...also by Erhus Cniversity Press, dealt almost exclusively with some "basic" consequences of the Smarandache function. In this one, the universe of dis... ...y from the interest and excitement that can be generated by exploring the consequences of such a problem It is a well-known cliche among writers tha... ... some of these problems. In mathematics, one often does not know what the consequences of a statement are. Cnlike a novel however, there are no compl... ... n, where n is the smallest number such that m divides n'. and associated consequences has spawned many new branches of mathematics. A previous volu... ...t occur in n! 0 This function has many uses when dealing with some of the consequences of the Smarandache function Sen), most notably, the number of... ... prime, the Smarandache values would form the same 3 x 3 magic square. A logical extension of this problem places a restriction on the numbers. The...

...ant role in fuzzy relation equations. While the t-norm i may be interpreted as logical conjunction, the corresponding operation w i may be interpr... ... as logical conjunction, the corresponding operation w i may be interpreted as logical implication. The following basic properties 31 of w i ... ...practice. For example, in fuzzy reasoning [70], when the inference rule and the consequences are known, a problem to determine antecedents to be use... ...sible solutions according to some levels of plausibility is out of the scope of logical reasoning, strictly speaking. However one may for instance... ... 134 there are manifestations which are neither certain nor impossible and consequences of the presence of a given disorder d which are only po... ...n power of the model, we have to refine the non–fuzzy model in such a way that consequences (resp. manifestations) previously expressed as certain ... ...p. certainly absent) remain classified in the same way and where some possible consequences (resp. possibly present manifestations) are now allowed... ...ication, negation and a quantifier for generalization are used. As usual, those logical operators are characterized by the way they operate on the t... ... B ∧ t B ⊆ t A. (16) Introducing also the notation |= for (generalized) logical validity as in [28, 29] by |= A ≡ t A . ( 1 7 ) W...

...d terminal edges. For proof refer [11]. The following results are easy consequences of the above theorem. Result: [4]: Let G be any connecte... ... Machine Intelligence, 9 (1979) 149- 194. 75. Zhang, W.R., and S. Chen. A Logical Architecture for Cognitive Maps, Proceedings of the 2 nd IEEE ...

...s to read “our daily paradoxes” Smarandache has not certainly referred to the logical, mathematical or linguistic meaning of the word/notion “parado... ...y creation plan. A sulking and introverted nature as that of Ion Barbu could, logically, straighten and aspire only towards a somehow utopian world;... ...erican playwright, without having claims to destroying myths, has unexpected consequences, as the result is almost a tragicomedy, in what the antiq... ... postmodernity- reality and term also large, having a historic and social, in consequence, first of all, a temporal motivation. This finding couldn’t... ...ncipation, of autonomy. Moreover, it is suggested the idea of a chronological consequence. G. Bajenaru in his study “The paradoxist post-modernism (... ...tions or emphasized through paradoxist means, replace the ample, rational and logical poems of the postmodernism. Only an attentive eye, a subtle mi... ...geous disputes for the latter. Thus, the new (post)industrial world supposes, logically, the performance (not only at an intentional level) as well a... ...eption, fore the romantic revolution”(p.8). The next reader’s question appears logically: what else will follow after the loop’s closing? If we admit...

... have your say during question & answer sessions. We are here to ferret out logical reasons for the presumed universal, impenetrable light barrier t... ...a cooperative process. There are those who say the reasons don't have to be logical. I, for one, find that smacks of religion, not science. We are... ... USA smarand@unm.edu Abstract: In this short paper, as an extension and consequence of the Einstein-Podolski-Rosen paradox and Bell's inequality... ...rrent theories of string-M theory and the theory of the big bang simply use logically inconsistent language. Namely, one cannot introduce geometry i... ...ually follows that Peanuts character around. But now we encounter a popular logical paradox, repeated over-and- over down through the years, generall...

...se to the reader as the proof requires vitally only the definitions and a logical use of them. A recent paper [27] which studies strictly wild al... ...utative ring II. Proof: Left for the reader to verify as it is an easy consequence of the definition. THEOREM 4.2.2: Let R be a ring. If R is ...

...standing/interpretation which might overlap. 2.3 Definition of Neutrosophic Logical Connectives: The connectives (rules of inference, or operator... ...oblem to solve; here we present the easiest ones: One notes the neutrosophic logical values of the propositions A 1 and A 2 by NL(A 1 ) = ( T 1... ...T 1 , I 1 , F 1 ) and NL(A 2 ) = ( T 2 , I 2 , F 2 ). For all neutrosophic logical values below: if, after calculations, one obtains numbers < 0 ... ...cgi?c=connection&f=0&t=255. [27] Le, Charles T. Le, Software for neutrosophic logical operators, Networking by Industry, Inc. Online, http://www.in... ...nt events, then (3) A4: (countable additivity) If are disjoint events (4) 2.2 Consequences of axioms and bayesian inference From these axioms, all o... ...ery important to note that these rules apply only on irreductible propositions (logical atoms) . A proposition is said to be irreductible (or equivale... ... 2000 MSC: 03E99, 03-99, 03B99, 60A99, 62A01, 62-99. Introduction: As a consequence to [1], [3], [4-7] we display the below unusual extension... ... effect to each other. 5. Representing the <Neut-A> <Neut-A> comes as the consequence of the contradiction between <A> and <Anti-A>, therefore ... ...ny contexts as we can, in order to be less-incomplete and discuss some possible consequences. 1. Introduction Upset because none of the logics I knew ...

...gram should be very suggestive to make them aware of the disease and the consequence of their high-risk behavior which will ultimately land them wi... ...ant to mention at least 4% of them acknowledged that they are reaping the consequences of their deeds. Some of them were stoic. When we asked what t... ...nt reveals that the other three conditions cannot be ignored and have its consequences in spreading HIV/ AIDS. Similarly by taking a vector Y K one... ...se refer Smarandache. DEFINITION 4.1.1: In the neutrosophic logic every logical variable x is described by an ordered triple x = (T, I, F) where T... ...tent logic, which means contradictory sources of information about a same logical variable, proposition or event one has T + I + F > 1. Thus ... ...t when he had sex with other women and with CSWs he was not aware of the consequences. He has two children. His wife is also affected with HIV. Hi... ...with no one to question and had no conscience and could not think of the consequences. o. The sudden change of atmosphere and the urban settings p... ...Association, 259 (1988) 1333-1337. 69. McCulloch, W.S., and Pitts, W., “A Logical Calculus of the Ideas Immanent in Nervous Activity,” Bulletin of ... ...ormation and Control, 8 (1965) 139-146. 122. Zhang, W., and Chen, S., “A Logical Architecture for Cognitive Maps,” Proceedings of the 2 nd IEEE I...

... megameters per second as "the speed of light," we paint ourselves into a logical corner in which light is automatically taken as the subject of dis... ... which can neither be reached nor exceeded by any real body." Then: "As a consequence of its motion the clock goes more slowly than when at rest. H... ...hat we can comprehend is my religion." [3] And are we to believe that our logical analyses are trumped by the Venerable Force, and further that Eins... ...r how you slice it. Born (1962, p. 254): "Thus the contraction is only a consequence of our way of regarding things and is not a change of a physica... ...he standpoint of existing knowledge, it is entirely possible, and it is a consequence of Einstein's new theory of relativity, that no signal can be ...

...od what I was saying. By referring to the universal constant c= 299.792 458 megameters per second as "the speed of light," we paint ourselves into a logical corner in which light is automatically taken as the subject of discussion even when it is not. The careful reader will know not to immediately think "light" when he hears or reads "the speed of light." But it is bett...

... Propositions Section 2 The Law of the Excluded Middle Section 3 Logical Equivalence Section 4 Well-Formed Formulas or WFFs Sectio... ...sophic Logic Section 1 Definition of Neutrosphic Logic Section 2 Logical Connectives in Neutrosophic Logic Section 3 Algebraic Propertie... ... 1 Classical Logic Section 1 Propositions In classical logic, a logical variable is restricted to the values of true(T) and false(F). The ... ...ry in the result column, there are 2 n different Boolean functions for n logical variables. Given the truth values in the column above the 5, ... ...on 1.1.4: In the expression p → q, p is known as the antecedent and q the consequence. The implication is often described as the if-then connective. ... ...on ( p /\ q ) \/ ( ¬ p /\ ¬q ). The ↔ connective can also be considered logical equality. Exclusive or (^) can be considered logical inequality ... ...is no middle between the two “extreme” values of true and false. One consequence of this law is the concept of a vacuous proof. What this means ... ...It is interpreted as a statement that if the antecedent is true, then the consequence is also true. The statement is then false if the antecedent is... ...also true. The statement is then false if the antecedent is true, but the consequence is false. With this notion, if it is not possible to prove the...