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1.
OVERSTREET GEORGE A. JR.; BRADLEY EDWIN L. JR.; KEMP ROBERT S. JR. 《IMA Journal of Management Mathematics》1992,4(1):97-109
Received on 1 July 1991. Predicting human behaviour patterns with linear correlationmodels has absorbed researchers for the past five decades. Althoughmost observers generally concede that humans are inferior tosuch models in combining information, linear scoring modelsare unfortunately, plagued by the flat-maximum effect or thecurse of insensitivity. As Lovie & Lovie(1986)observe: The predictive ability of linear models is insensitiveto large variations in the size of regression weights and tothe number of predictors. In essence, seemingly differentscoringmodels tend to produce indistinguishable predictive outcomes. Since its demonstration by Dawes & Corrigan (1974), observershave cast the flat maximum in a decidedly negative light. Incontrast, Lovie & Lovie (1986) present a provocatively contrarianview of the flat maximums positive potential. In thissame vein, we examine the predictive power of a generic credit-scoringmodel versus individual empirically derived systems. If, asWainer (1976) noted in regard to the flat maximum, itdont make no nevermind, generic credit-scoringmodels could provide cheaper alternatives to individual empiricallyderived models. During the period 1984–8, a series of linear credit-scoringmodels were developed for ten Southeastern U.S. credit unions.For each credit union, stepwise multiple regression was employedto select a subset of explanatory variables to be used in adiscriminant analysis. A generic credit-scoring equation wasdeveloped from the resulting discriminant analyses using weightedaverage coefficients from five systems. The predictive powerof the generic model was compared to the predictive power ofholdout sample of the five remaining credit-scoring models. In all cases, the generic model's performance was very closeto that of the empirically derived models. Thus, our findingssupport Lovie & Lovie's (1986) challenge to the conventionalwisdom that the flat maximum casts a pall on the successfulmodelling of judgement processes. Indeed, the flat maximum impliesa positive role for simpler, and hence cheaper, generic models.Although further research is needed, it should be possible todevelop hybrid models with generic cores that perform as wellas empirically derived linear models. 相似文献
2.
Grigori Mints 《Annals of Pure and Applied Logic》2010,162(3):237-242
A predicate extension SQHT= of the logic of here-and-there was introduced by V. Lifschitz, D. Pearce, and A. Valverde to characterize strong equivalence of logic programs with variables and equality with respect to stable models. The semantics for this logic is determined by intuitionistic Kripke models with two worlds (here and there) with constant individual domain and decidable equality. Our sequent formulation has special rules for implication and for pushing negation inside formulas. The soundness proof allows us to establish that SQHT= is a conservative extension of the logic of weak excluded middle with respect to sequents without positive occurrences of implication. The completeness proof uses a non-closed branch of a proof search tree. The interplay between rules for pushing negation inside and truth in the “there” (non-root) world of the resulting Kripke model can be of independent interest. We prove that existence is definable in terms of remaining connectives. 相似文献
3.
4.
A. B. Gordienko 《Algebra and Logic》2007,46(5):289-296
We deal with Sylvan’s logic CCω. It is proved that this logic is a conservative extension of positive intuitionistic logic. Moreover, a paraconsistent extension
of Sylvan’s logic is constructed, which is also a conservative extension of positive intuitionistic logic and has the property
of being decidable. The constructed logic, in which negation is defined via a total accessibility relation, is a natural intuitionistic
analog of the modal system S5. For this logic, an axiomatization is given and the completeness theorem is proved.
Supported by RFBR grant No. 06-01-00358 and by the Council for Grants (under RF President) and State Aid of Fundamental Science
Schools, project NSh-4787.2006.1.
__________
Translated from Algebra i Logika, Vol. 46, No. 5, pp. 533–547, September–October, 2007. 相似文献
5.
Saturated models constitute one of the powerful methods of conventional model theory, with many applications. Here we develop
a categorical abstract model theoretic approach to saturated models within the theory of institutions. The most important
consequence is that the method of saturated models becomes thus available to a multitude of logical systems from logic or
from computing science. In this paper we define the concept of saturated model at an abstract institution-independent level
and develop the fundamental existence and uniqueness theorems. As an application we prove a general institution-independent
version of the Keisler–Shelah isomorphism theorem “any two elementarily equivalent models have isomorphic ultrapowers” (assuming
Generalized Continuum Hypothesis). 相似文献
6.
In this paper we study semidefinite programming (SDP) models for a class of discrete and continuous quadratic optimization
problems in the complex Hermitian form. These problems capture a class of well-known combinatorial optimization problems,
as well as problems in control theory. For instance, they include the MAX-3-CUT problem where the Laplacian matrix is positive
semidefinite (in particular, some of the edge weights can be negative). We present a generic algorithm and a unified analysis
of the SDP relaxations which allow us to obtain good approximation guarantees for our models. Specifically, we give an -approximation algorithm for the discrete problem where the decision variables are k-ary and the objective matrix is positive semidefinite. To the best of our knowledge, this is the first known approximation
result for this family of problems. For the continuous problem where the objective matrix is positive semidefinite, we obtain
the well-known π /4 result due to Ben-Tal et al. [Math Oper Res 28(3):497–523, 2003], and independently, Zhang and Huang [SIAM
J Optim 16(3):871–890, 2006]. However, our techniques simplify their analyses and provide a unified framework for treating
those problems. In addition, we show for the first time that the gap between the optimal value of the original problem and
that of the SDP relaxation can be arbitrarily close to π /4. We also show that the unified analysis can be used to obtain
an Ω(1/ log n)-approximation algorithm for the continuous problem in which the objective matrix is not positive semidefinite.
This research was supported in part by NSF grant DMS-0306611. 相似文献
7.
《Annals of Pure and Applied Logic》2023,174(6):103268
We study the model theory of vector spaces with a bilinear form over a fixed field. For finite fields this can be, and has been, done in the classical framework of full first-order logic. For infinite fields we need different logical frameworks. First we take a category-theoretic approach, which requires very little set-up. We show that linear independence forms a simple unstable independence relation. With some more work we then show that we can also work in the framework of positive logic, which is much more powerful than the category-theoretic approach and much closer to the classical framework of full first-order logic. We fully characterise the existentially closed models of the arising positive theory. Using the independence relation from before we conclude that the theory is simple unstable, in the sense that dividing has local character but there are many distinct types. We also provide positive version of what is commonly known as the Ryll-Nardzewski theorem for ω-categorical theories in full first-order logic, from which we conclude that bilinear spaces over a countable field are ω-categorical. 相似文献
8.
Giangiacomo Gerla 《Mathematical Logic Quarterly》1994,40(3):357-380
Let S be a set, P(S) the class of all subsets of S and F(S) the class of all fuzzy subsets of S. In this paper an “extension principle” for closure operators and, in particular, for deduction systems is proposed and examined. Namely we propose a way to extend any closure operator J defined in P(S) into a fuzzy closure operator J* defined in F(S). This enables us to give the notion of canonical extension of a deduction system and to give interesting examples of fuzzy logics. In particular, the canonical extension of the classical propositional calculus is defined and it is showed its connection with possibility and necessity measures. Also, the canonical extension of first order logic enables us to extend some basic notions of programming logic, namely to define the fuzzy Herbrand models of a fuzzy program. Finally, we show that the extension principle enables us to obtain fuzzy logics related to fuzzy subalgebra theory and graded consequence relation theory. Mathematics Subject Classification : 03B52. 相似文献
9.
S. V. Sudoplatov 《Algebra and Logic》2007,46(2):134-146
A syntactic approach is described to constructing generic models which generalizes the known semantic one. A sufficient condition
of a generic model being homogeneous is specified. It is shown that, within the syntactic approach, any countable homogeneous
model is generic. Criteria and a sufficient condition are given for the generic models created in syntactic constructions
to be saturated.
Supported by RFBR grant No. 05-01-00411, and by the Council for Grants (under RF President) and State Aid of Fundamental Science
Schools via project NSh-4787.2006.1.
__________
Translated from Algebra i Logika, Vol. 46, No. 2, pp. 244–268, March–April, 2007. 相似文献
10.
D. Saracino 《Israel Journal of Mathematics》1976,25(3-4):241-248
Letn be a positive integer, letK
n denote the theory of groups nilpotent of class at mostn, and letK
n
+
denote the theory of torsion-free groups nilpotent of class at mostn. We show that ifn≧2 then neitherK
n norK
n
+
has a model companion. ForK
n we obtain the stronger result that the class of finitely generic models is disjoint from the class of infinitely generic
models. We also give some other results about existentially complete nilpotent groups.
Dedicated to the Memory of Abraham Robinson. 相似文献
11.
Disturbing Fuzzy Propositional Logic and its Operators 总被引:1,自引:0,他引:1
Xin Liu 《Fuzzy Optimization and Decision Making》2006,5(2):163-175
In this paper, the concept of disturbing fuzzy propositional logic is introduced, and the operators of disturbing fuzzy propositions
is defined. Then the 1-dimensional truth value of fuzzy logic operators is extended to be two-dimensional operators, which
include disturbing fuzzy negation operators, implication operators, “and” and “or” operators and continuous operators. The
properties of these logic operators are studied. 相似文献
12.
Alex M. McAllister 《Archive for Mathematical Logic》2001,40(3):147-165
Continuing work begun in [10], we utilize a notion of forcing for which the generic objects are structures and which allows
us to determine whether these “generic” structures compute certain sets and enumerations. The forcing conditions are bounded
complexity types which are consistent with a given theory and are elements of a given Scott set. These generic structures
will “represent” this given Scott set, in the sense that the structure has a certain weak saturation property with respect
to bounded complexity types in the Scott set. For example, if ? is a nonstandard model of PA, then ? represents the Scott
set ? = n∈ω | ?⊧“the nth prime divides a” | a∈?.
The notion of forcing yields two main results. The first characterizes the sets of natural numbers computable in all models
of a given theory representing a given Scott set. We show that the characteristic function of such a set must be enumeration
reducible to a complete existential type which is consistent with the given theory and is an element of the given Scott set.
The second provides a sufficient condition for the existence of a structure ? such that ? represents a countable jump ideal
and ? does not compute an enumeration of a given family of sets ?. This second result is of particular interest when the family
of sets which cannot be enumerated is ? = Rep[Th(?)]. Under this additional assumption, the second result generalizes a result on TA [6] and on certain other completions
of PA [10]. For example, we show that there also exist models of completions of ZF from which one cannot enumerate the family
of sets represented by the theory.
Received: 8 October 1997 / Published online: 25 January 2001 相似文献
13.
A. I. Stepanets 《Ukrainian Mathematical Journal》2006,58(1):54-102
We present a survey of results related to the approximation characteristics of the spaces S
ϕ
p
and their generalizations. The proposed approach enables one to obtain solutions of problems of classical approximation theory
in abstract linear spaces in explicit form. The results obtained yield statements that are new even in the case of approximations
in the functional Hilbert spaces L
2.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 1, pp. 47–92, January, 2006. 相似文献
14.
Alex Simpson 《Annals of Pure and Applied Logic》2004,130(1-3):207-275
This paper provides a unifying axiomatic account of the interpretation of recursive types that incorporates both domain-theoretic and realizability models as concrete instances. Our approach is to view such models as full subcategories of categorical models of intuitionistic set theory. It is shown that the existence of solutions to recursive domain equations depends upon the strength of the set theory. We observe that the internal set theory of an elementary topos is not strong enough to guarantee their existence. In contrast, as our first main result, we establish that solutions to recursive domain equations do exist when the category of sets is a model of full intuitionistic Zermelo–Fraenkel set theory. We then apply this result to obtain a denotational interpretation of FPC, a recursively typed lambda-calculus with call-by-value operational semantics. By exploiting the intuitionistic logic of the ambient model of intuitionistic set theory, we analyse the relationship between operational and denotational semantics. We first prove an “internal” computational adequacy theorem: the model always believes that the operational and denotational notions of termination agree. This allows us to identify, as our second main result, a necessary and sufficient condition for genuine “external” computational adequacy to hold, i.e. for the operational and denotational notions of termination to coincide in the real world. The condition is formulated as a simple property of the internal logic, related to the logical notion of 1-consistency. We provide useful sufficient conditions for establishing that the logical property holds in practice. Finally, we outline how the methods of the paper may be applied to concrete models of FPC. In doing so, we obtain computational adequacy results for an extensive range of realizability and domain-theoretic models. 相似文献
15.
Summary. We study the F?ppl—von Kármán theory for isotropically compressed thin plates in a geometrically linear setting, which is
commonly used to model weak buckling of thin films. We consider generic smooth domains with clamped boundary conditions, and
obtain rigorous upper and lower bounds on the minimum energy linear in the plate thickness σ . This energy is much lower than previous estimates based on certain dimensional reductions of the problem, which had lead
to energies of order 1+σ (scalar approximation) or σ
2/3
(two-component approximation).
Received August 7, 2000; accepted September 8, 2000 %%%Online publication November 15, 2000 Communicated by Robert V. Kohn 相似文献
16.
17.
Residuated fuzzy logics with an involutive negation 总被引:4,自引:0,他引:4
Francesc Esteva Lluís Godo Petr Hájek Mirko Navara 《Archive for Mathematical Logic》2000,39(2):103-124
Residuated fuzzy logic calculi are related to continuous t-norms, which are used as truth functions for conjunction, and
their residua as truth functions for implication. In these logics, a negation is also definable from the implication and the
truth constant , namely is $\varphi \to \overline{0}$. However, this negation behaves quite differently depending on the t-norm. For a nilpotent
t-norm (a t-norm which is isomorphic to Łukasiewicz t-norm), it turns out that is an involutive negation. However, for t-norms without non-trivial zero divisors, is G?del negation. In this paper we investigate the residuated fuzzy logics arising from continuous t-norms without non-trivial
zero divisors and extended with an involutive negation.
Received: 14 April 1998 相似文献
18.
Gemma Robles 《Logica Universalis》2013,7(4):507-532
Routley–Meyer semantics (RM-semantics) is defined for Gödel 3-valued logic G3 and some logics related to it among which a paraconsistent one differing only from G3 in the interpretation of negation is to be remarked. The logics are defined in the Hilbert-style way and also by means of proof-theoretical and semantical consequence relations. The RM-semantics is defined upon the models for Routley and Meyer’s basic positive logic B+, the weakest positive RM-semantics. In this way, it is to be expected that the models defined can be adapted to other related many-valued logics. 相似文献
19.
François Lepage 《Logica Universalis》2016,10(2-3):327-338
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. 相似文献
20.
Petr Cintula Erich Peter Klement Radko Mesiar Mirko Navara 《Mathematical Logic Quarterly》2006,52(3):269-282
In general, there is only one fuzzy logic in which the standard interpretation of the strong conjunction is a strict triangular norm, namely, the product logic. We study several equations which are satisfied by some strict t‐norms and their dual t‐conorms. Adding an involutive negation, these equations allow us to generate countably many logics based on strict t‐norms which are different from the product logic. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献