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Topic: Disjunctive sum

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	Complexity
		To understand this measure of complexity, it is useful to define the notion of disjunctive normal form .
		In certain implementations, disjunctions are expanded and kept in extensive form instead of being ``resolved'' as in FUF, by choosing one branch out of the set of branches.
		The problem with such an approach is that in practice many disjuncts stay ``alive'' during the unification process, and the result tends to take on sizes close to the normal form expansion of the grammar, which is clearly unmanageable.
	www.cs.bgu.ac.il /~yaeln/fufman/node56.html (506 words)

	CONDITION - LoveToKnow Article on CONDITION (Site not responding. Last check: 2007-10-10)
		It is also applied generally to the sum of the circumstances in which a person is situated, and more specifically to favorable or prosperous circumstances; thus a person of wealth or birth is described as a person of condition, or an athlete as being in condition, i.e.
		Conditional has been used as equivalent to hypothetical in the widest sense (including disjunctive); or narrowed down to be synonymous with conjunctive (the condition being there more explicit), as a subdivision of hypothetical.
		Thus all finite things exist in certain relations not only to all other things but also to thought; in other words, all finite existence is conditioned.
	100.1911encyclopedia.org /C/CO/CONDITION.htm (680 words)

	Homework 5 Solutions (Site not responding. Last check: 2007-10-10)
		Because the question was a bit ambiguous, both a) disjunctions of conjunctions, and b) one conjunctive rule were counted correctly.
		However, in the disjunction of rule case you should have adopted a GABIL like crossover, to swap similar parts of rules.
		Note also this sum is the number of interior nodes in a complete tree.
	www-2.cs.cmu.edu /afs/cs.cmu.edu/project/theo-3/www/hw5-solutions.html (484 words)

	Sensei's Library: disjunctive sums
		This is a fundamental concept in combinatorial game theory, where one defines the sum of two games, which is an easy idea: players may play in one or the other game.
		This is 'exclusive or', whence the term disjunctive.
		The real depth of the concept can be seen in go when you start to wonder whether the endgame marks the point at which the game breaks up into a sum of several games (independent endgame positions).
	senseis.xmp.net /?DisjunctiveSums (276 words)

	[No title] (Site not responding. Last check: 2007-10-10)
		The overall request weight is the weighted sum of the weight specified by each requester.
		Disjunctive requests: The optimizer should allow disjunctive requests, that is, requests for any one of several allocations.
		A disjunctive request consists of multiple simple requests, and the optimizer needs to satisfy only one of them.
	www-2.cs.cmu.edu /~eugene/Radar/Long/features.txt (767 words)

	[No title]
		To construct a logical expression in disjunctive normal form from a truth table: * Build a minterm for each row of the table where the function is true.
		The carry-in[0] is 0, and the sum is carry-out[31], z[31], z[30],..., z[0].
		The sum of the high-order bits (s2 and t2) does depend on whether there is a carry (gL and pL), so we take the carry bits from the first adder, and the summation results from the second adder, and combine them together in the circuit labeled FIXIT to get the final result.
	www.cs.rochester.edu /u/sandhya/csc173/notes/08_prop_logic.txt (4987 words)

	lfg99
		While disjunctive statements of linguistic constraints allow for a transparent and modular specification of linguistic generalizations, the resolution of disjunctive feature constraint systems is expensive, in the worst case exponential.
		The general pattern is that disjunctions that arise from distinct parts of the sentence do not interact, as they are embedded within distinct parts of the f-structure.
		If disjunctions are independent, they conclude, it is in fact not necessary to explore all combinations of disjuncts as they are rendered in DNF, in order to determine the satisfiability of the entire constraint system.
	www.dfki.de /~frank/papers/lfg99-ws-html/lfg99.html (11922 words)

	Encyclopedia topic: Disjunctive normal form (Site not responding. Last check: 2007-10-10)
		In Boolean logic (A system of symbolic logic devised by George Boole; used in computers), Disjunctive Normal Form (DNF) is a method of standardizing and normalizing logical formulas.
		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).
		Note that all logical formulas can be converted into disjunctive normal form.
	www.absoluteastronomy.com /encyclopedia/d/di/disjunctive_normal_form.htm (299 words)

	[No title]
		Whether requirements in a statute are to be treated as disjunctive or conjunctive does not always turn on whether the word "or" is used; rather it turns on context.
		Depending on the relevant context, a disjunctive test can always be reformulated as a conjunctive one.[fn19] To be fair to the 6109 Grubb Road panel, part of the problem in both 6109 Grubb Road and in this case stems from the language of the statute itself.
		Yet, by a disjunctive reading of § 881 (a)(4)(C), a subsequent owner who avoids investigating an obvious possibility that his or her property is forfeitable in the hands of the transferor, will always be able to establish innocent owner status because of his or her lack of consent.
	vls.law.vill.edu /locator/3d/Nov1994/94a0900p.txt (14288 words)

	[No title] (Site not responding. Last check: 2007-10-10)
		Given a function f as a sum of minterms (or as 1 entries in a Karnaugh map) we can determine in polynomial time (polynomial in the length of the canonical form) whether the function is logically equivalent to a read-once DNF.
		Secondly we do not know apriori that the given sum of minterms S represents a special read-twice DNF unlike in [9] where the task is to establish the exact read-twice DNF given that one exists.
		Comparing any pair of sums to determine if they are the same takes O(m2n2) time, as we must check if every term in one sum belongs to the other sum and vice-versa, and it takes O(n2) time to compare two terms of O(n) literals each to see if they are the same.
	www.seas.upenn.edu /~chandru/one-two.doc (7719 words)

	Conceptual Introduction to ANOVA
		I say "on the order of" because the true disjunctive probability here would not be precisely.15, owing to some rather complex conditional probabilities that creep into situations of this sort.
		Here is how you could construct a sum of squared deviates measure for the three group means of the present example.
		and the corresponding "sum" of squared deviates is the squared deviate multiplied by the appropriate value of N
	faculty.vassar.edu /lowry/ch13pt1.html (3369 words)

	State variable analysis of linear switched networks with
		The unipolar and bipolar implementation of conjunctive and disjunctive canonical functions (AND, OR) are shown in the figures 3 and 4, respectively.
		The unipolar implementation of the disjunctive canonical binary function does not allow the negation of the inputs inside the unit.
		The ANN implementation of the disjunctive normal form of a logical function is shown in figure 6 for the case of four variable logical functions.
	www.dsp.pub.ro /articles/ss2skc/ss2skc.html (3555 words)

	Petrick's Method (Site not responding. Last check: 2007-10-10)
		, then at least one disjunctive clause is not satisfied (0), meaning that at least one row is not covered.
		Each sum corresponds to a different row of the table.
		These sums are ANDed together, since all such requirements must be satisfied.
	www1.cs.columbia.edu /~cs4861/handouts/quine-mccluskey-handout/node31.html (329 words)

	syllabus (Site not responding. Last check: 2007-10-10)
		This is right, but it's much clearer if you realize that there are only two relevant probabilities: one that the car is behind the door I picked, and 1 - (that probability) that it's behind ANY of the other doors.
		That way, when Monty shows a goat it's not that he shows us that one of the "individual probabilities" is zero, but rather that he shows us that one of the disjuncts in the big disjunctive fact does not obtain (i.e.
		the car is not behind that door), and may thus be cancelled from the disjunction (and the probability of the whole disjunction will remain the same).
	www.ags.uci.edu /~mzyoung/page4.htm (293 words)

	Fodor on Narrow Content and Asymetric Dependency
		There is an intuitive sense in which narrow content is the disjunctive sum-total of all the broad contents a mental state would have in each and every context for which the function is defined.
		So if their contents were disjunctive, a broad content psychology would capture them; but since their broad contents are different, their behaving similarly will be missed by a broad content theory that assigns non-disjunctive contents to them.
		So the (disjunctive) meaning is in the head as meaning-making dispositional mechanisms are in the head ("internalism"), but their individuation essentially adverts to a range of different (actual or possible) contexts ("externalism").
	www.clas.ufl.edu /users/maydede/OnFodor.html (16144 words)

	Minimizing Boolean Functions
		Minterms 1 and 2 are in the second and fourth columns of the top row, while minterms 4, 5, 7, and 6 appear from left to right in the four columns of the bottom row.
		A Karnaugh Map is used to produce a minimal sum of products implementation of an expression by drawing rectangles around groups of adjacent minterms in the map; each rectangle will correspond to one product term, and the full expression will be constructed as the OR (sum) of all the product terms.
		A prime implicant is a product term that will generate ones only for combinations of inputs that are minterms of the disjunctive normal form of the function, and which cannot be further reduced by combining with any other term.
	babbage.cs.qc.edu /courses/Minimize/index.php (3638 words)

	COT 3100 Course Assignments: Fall, 1998 (Charles Winton) (Site not responding. Last check: 2007-10-10)
		Give the canonical sum of products (disjunctive normal form) and product of sums (conjunctive normal form) for the function given in problem 1.
		Use K-map reduction to produce a minimal sum of products expression for the function given in problem 1.
		Use K-map reduction to produce a minimal product of sums expression for the function given in problem 1.
	www.unf.edu /ccec/cis/cwinton/html/cot3100/f98/hw12.html (269 words)

	Fuzzy Logic: Example 3: Finding the Disjunctive Sum
		Find the disjunctive sum of the two fuzzy relations defined here.
		The disjunctive sum of fuzzy relations R and S in the universal space VxW can be found with the following formula.
		We can find disjunctive sum of the two fuzzy relations R and S by using the formula derived earlier and some of the functions from Fuzzy Logic.
	www.wolfram.com /products/applications/fuzzylogic/examples/sum.html (111 words)

	AcmeArticles - Discrete Mathematics In a Nutshell
		A necessary and sufficient condition for an elementary sum to be identically true is that it contains at least one pair of factors in which one is the negation of the other.
		All formulae of which no two are equal and are true for exactly one set of values and are composed of n-1 conjunctions of a variable or it's negation from a set of n variables are called the minterms.
		The fundamental logical connectors in predicate calculus are negation, conjunction, disjunction, equivalence, implication.
	www.geocities.com /acmearticles/dms.htm (4438 words)

	Playing Disjunctive Sums is Polynomial Space Complete (Site not responding. Last check: 2007-10-10)
		A position in a disjunctive sum of games is simply a collection of positions, one from each game: to move in a sum is to move in any one of its constituents.
		Sums have been studied extensively by Conway and others, and play an important role in Go.
		Hence it may be conjectured that there is no feasible algorithm for deriving a strategy of play in a sum from knowledge about its constituent games.
	www.cis.syr.edu /~lockwood/html/abdsums.html (101 words)

	intrinsicness
		[5] According to Langton and Lewis, G is "basic intrinsic" iff (i) G and its negation are independent of loneliness and its negation, and (ii) G is neither disjunctive nor the negation of a disjunctive property.
		That it can be expressed in disjunctive terms counts for little; roundness too can be expressed that way, e..g., as the the disjunction of round-and-charged with round-and-not-charged.
		What would suggest that S was disjunctive would be a finding that its disjuncts - the property of not being round, that of being round and accompanied by something round - were perfectly natural.
	www.mit.edu /~yablo/int.html (10988 words)

	The ring tactic
		Let a canonical sum be an ordered sum of monomials that are all different, i.e.
		This canonical sum is called the normal form of the polynomial.
		For the classical propositional calculus (or the boolean rings) the normal form is what logicians call disjunctive normal form: every formula is equivalent to a disjunction of conjunctions of atoms.
	pauillac.inria.fr /coq/doc/Reference-Manual022.html (2155 words)

	The Critique of Pure Reason (80)
		The logical determination of a conception is based upon a disjunctive syllogism, the major of which contains the logical division of the extent of a general conception, the minor limits this extent to a certain part, while the conclusion determines the conception by this part.
		The general conception of a reality cannot be divided a priori, because, without the aid of experience, we cannot know any determinate kinds of reality, standing under the former as the genus.
		And thus we are induced to hold the empirical principle of our conceptions of the possibility of things, as phenomena, by leaving out this limitative condition, to be a transcendental principle of the possibility of things in general.
	etext.library.adelaide.edu.au /k/kant/immanuel/k16p/k16p80.html (2017 words)

	Propositional Logic (Site not responding. Last check: 2007-10-10)
		Given a specific function expressed as the results of variable assignment (such as a circuit that adds two bits together and produces a sum and a carry bit, all of which is expressed in truth table form), we'd like the corresponding logical expression so that we can construct a circuit for the function.
		Conjunctive and disjunctive normal forms are duals of each other; either one may be used to generate a logical expression from a truth table.
		We could, of course, construct an expression in disjunctive normal form by using maxterms and AND.
	www.cs.rochester.edu /u/leblanc/csc173/proplogic/expressions.html (1815 words)

	Study notes, Mgmt. 321, ch. 10, Spring 2002
		Disjunctive tasks- no connection, so strongest member is key to performance, but must demonstrate his/her ability to other members and share unique information
		Discretionary tasks- nature of task can be analyzed and parceled out in conjunctive or disjunctive manner
		Increasing group size helps on disjunctive tasks, but not on conjunctive tasks
	www.personal.psu.edu /faculty/r/r/rrb10/m321spr02ch10.htm (597 words)

	Brian's Digest: Disjunctive Constraints
		I know this problem can be formulated as IP using disjunctive optimization technique.
		I am especially interested in a work specific to optimization with min() type constraint rather than disjunctive optimization in general.
		BUT, if y really is the sum of other variables then this might not be the best way.
	www.worms.ms.unimelb.edu.au /digest/disjunctive_c.html (350 words)

	Jarek Rossignac's publications (Site not responding. Last check: 2007-10-10)
		Disjunctive forms of CSG expressions are used in computer graphics instead of the equivalent CSG graphs because they alleviate the need for a stack of arbitrary length when evaluating CSG expressions.
		The drawback of these techniques is their need for storing an explicit representation of the disjunctive form, which may grow exponentially with the number of leaves in the original graph.
		The present paper proposes a new approach for processing the disjunctive form directly off the original CSG graph, thus avoiding the expensive rewrite mechanism and eliminating the associated storage requirements.
	www.gvu.gatech.edu /~jarek/papers10.html (6627 words)

	[No title]
		In the body of a rule this expression has the same meaning as the disjunction (p, not q) ; (q, not p).
		neither monotone nor antimonotone) aggregates occur [note that sum with positive and negative summands is nonmonotone], and (2) aggregates occur in recursion.
		This observation can be useful for implementation issues, since one can still employ an NP "machinery" to implement a rather large class of aggregates (with nice semantic properties).
	www.cs.utexas.edu /users/vl/tag/aggregates (1135 words)

	The DLV Project - A Disjunctive Datalog System (and more)
		DLV is a system for disjunctive datalog with constraints, true negation (à la Gelfond and Lifschitz) and queries.
		Allow for ";" and "" as alternate notions for disjunction; the keywords "non" and "not" are now case-sensitive.
		New i386-unknown-freebsd2.2.7 and i386-linux-elf-gnulibc2 ports; first version built with egcs 1.1 instead of egcs 1.0.3a; removed various kludges needed for gcc 2.7.2; new option -OM- to disable Model Checking; option -silent now causes omission of all empty lines in output; synchronized command-line help and manual; added support for anonymous variables.
	www.dbai.tuwien.ac.at /proj/dlv (4146 words)

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