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1.
Alessio Moretti 《Logica Universalis》2009,3(1):19-57
Whereas geometrical oppositions (logical squares and hexagons) have been so far investigated in many fields of modal logic
(both abstract and applied), the oppositional geometrical side of “deontic logic” (the logic of “obligatory”, “forbidden”,
“permitted”, . . .) has rather been neglected. Besides the classical “deontic square” (the deontic counterpart of Aristotle’s
“logical square”), some interesting attempts have nevertheless been made to deepen the geometrical investigation of the deontic
oppositions: Kalinowski (La logique des normes, PUF, Paris, 1972) has proposed a “deontic hexagon” as being the geometrical
representation of standard deontic logic, whereas Joerden (jointly with Hruschka, in Archiv für Rechtsund Sozialphilosophie
73:1, 1987), McNamara (Mind 105:419, 1996) and Wessels (Die gute Samariterin. Zur Struktur der Supererogation, Walter de Gruyter,
Berlin, 2002) have proposed some new “deontic polygons” for dealing with conservative extensions of standard deontic logic
internalising the concept of “supererogation”. Since 2004 a new formal science of the geometrical oppositions inside logic
has appeared, that is “n-opposition theory”, or “NOT”, which relies on the notion of “logical bi-simplex of dimension m” (m = n − 1). This theory has received a complete mathematical foundation in 2008, and since then several extensions. In this paper,
by using it, we show that in standard deontic logic there are in fact many more oppositional deontic figures than Kalinowski’s
unique “hexagon of norms” (more ones, and more complex ones, geometrically speaking: “deontic squares”, “deontic hexagons”,
“deontic cubes”, . . ., “deontic tetraicosahedra”, . . .): the real geometry of the oppositions between deontic modalities
is composed by the aforementioned structures (squares, hexagons, cubes, . . ., tetraicosahedra and hyper-tetraicosahedra),
whose complete mathematical closure happens in fact to be a “deontic 5-dimensional hyper-tetraicosahedron” (an oppositional
very regular solid).
相似文献
2.
Ahlswede Rudolf Khachatrian Levon H. Mauduit C. Sárközy A. 《Periodica Mathematica Hungarica》2003,46(2):107-118
In earlier papers finite pseudorandom binary sequences were studied, quantitative measures of pseudorandomness of them were
introduced and studied, and large families of “good” pseudorandom sequences were constructed. In certain applications (cryptography)
it is not enough to know that a family of “good” pseudorandom binary sequences is large, it is a more important property if
it has a “rich”, “complex” structure. Correspondingly, the notion of “f-complexity” of a family of binary sequences is introduced. It is shown that the family of “good” pseudorandom binary sequences
constructed earlier is also of high f-complexity. Finally, the cardinality of the smallest family achieving a prescibed f-complexity and multiplicity is estimated.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
3.
J. Sakalauskaitė 《Lithuanian Mathematical Journal》2007,47(3):266-276
In this paper, we consider branching time temporal logic CT L with epistemic modalities for knowledge (belief) and with awareness operators. These logics involve the discrete-time linear
temporal logic operators “next” and “until” with the branching temporal logic operator “on all paths”. In addition, the temporal
logic of knowledge (belief) contains an indexed set of unary modal operators “agent i knows” (“agent i believes”). In a language of these logics, there are awareness operators. For these logics, we present sequent calculi with
a restricted cut rule. Thus, we get proof systems where proof-search becomes decidable. The soundness and completeness for
these calculi are proved.
Published in Lietuvos Matematikos Rinkinys, Vol. 47, No. 3, pp. 328–340, July–September, 2007. 相似文献
4.
Summary As a criterion for the reduction to a complete class of decision rule in case where actions, samples and states are finite
in number, “regret-relief ratio” criterion and “incremental loss-gain ratio” criterion were introduced in 2-state of nature
case [2]. In this paper, “generalized regret-relief ratio” criterion ink-state of nature case is introduced as an extension of “regret-relief ratio” criterion and its usefulness is shown with an
example.
The Institute of Statistical Mathematics 相似文献
5.
We study the R-controllability (the controllability within the attainability set) and the R-observability of time-varying linear differential-algebraic equations (DAE). We analyze DAE under assumptions guaranteeing
the existence of a structural form (which is called “equivalent”) with separated “differential” and “algebraic” subsystems.
We prove that the existence of this form guarantees the solvability of the corresponding conjugate system, and construct the
corresponding “equivalent form” for the conjugate DAE. We obtain conditions for the R-controllability and R-observability, in particular, in terms of controllability and observability matrices. We prove theorems that establish certain
connections between these properties. 相似文献
6.
T. V. Panchapagesan 《Rendiconti del Circolo Matematico di Palermo》1995,44(3):417-440
The concept of an orthogonal spectral representation (OTSR) of a Hilbert spaceH relative to a spectral measureE(.) is introduced and it is shown that every Hilbert space admits an OTSR relative to a given spectral measure. Apart from
the various results obtained about OTSRs, the principal result of Allan Brown (1974) is deduced as an easy consequence of
this study. A new complete system of unitary invariants called the “equivalence of OTSRs”, is given for spectral measures.
Two special types of OTSRs called “BOTSR” and “COBOTSR” are introduced and characterized respectively in terms of the “GCGS-property”
and “CGS-property” of the associated spectral measure. Various complete systems of unitary invariants are given for spectral
measures with the GCGS-property. Finally, the Wecken-Plesner-Rohlin theorem on hermitian operators with simple spectra is
generalized to arbitrary spectral measures. 相似文献
7.
Rade T. Živaljević 《Discrete and Computational Geometry》2009,41(1):135-161
This paper lays the foundation for a theory of combinatorial groupoids that allows us to use concepts like “holonomy”, “parallel transport”, “bundles”, “combinatorial curvature”, etc. in the context
of simplicial (polyhedral) complexes, posets, graphs, polytopes and other combinatorial objects. We introduce a new, holonomy-type
invariant for cubical complexes, leading to a combinatorial “Theorema Egregium” for cubical complexes that are non-embeddable
into cubical lattices. Parallel transport of Hom-complexes and maps is used as a tool to extend Babson–Kozlov–Lovász graph coloring results to more general statements about
nondegenerate maps (colorings) of simplicial complexes and graphs.
The author was supported by grants 144014 and 144026 of the Serbian Ministry of Science and Technology. 相似文献
8.
The Generalized Riemann Problem (GRP) for a nonlinear hyperbolic system of m balance laws (or alternatively “quasi-conservative” laws) in one space dimension is now well-known and can be formulated
as follows: Given initial-data which are analytic on two sides of a discontinuity, determine the time evolution of the solution
at the discontinuity. In particular, the GRP numerical scheme (second-order high resolution) is based on an analytical evaluation
of the first time derivative. It turns out that this derivative depends only on the first-order spatial derivatives, hence
the initial data can be taken as piecewise linear. The analytical solution is readily obtained for a single equation (m = 1) and, more generally, if the system is endowed with a complete (coordinate) set of Riemann invariants. In this case it
can be “diagonalized” and reduced to the scalar case. However, most systems with m > 2 do not admit such a set of Riemann invariants. This paper introduces a generalization of this concept: weakly coupled
systems (WCS). Such systems have only “partial set” of Riemann invariants, but these sets are weakly coupled in a way which
enables a “diagonalized” treatment of the GRP. An important example of a WCS is the Euler system of compressible, nonisentropic
fluid flow (m = 3). The solution of the GRP discussed here is based on a careful analysis of rarefaction waves. A “propagation of singularities”
argument is applied to appropriate Riemann invariants across the rarefaction fan. It serves to “rotate” initial spatial slopes
into “time derivative”. In particular, the case of a “sonic point” is incorporated easily into the general treatment. A GRP
scheme based on this solution is derived, and several numerical examples are presented. Special attention is given to the
“acoustic approximation” of the analytical solution. It can be viewed as a proper linearization (different from the approach
of Roe) of the nonlinear system. The resulting numerical scheme is the simplest (second-order, high-resolution) generalization
of the Godunov scheme. 相似文献
9.
The relationships between piecewise-Koszul algebras and other “Koszul-type” algebras are discussed. The Yoneda-Ext algebra
and the dual algebra of a piecewise-Koszul algebra are studied, and a sufficient condition for the dual algebra A
! to be piecewise-Koszul is given. Finally, by studying the trivial extension algebras of the path algebras of Dynkin quivers
in bipartite orientation, we give explicit constructions for piecewise-Koszul algebras with arbitrary “period” and piecewise-Koszul
algebras with arbitrary “jump-degree”. 相似文献
10.
O. D. Frolkina 《Moscow University Mathematics Bulletin》2009,64(6):253-258
In 1998, Y. Benyamini published interesting results concerning interpolation of sequences using continuous functions ℝ → ℝ.
In particular, he proved that there exists a continuous function ℝ → ℝ which in some sense “interpolates” all sequences (x
n
)
n∈ℤ ∈ [0, 1]ℤ “simultaneously.” In 2005, M.R. Naulin and C. Uzcátegui unified and generalized Benyamini’s results. In this paper, the case
of topological spaces X and Y with an Abelian group acting on X is considered. A similar problem of “simultaneous interpolation” of all “generalized sequences” using continuous mappings
X → Y is posed. Further generalizations of Naulin-Uncátegui theorems, in particular, multidimensional analogues of Benyamini’s
results are obtained. 相似文献
11.
R. Douglas Chatham 《Rendiconti del Circolo Matematico di Palermo》2001,50(3):509-542
Résumé D'après D. E. Dobbs, Houston J. Math. 23 (1997), 1–11, nous disons que l'anneau (commutatif)A est un anneau-“going-down” siA/P est un domaine-“going-down” pour chaque idéal premier deA. Etant donné une extension,R⊆T, nous disons que (R, T) est une paire d'anneaux-“going-down” (respectivement, une paire “going-down”) siS est un anneau-“going-down” pour chaque anneau tels queR⊆S⊆T (resp., si “going-down” est satisfait par chaque extension d'anneauxA⊆B tels queR⊆A⊆B⊆T). On montre que siR est un anneau de la dimension 0 (au sens de Krull), alors (R, T) est une paire d'anneaux-“going-down” si et seulement sitr.deg.
R/(P∩R)
T/P≤1 pour chaque idéal premier minimalP deT. Des résultats partiels sont obtenus quandR n'est pas de dimension 0. En outre, si (R, T) est une paire d'anneaux-“going-down” tel queT ait un seul idéal premier minimal, alors (R, T) est une paire “going-down”. Des résultats dans l'esprit ci-dessus sont également obtenus pour quelques autres types de paires.
This paper is taken from the author's doctoral dissertation of May 2000, written under the direction of Professor David E. Dobbs of the University of Tennessee, Knoxville. 相似文献
This paper is taken from the author's doctoral dissertation of May 2000, written under the direction of Professor David E. Dobbs of the University of Tennessee, Knoxville. 相似文献
12.
V. G. Durnev 《Mathematical Notes》2000,67(2):152-159
In the paper we study the algorithmic nature of some “simple” fragments of positive theories with “few” constants for free
noncyclic semigroups.
Translated fromMatematicheskie Zametki, Vol. 67, No. 2, pp. 191–200, February, 2000. 相似文献
13.
Aubrey Blecher Charlotte Brennan Toufik Mansour 《Central European Journal of Mathematics》2012,10(2):788-796
Compositions and partitions of positive integers are often studied in separate frameworks where partitions are given by q-series generating functions and compositions exhibiting specific patterns are designated by generating functions for these
patterns. Here, we view compositions as alternating sequences of weakly increasing and strictly decreasing partitions (i.e.
alternating blocks). We obtain generating functions for the number of such partitions in terms of the size of the composition,
the number of parts and the total number of “valleys” and “peaks”. From this, we find the total number of “peaks” and “valleys”
in the composition of n which have the mentioned pattern. We also obtain the generating function for compositions which split into just two partition
blocks. Finally, we obtain the two generating functions for compositions of n that start either with a weakly increasing partition or a strictly decreasing partition. 相似文献
14.
We construct an asymptotics of the solution the Laplace equation in a “long” rectangle with the directional derivative given
on its “long sides” and Dirichlet data on its “short sides.” By using the asymptotics, we calculate one of the integral characteristics,
namely, the magnetoresistance. We obtain new formulas for the low-magnetic field magnetoresistance.
Translated fromMatematicheskie Zametki, Vol. 65, No. 4, pp. 520–532, April, 1999. 相似文献
15.
Acceptable moves for the “worthwhile-to-move” incremental principle are such that “advantages-to-move” are higher than some
fraction of “costs-to-move”. When combined with optimization, this principle gives raise to adaptive local search proximal
algorithms. Convergence results are given in two distinctive cases, namely low local costs-to-move and high local costs-to-move.
In this last case, one obtains a dynamic cognitive approach to Ekeland’s ϵ-variational principle. Introduction of costs-to-move in the algorithms yields robustness and stability properties. 相似文献
16.
We calculate the distribution of the sextuple statistic over the hyperoctahedral group B
n
that involves the flag-excedance and flag-descent numbers “fexc” and “fdes,” the flag-major index “fmaj,” the positive and
negative fixed point numbers “
” and “
” and the negative letter number “neg.” Several specializations are considered. In particular, the joint distribution for
the pair
is explicitly derived.
相似文献
17.
Summary The formal asymptotic analysis of Latifi et al. [4] suggests that the Mixmaster Universe model possesses movable transcendental
singularities and thus is nonintegrable in the sense that it does not satisfy the Painlevé property (i.e., singularities with
nonalgebraic branching). In this paper, we present numerical evidence of the nonintegrability of the Mixmaster model by studying
the singularity patterns in the complext-plane, wheret is the “physical” time, as well as in the complex τ-plane, where τ is the associated “logarithmic” time. More specifically,
we show that in the τ-plane there appears to exist a “natural boundary” of remarkably intricate structure. This boundary lies
at the ends of a sequence of smaller and smaller “chimneys” and consists of the type of singularities studied in [4], on which
pole-like singularities accumulate densely. We also show numerically that in the complext-plane there appear to exist complicated, dense singularity patterns and infinitely-sheeted solutions with sensitive dependence
on initial conditions. 相似文献
18.
This paper presents a method of estimation of an “optimal” smoothing parameter (window width) in kernel estimators for a probability
density. The obtained estimator is calculated directly from observations. By “optimal” smoothing parameters we mean those
parameters which minimize the mean integral square error (MISE) or the integral square error (ISE) of approximation of an
unknown density by the kernel estimator. It is shown that the asymptotic “optimality” properties of the proposed estimator
correspond (with respect to the order) to those of the well-known cross-validation procedure [1, 2].
Translated fromStatisticheskie Metody Otsenivaniya i Proverki Gipotez, pp. 67–80, Perm, 1990. 相似文献
19.
G. I. Bizhanova 《Journal of Mathematical Sciences》2006,136(2):3672-3681
We construct automodel solutions for the one-dimensional two-phase Stefan, Florin, and Verigin free boundary problems for
parabolic equations in the case where the initial and boundary data are not adjusted. It is shown that in the Stefan problem
with “supercooling,” the liquid temperature may be less than the temperature of the phase transition, i.e., the liquid may
be “supercooled” while the solid may be “superheated.” Bibliography: 8 titles.
Dedicated to the memory of Olga Aleksandrovna Ladyzhenskaya
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 318, 2004, pp. 42–59. 相似文献