[No title]
		Where a Term is a distinct (for each conjunct) proposition of the form, p, or ~p.
		Read the entire database (the "world") as "It is a TRUE statement that conjunct One is a true statement and conjunct Two is a true statement and conjunct Three is a true statement...
		By writing the conjuncts down in a database, we are stating that, for our logical purposes, we are assuming that each statement is true.
	condor.depaul.edu /~elliott/457/logic.mem (1154 words)

	Normal forms (Site not responding. Last check: 2007-10-20)
		The disjunctive normal form is used by default.
		Alternatively a conjunctive normal form can be selected as simplification target, which is a form with leading operator and.
		Internally the full normal forms are computed as intermediate result; in these forms each term contains all leaf expressions, each one exactly once.
	www.uni-koeln.de /REDUCE/boolean/node3.html (196 words)

	Convert Sentences to Conjunctive Normal Form
		, it needs to be converted into a normal form, which is also of the type
		However, it is much easier to make inferences using resolution in normal form (conjunctive or implicative).
		This is basically the top level function that use the listed helper function as pipeline for transforming a raw sentence into one in conjunctive normal form
	www.cs.yale.edu /homes/cc392/node5.html (167 words)

	11 (Site not responding. Last check: 2007-10-20)
		In the conjunctive Normal form of a Wff with more than one atomic variable it is possible that the terms like
		A conjunctive Normal form of the given formula is,
		Therefore the Principle Conjunctive Normal Form of the given formula is
	www.annauniv.edu /shan/site2/Html/Lesson/11.5.6.htm (97 words)

	cnfnv (Site not responding. Last check: 2007-10-20)
		, the length of the conjunctive normal form is bounded by a linear function in the length of A.
		A formula is in conjunctive normal form if it is either
		or an arranged conjunction of disjunctions of variables and negated variables.
	www.lwb.unibe.ch /modules/cpc/cpc_cnfnv.html (110 words)

	[No title]
		;;;; Top-Level Functions (defun prefix->cnf (p &optional vars) "Convert a sentence p to conjunctive normal form [p 279-280]." ;; That is, return (and (or...)...) where ;; each of the conjuncts has all literal disjuncts.
		(conjuncts q))) (warn "~A, converted to ~A, is not a Horn clause." p q)) q)) ;;;; Auxiliary Functions (defun cnf1->inf1 (p) ;; P is of the form (or (not a) (not b)...
		,s1,s2)) ;;; Indexed cnf representation for efficient implementation of propositional algorithms ;;; An icnf instance represents its symbols by the integers 0,1,...,n-1 ;;; and numbers its clauses by integers 0,1,...,m-1.
	www.cs.berkeley.edu /~russell/classes/cs289/f04/assignments/sat289.lisp (1167 words)

	CIS 301 Index (Site not responding. Last check: 2007-10-20)
		We may compute the cnf of a conjunction by first computing cnfs for each conjunct and then forming their conjunction.
		The computation of a cnf for a disjunction also computes cnfs for its two arguments, but we have to rely on a function DIST that "animates" the distributivity law; if we simply returned CNF(phi1)
		CNF(phi2), then this would not be a cnf if one of its arguments were a conjunction, which is generally the case.
	www.cis.ksu.edu /~huth/301/cnf.html (160 words)

	Florida Tech, CSE3001: ML Project (Fall 2002)
		A \/ B A \/ B (negation normal form) A \/ B (conjunctive normal form, one conjunct)
		A \/ ~((A & ~B) \/ (~C & C)) A \/ ((~A \/ B) & (C \/ ~C)) (negation normal form) A \/ ~A \/ B & A \/ C \/ ~C (conjunctive normal form, two conjuncts)
		Since all conjuncts contain an atom and its negation, the proposition is a tautology.
	www.cs.fit.edu /~ryan/cse4250/proj-taut.html (710 words)

	Propositional Logic: normal forms (Site not responding. Last check: 2007-10-20)
		(c→(a∧b)) is equivalent to ((a∨¬c) ∧(b∨¬c)) ; this latter formula is in CNF (it is the conjunction of disjunctions).
		Another format, Disjunctive Normal Form, or DNF is the dual of conjunctive normal form.
		A CNF formula is the pessimistic approach, focusing on the rows where the function is false: ``I'm not in this row, and not in this row, and …''.
	cnx.rice.edu /content/m12075/latest (902 words)

	Resolution in CycL
		By analogy with the CNF case, each conjunct in the outer disjunct is also called a 'clause'.
		Moreover, since each clause is a single conjunct of a set of literals, we can again very tersely represent a clause as a list of two items: a set of negated literals and a set of the non-negated (positive) literals.
		(1) Assuming that the parent DNF and inference CNF clauses are variable disjoint, identify a most general unifier of the resolvent literal in the parent DNF and the resolvent literal in the inference CNF.
	www.cyc.com /cycdoc/ref/resolution.html (1460 words)

	[No title] (Site not responding. Last check: 2007-10-20)
		A read-once CNF (conjunctive normal form) formula is a special case of a read-once formula as it is a product of sums of literals and can be implemented by a Boolean circuit with only two levels.
		We show that if the input formula is given in canonical form as a sum of minterms, then the problem of recognising whether it is logically equivalent to a read-once formula is polymomial time.
		A CNF X is logically equivalent to a CNF Y if Var(X) = Var(Y), that is the variable sets for the two formulae are identical, and if SAT(X) = SAT(Y), that is, the sets of satisfying assignments to the two formulae are identical.
	www.seas.upenn.edu /~chandru/one-two.doc (7719 words)

	22C:54
		A formula is in Conjunctive Normal Form (CNF) is it is conjunction of disjunctions of literals.
		Every formula in Conjunctive Normal Form can be converted into a list of lists of literals.
		This is done by first turning the (possibly nested) conjunction into a (flat) list of disjunctions and then turning each (possibly nested) disjunction in the list into a (flat) list of literals.
	www.cs.uiowa.edu /~tinelli/classes/22c054-Spring00/html/projects/validity.html (852 words)

	Maggie Johnson
		And voila, we have an expression where the variables are OR’d together in groups, and then these groups are ANDed together, i.e., conjunctive normal form.
		Before we can apply resolution, remember that the premises and the negation of the conclusion must be in conjunctive normal form.
		Note that it is usually much more involved converting predicate expressions to conjunctive normal form.
	cse.stanford.edu /classes/cs103a/h22Res.htm (2441 words)

	Wikinfo \| Disjunctive normal form
		Disjunctive Normal Form or DNF is a method of standardizing and normalizing logical formulas.
		A logical formula is considered to be in DNF if and only if it is a single disjunction of conjunctions.
		More simply stated, the outermost operators of the formula are all ORs, and there is only one level of nesting allowed, which may only contain literals or conjunctions of literals.
	www.wikinfo.org /wiki.php?title=DNF (253 words)

	[No title]
		;;; -- Mode: Lisp; Syntax: Common-Lisp; -- File: logic/normal.lisp ;;;; Convert Expressions to Normal Form (Conjunctive, Implicative or Horn) ;;; This could be done much more efficiently by using a special ;;; representation for CNF, which eliminates the explicit ANDs ;;; and ORs.
		;;;; Top-Level Functions (defun ->cnf (p &optional vars) "Convert a sentence p to conjunctive normal form [p 279-280]." ;; That is, return (and (or...)...) where ;; each of the conjuncts has all literal disjuncts.
		(conjuncts q))) (warn "~A, converted to ~A, is not a Horn clause." p q)) q)) (defun logic (sentence) "Canonicalize a sentence into proper logical form." (cond ((stringp sentence) (->prefix sentence)) (t sentence))) ;;;; Auxiliary Functions (defun cnf1->inf1 (p) ;; P is of the form (or (not a) (not b)...
	aima.cs.berkeley.edu /lisp/logic/algorithms/normal.lisp (412 words)

Try your search on: Qwika (all wikis)