multi adjoint t concept lattices the t concept lattice is introduced as a set of triples associated to graded tabular information interpreted in a non commutative fuzzy logic following the general techniques of formal concept analysis and based on the works by georgescu and popescu given a non commutative conjunctor it is possible to provide generalizations of the mappings for the intension and the extension in two different ways and this generates a pair of concept lattices in this paper we show that the information common to both concept lattices can be seen as a sublattice of the cartesian product of both concept lattices the multi adjoint framework can be applied to this general t concept lattice and its usefulness is illustrated by a working example

a comparative study of adjoint triples adjoint triples are helpful as basic operators used in several domains for example adjoint triples play an important role in two important frameworks multi adjoint logic programming and multi adjoint concept lattices this paper shows that adjoint triples are an interesting generalization of t norms and their residuated implications since they preserve their main properties as well as they help to increase the flexibility of the operators used for computation in the considered framework furthermore these operators will be related to other important general triples specifically implication triples and the definition of these latter operators will be improved

identification of complete information games this paper establishes sufficient conditions for point identification of the utility functions in generalized complete information game models these models allow generalized interaction structures and generalized behavioral assumptions the generalized interaction structures allow that the dependence of an agent s utility function on the other agents actions can itself depend on characteristics of the agents including an endogenous network of connections among the agents the generalized behavioral assumptions relax the solution concept from nash equilibrium play to weaker solution concepts like rationalizability the results allow a non parametric specification of the unobservables

bounding parameter estimates with nonclassical measurement error abstract the bias introduced by errors in the measurement of independent variables has increasingly been a topic of interest among researchers estimating economic parameters however studies typically use the assumption of classical measurement error that is the variable of interest and its measurement error are uncorrelated and the expected value of the mismeasured variable is equal to the expected value of the true measure these assumptions often arise from convenience rather than conviction when a variable is bounded it is likely that the measurement error and the true value of the variable are negatively correlated we consider the case of a noisily measured variable with a negative covariance between the measurement error and the true value of the variable we show that asymptotically the parameter in a univariate regression is bounded between the ordinary least squares ols estimator and an instrumental variables iv estimator further we demonstrate that the ols bound can be improved in

bounding the effects of proxy variables on regression coefficients we consider a regression in which one of the observed variables is a proxy for some unobserved true variable given a lower bound for the correlation between the proxy and the unobserved true variable for which it substitutes we derive intervals in which the coefficients of the unobserved true regression must lie regardless of any other correlations involving unobserved variables or disturbances we present a simple solution for the important special case in which only the signs of the coefficients are of concern and one seeks the smallest correlation between the proxy and the true variable that guarantees the correctness of the signs of the coefficients in the proxy regression we also present an algorithm for extending these results to the multiple proxy problem attemprs to confront economic theories with data are often hampered by the problem that some of the relevant variables are unavailable or even unobservable in the case of regression models it is customary to substitute proxies for the unavailable variables though the coefficients in the proxy regression will not coincide with those in the regression of the dependent variable on the true explanatory variables it is clear by continuity that the differences will be small if each proxy is sufficiently highly correlated with the unobserved true variable for which it substitutes even if its error is correlated with other errors or variables moreover in many instances the theory predicts not the magnitudes but only the signs of the regression coefficients correct inferences will then be drawn from the model provided that the pairwise correlations between the proxies and the true variables are high enough to guarantee that the signs of the regression coefficients would be unchanged if the proxies were replaced by the true variables in applications econometricians can generally assess those pairwise correlations subjectively but how high do they need to be in this paper we present a complete answer to this question when only one variable is a proxy and describe an algorithm for determining the required correlations when there are several proxies the effects of proxy variables have been extensively studied in the special case of errors in variables eiv in which the differences between the proxies and the corresponding true variables the measurement errors are independent of the true variables of each other and of the disturbances in the true regression we require no such independence in the eiv case it is sometimes possible to guarantee correctness of the signs of the coefficients even without prior information about the variances of the measurement errors for example if the coefficient vector from the direct regression and the coefficient vectors from the reverse regressions as one varies the left side variable all lie in the same orthant then the coefficient vector in the true regression must also lie in that orthant see

associatively tied implications we say that an implication operator a on a complete lattice l is associatively tied if there is a binary operation t on l that ties a that is the identity a a gamma a t holds for all in l this property extends to multiple valued logic the following equivalence in classical logic x y z x y z we show that in this case there exists an associative binary operation ta that ties a hence the nomenclature we study properties of that ta when a is associatively tied we then seek a characterization for the validity of associative tiedness for an implication a phrased in terms of a and two adjoints of it

minimal solutions of general fuzzy relation equations on linear carriers an algebraic characterization abstract this paper considers a general fuzzy relation equation which has minimal solutions if it is solvable in this case an algebraic characterization is introduced which provides an interesting method to compute minimal solutions in this general setting moreover a comparison with other frameworks is also given

formal concept analysis via multi adjoint concept lattices several fuzzifications of formal concept analysis have been proposed to deal with uncertain information in this paper we focus on concept lattices under a multi adjoint paradigm which enriches the language providing greater flexibility to the user in that he she can choose from a number of different connectives multi adjoint concept lattices are shown to embed different fuzzy extensions of concept lattices found in the literature the main results of the paper being the representation theorem of this paradigm and the embedding of other well known approaches

stochastic urn models of innovation and search dynamics abstract this work is devoted to applications of the ehrenfest urn model to innovation and search processes in the first part we discuss systems of two urns serving as models of innovation processes the elementary act of innovation is considered as a transition from old technologies way of production behavior decisions to new the survival probability of the new under the influence of stochastic effects is discussed in the second part we study systems of s 1 urns serving as models for optimal solution searching in optimization problems the problem is to find the minimum on a large set of real numbers ui using a total of n seekers n 2 100 simultaneously the potential ui is defined on the integer set i 1 s where s is extremely large in particular we consider the frustrated periodic strings and the merit problem the known equations for thermodynamic search processes and for simple models of biological evolution are unified by defining a two parameter family of equations which embeds both cases the search parameters are controlled by means of seeker ensemble dispersion

the logic of tied implications part 1 properties applications and representation a conjunction t ties an implication operator a if the identity a a a b z a t a b z holds a a abdel hamid n n morsi associatively tied implications fuzzy sets and systems 136 2003 291 311 we study the class of tied adjointness algebras which are five connective algebras on two partially ordered sets in which the implications are tied by triangular norms this class contains besides residuated implications several other implications employed in fuzzy logic nevertheless we show that the algebraic inequalities of residuated algebras remain true for our tied implications but in forms that distribute roles over the five connectives of the algebra we apply the properties of tied implications to a generalized modus ponens inference scheme with two successive rules we prove its equivalence to a scheme with one compound rule when both schemata are interpreted by the compositional rule of inference and all connectives are taken from one tied adjointness algebra then we quote another application of this rich theory a notion of many valued rough sets which exhibit the basic mathematical behaviour of the rough sets of pawlak a comparator h is said to be prelinear if it satisfies h y z h z y 1 for all y z hajek we introduce prelinear tied adjointness algebras in which two comparators are prelinear we provide a representation of those algebras as subdirect products of tied adjointness chains on the lines of hajek s representation of bl algebras but our representations are more economical because we employ minimal prime filters on residuated lattices only rather than all prime filters

the logic of tied implications part 2 syntax an implication operator a is said to be tied if there is a binary operation t that ties a that is the identity a a a b z a t a b z holds for all a b z we aim at the construction of a complete predicate logic for prelinear tied adjointness algebras we realize this in three steps in the first step we establish a propositional calculus adjtpc complete for the class of all tied adjointness algebras on partially ordered sets without prelinearity and ignoring the lattice operations for that we supply a hilbert system based on seven axioms and one deduction rule modus ponens in the second and third steps we extend adjtpc to propositional and predicate calculi complete for prelinear tied adjointness algebras we apply a duality principle due to morsi in all three calculi through which we manage to cut down the number of proofs

estimation of average treatment effects with misclassification this paper considers identification and estimation of the effect of a mismeasured binary regressor in a nonparametric or semiparametric regression or the conditional average effect of a binary treatment or policy on some outcome where treatment may be misclassified failure to account for misclassification is shown to result in attenua tion bias in the estimated treatment effect an identifying assumption that overcomes this bias is the existence of an instrument for the binary regressor that is conditionally independent of the treatment effect a discrete instrument suffices for nonparametric identification this paper provides conditions for identification and estimation of the av erage effect conditioned on covariates of a binary treatment program or pol icy on a scalar outcome when treatment may be misclassified more generally what is provided is an estimator of the effect of a binary regressor in a con ditional mean regression which may also include other regressors when the binary regressor is observed with error this equals the conditional average treatment effect given a weak unconfoundedness assumption misclassification occurs when a binary variable the treatment indicator is measured with error that is some units are reported to have received treat ment when they actually have not and vice versa for example in a returns to schooling analysis the outcome could be wages the binary variable could be attaining a college degree and misclassification could arise from school tran script reporting errors see e g kane and rouse 1995 and kane rouse and staiger 1999 bollinger 1996 considers misclassification of union status in wage equations if treatment is a job training program misclassification may arise if individuals assigned to the program fail to attend or if those not as signed obtain training elsewhere similarly for medical treatment individuals assigned a drug might fail to take it and those assigned a placebo might obtain treatment from another source more generally misclassification describes any binary variable that is sometimes mismeasured this paper first shows that misclassification causes attenuation bias in esti mated treatment effects analogous to the attenuation bias of classically mis measured variables in linear regression models additional assumptions on

partial identification of probability distributions with misclassified data abstract this paper addresses the problem of data errors in discrete variables when data errors occur the observed variable is a misclassified version of the variable of interest whose distribution is not identified inferential problems caused by data errors have been conceptualized through convolution and mixture models this paper introduces the direct misclassification approach the approach is based on the observation that in the presence of classification errors the relation between the distribution of the true but unobservable variable and its misclassified representation is given by a linear system of simultaneous equations in which the coefficient matrix is the matrix of misclassification probabilities formalizing the problem in these terms allows one to incorporate any prior information into the analysis through sets of restrictions on the matrix of misclassification probabilities such information can have strong identifying power the direct misclassification approach fully exploits it to derive identification regions for any real functional of the distribution of interest a method for estimating the identification regions and construct their confidence sets is given and illustrated with an empirical analysis of the distribution of pension plan types using data from the health and retirement study

bounding the effects of measurement error in regressions involving dichotomous variables abstract in a multiple regression involving dichotomous independent variables the effects of measurement error in the dichotomous variables is analyzed unlike the case of classical i e white noise measurement error the measurement error in a dichotomous variable must be correlated with the true variable and any other variables correlated with the true variable nonetheless it is shown that the results for the classical errors in variables model can be used to analyze the implications of measurement error in dichotomous variables it is shown how the bounding procedure developed by klepper and leamer 1984 for the classical errors in variables model can be adapted to bound the coefficients when the regression contains mismeasured dichotomous variables the classical results are also used to analyze the inconsistency in least squares regression coefficient estimators computed from data on the mismeasured variables

issues on adjointness in multiple valued logics we contribute to the theory of implications and conjunctions related by adjointness in multiple valued logics we suggest their use in zadeh s compositional rule of inference to interpret generalized modus ponens inference schemata we provide new complete characterizations of implications that distinguish left arguments implications that satisfy the exchange principle divisible conjunctions commutative conjunctions associative conjunctions and triangular norms we also introduce and characterize pseudo strict and pseudo continuous implications and conjunctions and we explore the close relationship between these two notions

set identified linear models we analyze the identification and estimation of parameters satisfying the incomplete linear moment restrictions e z x y e z u z where z is a set of instruments and u z an unknown bounded scalar function we first provide empirically relevant examples of such a set up second we show that these conditions set identify where the identified set b is bounded and convex we provide a sharp characterization of the identified set not only when the number of moment conditions is equal to the number of parameters of interest but also in the case in which the number of conditions is strictly larger than the number of parameters we derive a necessary and sufficient condition of the validity of supernumerary restrictions which generalizes the familiar sargan condition third we provide new results on the asymptotics of analog estimates constructed from the identification results when b is a strictly convex set we also construct a test of the null hypothesis 0 2 b whose size is asymptotically correct and which relies on the minimization of the support function of the set b 0 results of some monte carlo experiments are presented

misclassification in binary choice models abstract bias from misclassification of binary dependent variables can be pronounced we examine what can be learned from such contaminated data first we derive the asymptotic bias in parametric models allowing misclassification to be correlated with observables and unobservables simulations and validation data show that the bias formulas are accurate in finite samples and in most situations imply attenuation second we examine the bias in a prototypical application erroneously restricting the covariance of misclassification and covariates aggravates the bias for all estimators we examine estimators that relax this restriction perform well if a model of misclassification or validation data is available

bayesian moment based inference in a regression model with misclassification error we present a bayesian analysis of a regression model with a binary covariate that may have classification measurement error prior research demonstrates that the regression coefficient is only partially identified we take a bayesian approach which adds assumptions in the form of priors on the unknown misclassification probabilities the approach is intermediate between the frequentist bounds of previous literature and strong assumptions which achieve point identification and thus preferable in many settings we present two simple algorithms to sample from the posterior distribution when the likelihood function is not fully parametric but only satisfies a set of moment restrictions we focus on how varying amounts of information contained in a prior distribution on the misclassification probabilities change the posterior of the parameters of interest while the priors add information to the model they do not necessarily tighten the identified set however the information is sufficient to tighten bayesian inferences we also consider the case where the mismeasured binary regressor is endogenous we illustrate the use of our bayesian approach in a simulated data set and an empirical application investigating the association between narcotic pain reliever use and earnings

a general instrumental variable framework for regression analysis with outcome missing not at random summary the instrumental variable iv design is a well known approach for unbiased evaluation of causal effects in the presence of unobserved confounding in this article we study the iv approach to account for selection bias in regression analysis with outcome missing not at random in such a setting a valid iv is a variable which i predicts the nonresponse process and ii is independent of the outcome in the underlying population we show that under the additional assumption iii that the iv is independent of the magnitude of selection bias due to nonresponse the population regression in view is nonparametrically identified for point estimation under i iii we propose a simple complete case analysis which modifies the regression of primary interest by carefully incorporating the iv to account for selection bias the approach is developed for the identity log and logit link functions for inferences about the marginal mean of a binary outcome assuming i and ii only we describe novel and approximately sharp bounds which unlike robins manski bounds are smooth in model parameters therefore allowing for a straightforward approach to account for uncertainty due to sampling variability these bounds provide a more honest account of uncertainty and allows one to assess the extent to which a violation of the key identifying condition iii might affect inferences for illustration the methods are used to account for selection bias induced by hiv testing nonparticipation in the evaluation of hiv prevalence in the zambian demographic and health surveys

an improved reductant calculus using fuzzy partial evaluation techniques partial evaluation pe is an automatic program transformation technique aiming to obtain among other advantages the optimization of a program with respect to parts of its input hence it is also known as program specialization this paper introduces the subject of pe into the field of fuzzy logic programming we define the concept of pe for multi adjoint logic programs and goals and apart from discussing the benefits achieved by this technique we also introduce in the fuzzy setting a completely novel application of pe which allows us the computation of reductants guaranteeing completeness properties without harming the computational efficiency reductants are a special kind of fuzzy rules which constitute an essential theoretical tool for proving correctness properties as observed in the specialized literature a multi adjoint logic program when interpreted on a partially ordered lattice has to include all its reductants in order to preserve the approximate completeness property this introduces severe penalties in the implementation of efficient multi adjoint logic programming systems not only the size of programs increases but also their execution time in this paper we define a refinement to the notion of reductant based on pe techniques that we call pe reductant we establish the main properties of pe reductants i e the classical concept of reductant and the new notion of pe reductant are both semantically and operationally equivalent and what is the best we demonstrate that our refined notion of pe reductant is even able to increase the efficiency of multi adjoint logic programs

multi adjoint property oriented and object oriented concept lattices this paper presents a generalisation of the classical property and object oriented concept lattices to a fuzzy environment based on the philosophy of the multi adjoint paradigm these concept lattices are generalisations of rough set theory used to consider two different sets the set of objects and the set of attributes to apply the corresponding modal operators as in formal concept analysis first of all the paper presents several specific properties of adjoint triples in which the duals of several supports are considered these properties are then used to introduce the multi adjoint property and object oriented concept lattices in which different adjoint triples can be used in non linear sets as well as the corresponding representation fundamental theorems moreover these lattices are related to the multi adjoint concept lattice in which negation operators are not needed as a result this relation allows the properties to be translated from one to another

confidence intervals for partially identified parameters recently a growing body of research has studied inference in settings where parameters of interest are partially identified in many cases the parameter is real valued and the identification region is an interval whose lower and upper bounds may be estimated from sample data for this case confidence intervals cis have been proposed that cover the entire identification region with fixed probability here we introduce a conceptually different type of confidence interval rather than cover the entire identification region with fixed probability we propose cis that asymptotically cover the true value of the parameter with this probability however the exact coverage probabilities of the simplest version of our new cis do not converge to their nominal values uniformly across different values for the width of the identification region to avoid the problems associated with this we modify the proposed ci to ensure that its exact coverage probabilities do converge uniformly to their nominal values we motivate this modified ci through exact results for the gaussian case

adjoint negations more than residuated negations negation operators are useful operators which have extensively been studied and used in different fuzzy settings such as in fuzzy logic this paper introduces a new and flexible kind of negation operator based on adjoint triples and which is called adjoint negation relative to a fixed element besides proving several interesting properties the comparison with weak negations studied by trillas esteva et al and pairs of weak negations introduced by georgescu and popescu is presented furthermore adjoint negations are used in order to define the corresponding dual disjunctive to an adjoint conjunctor

nonparametric identification of a binary random factor in cross section data suppose v and u are two independent mean zero random variables where v has an asymmetric distribution with two mass points and u has a symmetric distribution we show that the distributions of v and u are nonparametrically identifled just from observing the sum v u and provide a rate root n estimator we apply these results to the world income distribution to measure the extent of convergence over time where the values v can take on correspond to country types i e wealthy versus poor countries we also extend our results to include covariates x showing that we can nonparametrically identify and estimate cross section regression models of the form y g x d u where d is an unobserved

bounding mean regressions when a binary regressor is mismeasured in this paper i examine identification and estimation of mean regression models when a binary regressor is mismeasured i prove that bounds for the model parameters are identified and provide simple estimators which are consistent and asymptotically normal when stronger prior information about the probability of misclassification is available the bounds can be made tighter again a simple estimator for these cases is provided all results apply to parametric and nonparametric models the paper concludes with a short empirical example

fuzzy logic programming in this paper we consider the theory of fuzzy logic programming without negation our results cover logical systems with a wide variety of connectives ranging from t norm and conorms through conjunctors and disjunctors and their residuals to aggregation operators rules of our programs are many valued implications we emphasize that in contrast to other approaches our logic is truth functional i e according to p hajek we work in fuzzy logic in narrow sense we prove the soundness and the completeness of our formal model we deal with applications to threshold computation abduction fuzzy unification based on similarity we show that fuzzy unification based on similarities has applications to fuzzy databases and flexible querying

identification and estimation of nonlinear models with misclassification error using instrumental variables a general solution abstract this paper provides a general solution to the problem of identification and estimation of nonlinear models with misclassification error in a general discrete explanatory variable using instrumental variables the misclassification error is allowed to be correlated with all the explanatory variables in the model it is not enough to identify the model by simply generalizing the identification in the binary case with a claim that the number of restrictions is no less than that of the unknowns such a claim requires solving a complicated nonlinear system of equations this paper introduces a matrix diagonalization technique which allows one to easily find the unique solution of the system the solution shows that the latent model can be expressed as an explicit function of directly observed distribution functions therefore the latent model is nonparametrically identifiable and directly estimable using instrumental variables the results show that certain monotonicity restrictions on the latent model may lead to its identification with virtually no restrictions on the misclassification probabilities an alternative identification condition suggests that the nonparametric identification may rely on the belief that people always have a higher probability of telling the truth than of misreporting the nonparametric identification in this paper directly leads to a n consistent semiparametric estimator the monte carlo simulation and empirical illustration show that the estimator performs well with a finite sample and real data

propositional calculus under adjointness we develop a formal system for the class of all implications a and conjunctions k on partially ordered sets l with top elements 1 such that a and k are related by adjointness and they satisfy the neutrality principle that is 1 is their left identity element we call the resulting logic propositional calculus under adjointness abbreviated adjpc most algebraic theorems on those l a and k are inequalities in the posets l of truth values in consequence we have to find means for abstracting inequalities within syntax which must be free from partial truth values this is achieved by employing a further implication like adjoint h of a and k whereby the partial order of l coincides with the binary relation h 1 accordingly the semantical domain for adjpc should become the class of all such quintuples l a k h which we call adjointness algebras our axiom scheme for adjpc features seven axioms however it may be the case that no finite set of axioms can complete adjpc if inference is carried out by means of modus ponens mp alone this is because adjpc is too general it lacks some basic theorems of the more restricted logics such as residuated logic and intuitionistic logic as a result we have to adopt four inference rules for adjpc namely mp and three bits of the substitution theorem we deduce enough theorems and inferences in adjpc to delineate its basic structure this enables us to establish the completeness of adjpc for the semantical domain of adjointness algebras by means of a quotient algebra structure a lindenbaum type of algebra we also show how certain models can help disprove some incorrect inferences in adjpc we end by developing complete syntax with fewer axioms and inference rules for the smaller semantical domain of all adjointness algebras whose implications satisfy the exchange principle

measurement of higher education in the census and current population survey we examine measurement error in the reporting of higher education in the 1990 decennial census and the post 1991 current population survey cps we document that measurement error in the reporting of higher education is prevalent in census data further these errors violate models of classical measurement error in important ways the level of education is consistently reported as higher than it is errors are not mean 0 errors in the reporting of education are correlated with covariates that appear in earnings regressions and errors in the reporting of education appear correlated with the error term in a model of earnings determination thus neither well known results on classical measurement error nor recent models of nonclassical measurement error are likely valid when using census and cps data we find some evidence that the measurement error is lower in the cps than in the census presumably because first interviews are generally conducted in person

bounding parameters in a linear regression model with a mismeasured regressor using additional information this paper discusses a linear regression model with a mismeasured regressor in which the measurement error is correlated with both the latent variable and the regression error we use a linear structure to capture the correlation between the measurement error and the latent variable this paper shows that the variance of the latent variable is very useful for revealing information on the parameters which otherwise cannot be obtained with such a nonclassical measurement error the main result is that the finite bounds on the parameters can be found using the variance of the latent variable regardless of how severely the measurement error and the regression error are correlated if the mismeasured regressor contains enough information on the latent one this paper also discusses the special but interesting case of the latent variable being dichotomous in this case the mean of the latent variable may even reveal information on the correlation between the measurement error and the regression error all the bounds developed in the paper are tight