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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.
As systems dealing with preferences become more sophisticated, it becomes essential to deal with various kinds of preference
statements and their interaction. We introduce a non-monotonic logic distinguishing sixteen kinds of preferences, ranging
from strict to loose and from careful to opportunistic, and two kinds of ways to deal with uncertainty, either optimistically
or pessimistically. The classification of the various kinds of preferences is inspired by a hypothetical agent comparing the
two alternatives of a preference statement. The optimistic and pessimistic way of dealing with uncertainty correspond on the
one hand to considering either the best or the worst states in the comparison of the two alternatives of a preference statement,
and on the other hand to the calculation of least or most specific “distinguished” preference orders from a set of preference
statements. We show that each way to calculate distinguished preference orders is compatible with eight kinds of preferences,
in the sense that it calculates a unique distinguished preference order for a set of such preference statements, and we provide
efficient algorithms that calculate these unique distinguished preference orders. In general, optimistic kinds of preferences
are compatible with optimism in calculating distinguished preference orders, and pessimistic kinds of preferences are compatible
with pessimism in calculating distinguished preference orders. However, these two sets of eight kinds of preferences are not
exclusive, such that some kinds of preferences can be used in both ways to calculate distinguished preference orders, and
other kinds of preferences cannot be used in either of them. We also consider the merging of optimistically and pessimistically
constructed distinguished preferences orders. 相似文献
3.
“Setting” n-Opposition 总被引:1,自引:1,他引:0
Régis Pellissier 《Logica Universalis》2008,2(2):235-263
Our aim is to show that translating the modal graphs of Moretti’s “n-opposition theory” (2004) into set theory by a suited device, through identifying logical modal formulas with appropriate
subsets of a characteristic set, one can, in a constructive and exhaustive way, by means of a simple recurring combinatory,
exhibit all so-called “logical bi-simplexes of dimension n” (or n-oppositional figures, that is the logical squares, logical hexagons, logical cubes, etc.) contained in the logic produced
by any given modal graph (an exhaustiveness which was not possible before). In this paper we shall handle explicitly the classical
case of the so-called 3(3)-modal graph (which is, among others, the one of S5), getting to a very elegant tetraicosahedronal
geometrisation of this logic.
相似文献
4.
Benedikt Löwe 《Archive for Mathematical Logic》2001,40(8):651-664
We investigate Turing cones as sets of reals, and look at the relationship between Turing cones, measures, Baire category
and special sets of reals, using these methods to show that Martin's proof of Turing Determinacy (every determined Turing
closed set contains a Turing cone or is disjoint from one) does not work when you replace “determined” with “Blackwell determined”.
This answers a question of Tony Martin.
Received: 6 December 1999 / Revised version: 28 June 2000 Published online: 3 October 2001 相似文献
5.
John-Michael Kuczynski 《Acta Analytica》2004,19(32):107-141
Recently, many have argued that phenomenal content supervenes on representational content; i.e. that the phenomenal character of an experience is wholly determined (metaphysically, not
causally) by the representational content of that experience. This paper it identifies many counter-examples to intentionalism.
Further, this paper shows that, if intentionalism were correct, that would require that an untenable form of representational
atomism also be correct. Our argument works both against the idea that phenomenal content supervenes on “conceptual” content
and also against the idea that it supervenes on “non-conceptual” content. It is also shown that the distinction between conceptual
and non-conceptual content has been wrongly conceived as distinction between different kinds of information: in fact, it is
a distinction between ways of packaging information that is, in itself, neither conceptual or non-conceptual. 相似文献
6.
A certain class of atomic, semimodular, semisimple partition lattices is studied. It is shown that this class is precisely
the class of congruence lattices of equivalence algebras.
The first author is granted by project POCTI-ISFL-1-143 of the “Centro de álgebra da Universidade de Lisboa”, supported by
FCT and FEDER. 相似文献
7.
Higgs bundles and non-abelian Hodge theory provide holomorphic methods with which to study the moduli spaces of surface group
representations in a reductive Lie group G. In this paper we survey the case in which G is the isometry group of a classical Hermitian symmetric space of non-compact type. Using Morse theory on the moduli spaces
of Higgs bundles, we compute the number of connected components of the moduli space of representations with maximal Toledo
invariant
Members of VBAC (Vector Bundles on Algebraic Curves). Second and Third authors partially supported by Ministerio de Educación
y Ciencia and Conselho de Reitores das Universidades Portuguesas through Acción Integrada Hispano-Lusa HP2002-0017 (Spain)/E–30/03
(Portugal). First and Second authors partially supported by Ministerio de Educación y Ciencia (Spain) through Project MTM2004-07090-C03-01.
Third author partially supported by the Centro de Matemática da Universidade do Porto and the project POCTI/MAT/58549/2004,
financed by FCT (Portugal) through the programmes POCTI and POSI of the QCA III (2000–2006) with European Community (FEDER)
and national funds. The second author visited the IHES with the partial support of the European Commission through its 6th
Framework Programme “Structuring the European Research Area” and the Contract No. RITA-CT-2004-505493 for the provision of
Transnational Access implemented as Specific Support Action 相似文献
8.
In statistics of extremes, inference is often based on the excesses over a high random threshold. Those excesses are approximately
distributed as the set of order statistics associated to a sample from a generalized Pareto model. We then get the so-called
“maximum likelihood” estimators of the tail index γ. In this paper, we are interested in the derivation of the asymptotic distributional properties of a similar “maximum likelihood”
estimator of a positive tail index γ, based also on the excesses over a high random threshold, but with a trial of accommodation of bias in the Pareto model underlying
those excesses. We next proceed to an asymptotic comparison of the two estimators at their optimal levels. An illustration
of the finite sample behaviour of the estimators is provided through a small-scale Monte Carlo simulation study.
Research partially supported by FCT/POCTI and POCI/FEDER. 相似文献
9.
Giuseppe Mingione 《Applications of Mathematics》2006,51(4):355-426
I am presenting a survey of regularity results for both minima of variational integrals, and solutions to non-linear elliptic,
and sometimes parabolic, systems of partial differential equations. I will try to take the reader to the Dark Side...
This work has been partially supported by MIUR via the project “Calcolo delle Variazioni” (Cofin 2004), and by GNAMPA via
the project “Studio delle singolarità in problemi geometrici e variazionali”. 相似文献
10.
Many classes of graphs where the vertex coloring problem is polynomially solvable are known, the most prominent being the
class of perfect graphs. However, the list-coloring problem is NP-complete for many subclasses of perfect graphs. In this
work we explore the complexity boundary between vertex coloring and list-coloring on such subclasses of perfect graphs where
the former admits polynomial-time algorithms but the latter is NP-complete. Our goal is to analyze the computational complexity
of coloring problems lying “between” (from a computational complexity viewpoint) these two problems: precoloring extension,
μ-coloring, and (γ,μ)-coloring.
Flavia Bonomo partially supported by UBACyT Grants X606 and X069 (Argentina), and CNPq under PROSUL project Proc. 490333/2004-4
(Brazil).
Guillermo Durán partially supported by FONDECyT Grant 1080286 and Millennium Science Institute “Complex Engineering Systems”
(Chile), and CNPq under PROSUL project Proc. 490333/2004-4 (Brazil).
Javier Marenco partially supported by UBACyT Grant X069 (Argentina), and CNPq under PROSUL project Proc. 490333/2004-4 (Brazil). 相似文献
11.
Wolfgang Lenzen 《Logica Universalis》2008,2(1):43-58
In the 18th century, Gottfried Ploucquet developed a new syllogistic logic where the categorical forms are interpreted as
set-theoretical identities, or diversities, between the full extension, or a non-empty part of the extension, of the subject
and the predicate. With the help of two operators ‘O’ (for “Omne”) and ‘Q’ (for “Quoddam”), the UA and PA are represented
as ‘O(S) – Q(P)’ and ‘Q(S) – Q(P)’, respectively, while UN and PN take the form ‘O(S) > O(P)’ and ‘Q(S) > O(P)’, where ‘>’ denotes set-theoretical disjointness. The use of the symmetric operators ‘–’ and ‘>’ gave rise to a new conception
of conversion which in turn lead Ploucquet to consider also the unorthodox propositions O(S) – O(P), Q(S) – O(P), O(S) > Q(P), and Q(S) > Q(P). Although Ploucquet’s critique of the traditional theory of opposition turns out to be mistaken, his theory of the “Quantification
of the Predicate” is basically sound and involves an interesting “Double Square of Opposition”.
My thanks are due to Hanno von Wulfen for helpful discussions and for transforming the word-document into a Latex-file. 相似文献
12.
A new class of estimators of a “scale” second order parameter 总被引:1,自引:0,他引:1
For a large class of heavy-tailed distribution functions F in the domain of attraction for maxima of an Extreme Value distribution with tail index γ>0, the function A(t), controlling the speed of convergence of maximum values, linearly normalized, towards a non-degenerate limiting random variable,
may be parameterized as , ρ < 0, β∈ℝ, where β and ρ are second order parameters. The estimation of ρ, the “shape” second order parameter has been extensively addressed in the literature, but practically nothing has been done
related to the estimation of the “scale” second order parameter β. In this paper, and motivated by the importance of a reliable β-estimation in recent reduced bias tail index estimators, we shall deal with such a topic. Under a semi-parametric framework,
we introduce a class of β-estimators and study their consistency. We deal with the conditions enabling us to get the asymptotic normality of the members
of this class, and we illustrate the behaviour of the estimators, through Monte Carlo simulation techniques.
Research partially supported by FCT / POCTI and POCI / FEDER. 相似文献
13.
Kenneth May in 1952 proved a classical theorem characterizing simple majority rule for two alternatives. The present paper
generalizes May’s theorem to the case of three alternatives, but where the voters’ preference relations are required to be
trees with alternatives at the leaves.
This paper with title “May’s Theorem for Trees” was presented at the joint DIMACS-LAMSADE workshop on Computer Science and
Decision Theory, Université Paris-Dauphine, Paris 27–29 October 2004. It appeared in the proceedings Annales du LAMSADE 3 (2004), 259–266. 相似文献
14.
David P. Hunt 《Acta Analytica》2007,22(1):3-15
The most serious challenge to Frankfurt-type counterexamples to the Principle of Alternate Possibilities (PAP) comes in the
form of a dilemma: either the counterexample presupposes determinism, in which case it begs the question; or it does not presuppose
determinism, in which case it fails to deliver on its promise to eliminate all alternatives that might plausibly be thought
to satisfy PAP. I respond to this challenge with a counterexample in whichconsidering an alternative course of action is anecessary condition fordeciding to act otherwise, and the agent does not in fact consider the alternative. I call this a “buffer case,” because the morally
relevant alternative is “buffered” by the requirement that the agent first consider the alternative. Suppose further that
the agent’s considering an alternative action—entering the buffer zone—is what would trigger the counterfactual intervener.
Then it would appear that PAP-relevant alternatives are out of reach.
I defend this counterexample to PAP against three objections: that considering an alternative isitself a morally relevant alternative; that buffer cases can be shown to containother alternatives that arguably satisfy PAP; and that even if the agent’spresent access to PAP-relevant alternatives were eliminated, PAP could still be satisfied in virtue ofearlier alternatives. I conclude that alternative possibilities are a normal symptom, but not an essential constituent, of moral
agency. 相似文献
15.
We study Lebesgue and Atsuji spaces within subsystems of second order arithmetic. The former spaces are those such that every
open covering has a Lebesgue number, while the latter are those such that every continuous function defined on them is uniformly
continuous. The main results we obtain are the following: the statement “every compact space is Lebesgue” is equivalent to
; the statements “every perfect Lebesgue space is compact” and “every perfect Atsuji space is compact” are equivalent to ; the statement “every Lebesgue space is Atsuji” is provable in ; the statement “every Atsuji space is Lebesgue” is provable in . We also prove that the statement “the distance from a closed set is a continuous function” is equivalent to .
Received: February 2, 1996 相似文献
16.
Valentin A. Bazhanov 《Logica Universalis》2008,2(1):71-76
In the XIXth century there was a persistent opposition to Aristotelian logic. Nicolai A. Vasiliev (1880–1940) noted this opposition
and stressed that the way for the novel – non-Aristotelian – logic was already paved. He made an attempt to construct non-Aristotelian
logic (1910) within, so to speak, the form (but not in the spirit) of the Aristotelian paradigm (mode of reasoning). What
reasons forced him to reassess the status of particular propositions and to replace the square of opposition by the triangle
of opposition? What arguments did Vasiliev use for the introduction of new classes of propositions and statement of existence
of various levels in logic? What was the meaning and role of the “method of Lobachevsky” which was implemented in construction
of imaginary logic? Why did psychologism in the case of Vasiliev happen to be an important factor in the composition of the
new ‘imaginary’ logic, as he called it?
相似文献
17.
Greedoids were introduced by the authors as generalizations of matroids providing a framework for the greedy algorithm. In
this paper they are studied from a structural aspect. Definitions of basic matroid-theoretical concepts such as rank and closure
can be generalized to greedoids, even though they loose some of their fundamental properties. The rank function of a greedoid
is only “locally” submodular. The closure operator is not monotone but possesses a (relaxed) Steinitz—McLane exchange property.
We define two classes of subsets, called rank-feasible and closure-feasible, so that the rank and closure behave nicely for
them. In particular, restricted to rank-feasible sets the rank function is submodular. Finally we show that Rado’s theorem
on independent transversals of subsets of matroids remains valid for feasible transversals of certain sets of greedoids.
Dedicated to Paul Erdős on his seventieth birthday
Supported by the joint research project “Algorithmic Aspects of Combinatorial Optimization” of the Hungarian Academy of Sciences
(Magyar Tudományos Akadémia) and the German Research Association (Deutsche Forschungsgemeinschaft, SFB 21). 相似文献
18.
Wayne A. Davis 《Acta Analytica》2005,20(1):29-42
Contextualist theories of knowledge offer a semantic hypothesis to explain the observed contextual variation in what people
say they know, and the difficulty people have resolving skeptical paradoxes. Subject or speaker relative versions make the
truth conditions of “S knows that p” depend on the standards of either the knower’s context (Hawthorne and Stanley) or those
of the speaker’s context (Cohen and DeRose). Speaker contextualism avoids objections to subject contextualism, but is implausible
in light of evidence that “know” does not behave like an indexical. I deepen and extend these criticisms in light of recent
defenses by contextualists (including Ludlow). Another difficulty is that whether certain standards are salient or intended
does not entail that they are the proper standards. A normative form of contextualism on which the truth of a knowledge claim
depends on the proper standards for the context is more promising, but still unsatisfactory whether the view is speaker or
subject relative. I defend alternative explanations for the observed linguistic and psychological data: a pragmatic account
for some cases and a cognitive account for others.1
I presented this paper at the 2004 Bled Conference on Contextualism, sponsored by Mirabor and Northern Illinois Universities. 相似文献
19.
Jue Wang San-Yang Liu Jie Zhang Shou-Yang Wang 《Fuzzy Optimization and Decision Making》2006,5(1):5-20
The family of Ordered Weighted Averaging (OWA) operators, as introduced by Yager, appears to be very useful in multi-criteria
decision-making (MCDM). In this paper, we extend a family of parameterized OWA operators to fuzzy MCDM based on vague set
theory, where the characteristics of the alternatives are presented by vague sets. These families are specified by a few parameters
to aggregate vague values instead of the intersection and union operators proposed by Chen. The proposed method provides a
“soft” and expansive way to help the decision maker to make his decisions. Examples are shown to illustrate the procedure
of the proposed method at the end of this paper. 相似文献
20.
Jorge J. Betancor Jacek Dziubański Jose Luis Torrea 《Journal d'Analyse Mathématique》2009,107(1):195-219
In this paper, we study Hardy spaces associated with two Bessel operators. Two different kind of Hardy spaces appear. These
differences are transparent in the corresponding atomic decompositions.
The first author was partially supported by MTM2004/05878.
The second author was supported by the European Commission Marie Curie Host Fellowship for the Transfer of Knowledge “Harmonic
Analysis, Nonlinear Analysis and Probability” MTKD-CT-2004-013389 and by Polish funds for science in years 2005–2008 (research
project 1P03A03029). 相似文献