Negation and Paraconsistent Logics

Does there exist any equivalence between the notions of inconsistency and consequence in paraconsistent logics as is present in the classical two valued logic? This is the key issue of this paper. Starting with a language where negation (?{neg}) is the only connective, two sets of axioms for consequence and inconsistency of paraconsistent logics are presented. During this study two points have come out. The first one is that the notion of inconsistency of paraconsistent logics turns out to be a formula-dependent notion and the second one is that the characterization (i.e. equivalence) appears to be pertinent to a class of paraconsistent logics which have double negation property.     

Negation of binomial coefficients

We extend the concept of a binomial coefficient to all integer values of its parameters. Our approach is purely algebraic, but we show that it is equivalent to the evaluation of binomial coefficients by means of the Γ-function. In particular, we prove that the traditional rule of “negation” is wrong and should be substituted by a slightly more complex rule. We also show that the “cross product” rule remains valid for the extended definition.     

三个测度猜想的否定

给出三个非常容易让人误以为真的测度猜想,通过定理与λ-Cantor集及其余集的构造给出三个猜想的否定答案.     

Negation in bounded commutative DRℓ-monoids

The class of commutative dually residuated lattice ordered monoids (DRℓ-monoids) contains among others Abelian lattice ordered groups, algebras of Hájek’s Basic fuzzy logic and Brouwerian algebras. In the paper, a unary operation of negation in bounded DRℓ-monoids is introduced, its properties are studied and the sets of regular and dense elements of DRℓ-monoids are described.     

关于“两个不等式的推广”的否定

本文指出文 [1 ]中所得的结论是错误的 ,并给出了修正后的结论及其推广和应用 .     

Singular Propositions,Negation and the Square of Opposition

This paper contains two traditions of diagrammatic studies namely one, the Euler–Venn–Peirce diagram and the other, following tradition of Aristotle, the square of oppositions. We put together both the traditions to study representations of singular propositions (through a diagram system Venn-i, involving constants), their negations and the inter relationship between the two. Along with classical negation we have incorporated negation of another kind viz. absence (taking a cue from the notion of ‘abhãva’ existing in ancient Indian knowledge system). We have also considered the changes that take place in the context of open universe.     

Thinking Negation in Early Hinduism and Classical Indian Philosophy

A number of different kinds of negation and negation of negation are developed in Indian thought, from ancient religious texts to classical philosophy. The paper explores the Mīmā?sā, Nyāya, Jaina and Buddhist theorizing on the various forms and permutations of negation, denial, nullity, nothing and nothingness, or emptiness. The main thesis argued for is that in the broad Indic tradition, negation cannot be viewed as a mere classical operator turning the true into the false (and conversely), nor reduced to the mainstream Boolean dichotomy: 1 versus 0. Special attention is given to how contradiction is handled in Jaina and Buddhist logic.     

A Square of Oppositions in Intuitionistic Logic with Strong Negation

In this paper, we introduce a Hilbert style axiomatic calculus for intutionistic logic with strong negation. This calculus is a preservative extension of intuitionistic logic, but it can express that some falsity are constructive. We show that the introduction of strong negation allows us to define a square of opposition based on quantification on possible worlds.     

Negation and partial axiomatizations of dependence and independence logic revisited

In this paper, we axiomatize the negatable consequences in dependence and independence logic by extending the systems of natural deduction of the logics given in [22] and [11]. We prove a characterization theorem for negatable formulas in independence logic and negatable sentences in dependence logic, and identify an interesting class of formulas that are negatable in independence logic. Dependence and independence atoms, first-order formulas belong to this class. We also demonstrate our extended system of independence logic by giving explicit derivations for Armstrong's Axioms and the Geiger-Paz-Pearl axioms of dependence and independence atoms.     

Empirical kalman-Credibility

Blätter der DGVFM - In a dynamic linear model the credibility estimator is given by the famous Kalman-filter algorithm. By inserting adequate parameter estimators one gets an empirical...     

Empirical minimization

We investigate the behavior of the empirical minimization algorithm using various methods. We first analyze it by comparing the empirical, random, structure and the original one on the class, either in an additive sense, via the uniform law of large numbers, or in a multiplicative sense, using isomorphic coordinate projections. We then show that a direct analysis of the empirical minimization algorithm yields a significantly better bound, and that the estimates we obtain are essentially sharp. The method of proof we use is based on Talagrand's concentration inequality for empirical processes. Research partially supported by NSF under award DMS-0434393. Research partially supported by the Australian Research Council Discovery Porject DP0343616.     

Empirical chaotic dynamics in economics

Barnett and Chen [4–6] have displayed evidence of chaos in certain monetary aggregates, but the tests have unknown statistical sampling properties. Using monthly growth rates in monetary aggregates, we conduct bispectral tests for nonlinearity. Our tests have known sampling properties, and we find deep nonlinearity in some monetary aggregate series.     

Thinning Out Redundant Empirical Data

Given a set of “empirical” points, whose coordinates are perturbed by errors, we analyze whether it contains redundant information, that is whether some of its elements could be represented by a single equivalent point. If this is the case, the empirical information associated to could be described by fewer points, chosen in a suitable way. We present two different methods to reduce the cardinality of which compute a new set of points equivalent to the original one, that is representing the same empirical information. Though our algorithms use basic notions of Cluster Analysis they are specifically designed for “thinning out” redundant data. We include some experimental results which illustrate the practical effectiveness of our methods.      

渐近最优的经验贝叶斯决策

本文获得了刻度指数族变量带误差情形下的贝叶斯决策,且利用解卷积的核方法构造出了经验贝叶斯决策.在适当的条件下,证明了经验贝叶斯决策的渐近最优性.     

Empirical likelihood for single-index models

The empirical likelihood method is especially useful for constructing confidence intervals or regions of the parameter of interest. This method has been extensively applied to linear regression and generalized linear regression models. In this paper, the empirical likelihood method for single-index regression models is studied. An estimated empirical log-likelihood approach to construct the confidence region of the regression parameter is developed. An adjusted empirical log-likelihood ratio is proved to be asymptotically standard chi-square. A simulation study indicates that compared with a normal approximation-based approach, the proposed method described herein works better in terms of coverage probabilities and areas (lengths) of confidence regions (intervals).     

Empirical bounds for ruin probabilities

We consider the classical model for an insurance business where the claims occur according to a Poisson process and where the distribution for the cost of each claim fulfills Cramér's tail-condition. Under these conditions Lundberg's constant R is of fundamental importance for ruin calculations.We derive estimates of R, based on an observation of the insurance business and investigate the statistical properties of those estimates. We further derive bounds and confidence intervals for ruin probabilities.     

Empirical modeling in dynamic econometrics

The roles of evaluation, discovery, and theory in modeling economic time series are analyzed. Being reductions of data processes, models reflect economic behavior, filtered by the measurement system; the reductions entail a taxonomy of information sets and hence of selection criteria characterizing congruency. No method of model construction is necessarily valid, but search affects only research efficiency, not the intrinsic usefulness of a model. Moreover, critical evaluation remains justifiable, with predictive failure revealing the information content of tiny samples, and encompassing sustaining progressivity. Theory-models of start and completions of private dwellings based on dynamized static equilibria and intertemporal optimization are contrasted. Empirical modeling illustrates the analysis.     

Empirical processes and random projections

In this note, we establish some bounds on the supremum of certain empirical processes indexed by sets of functions with the same L₂ norm. We present several geometric applications of this result, the most important of which is a sharpening of the Johnson-Lindenstrauss embedding Lemma. Our results apply to a large class of random matrices, as we only require that the matrix entries have a subgaussian tail.     

Empirical examination of Edgeworth series

The material presented is based on a numerical investigation that was made for five types of probability approximations which involve the first seven terms of the Edgeworth series expansion for the distribution of a continuous random variableT. For each approximation, the probability expressions considered in the investigation were Pr(T≦t), Pr(?t≦T≦t) and Pr(?t+1≦T≦t), whereT has zero mean, unit variance, and specified central momentsμ ₃,μ ₄,μ ₅. Computations were made for thoset values in the set ?4.00(0.25) 4.00 that are pertinent for the probability expression being considered and for all combinations of the following values forμ ₃,μ ₄,μ ₅∶μ ₃=?2.0, ?1.0, ?0.5,0.0, 0.5, 1.0, 2.0;μ ₄=1, 2, 3, 5, 10;μ ₅=0.0, 3μ ₃?6.0, 3μ ₃, 3μ ₃+6.0. The principal results of this paper consist of a specification (for each approximation, probability expression, andμ ₃,μ ₄,μ ₅ combination) of limits ont such that within these limits the computed values of the probability expression are meaningful; that is, satisfy required monotonicity properties as a function oft and are neither negative nor greater than unity. Also the values of Pr(T≦0) and of Pr(?1.75≦T≦1.75) are listed for the cases considered. These results indicate that the types of approximations investigated are of doubtful usefulness for the situations examined; that is, for cases where the third and higher order moments of the random variable considered differ substantially from those for the normal variable having the same mean and variance.