automatic recognition of tractability in inference relations a procedure is given for recognizing sets of inference rules that generate polynomial time decidable inference relations the procedure can automatically recognize the tractability of the inference rules underlying congruence closure the recognition of tractability for that particular rule set constitutes mechanical verification of a theorem originally proved independently by kozen and shostak the procedure is algorithmic rather than heuristic and the class of automatically recognizable tractable rule sets can be precisely characterized a series of examples of rule sets whose tractability is nontrivial yet machine recognizable is also given the technical framework developed here is viewed as a first step toward a general theory of tractable inference relations

non monotonic fuzzy measures and the choquet integral abstract this paper discusses non monotonic fuzzy measures which are set functions without monotonicity and the choquet integral with respect to non monotonic fuzzy measures a concrete example shows that the choquet integral is meaningful in the case of non monotonic fuzzy measures as well as in the case of ordinary fuzzy measures every comonotonically additive positively homogeneous functional of bounded variation can be represented as a choquet integral with respect to a non monotonic fuzzy measure of bounded variation the space of such functionals is a real banach space isometrically isomorphic to the space of non monotonic fuzzy measures of bounded variation

citation based journal ranks the use of fuzzy measures this article considers a real world application of the choquet integral based classifier to the problem of ranking of scientific journals we attempted to predict rankings given by panels of experts by using available citation indices we compare the choquet integral fit by the least absolute deviation criterion as a classifier against other ordinal classification methods before interpreting the fuzzy measure weights and indices our findings show that the journal rankings data set is difficult to model accurately due to inconsistencies and lack of monotonicity but that the choquet integral still performs well as a classifier

equivalence of slice semi regular functions via sylvester operators abstract the aim of this paper is to study some features of slice semi regular functions sem on a circular domain contained in the skew symmetric algebra of quaternions h via the analysis of a family of linear operators built from left and right multiplication on sem this class of operators includes the family of sylvester type operators s f g our goal is achieved by a strategy based on a matrix interpretation of these operators as we show that sem can be seen as a 4 dimensional vector space on the field sem r we then study the rank of s f g and describe its kernel and image when it is not invertible finding meaningful differences in the cases when the rank is either 2 or 3 by using these results we are able to characterize when the functions f and g are either equivalent under conjugation or intertwined by means of a zero divisor thus proving a number of statements on the behaviour of slice semi regular functions in this way information about the operator obtained by linear algebra techniques give as a significant application the solution of a problem in an area of function theory which had a remarkable development in the last decade see 16 we also provide a complete classification of idempotents and zero divisors on product domains of h

protocol insecurity with a finite number of sessions and composed keys is np complete we investigate the complexity of the protocol insecurity problem for a finite number of sessions fixed number of interleaved runs we show that this problem is np complete with respect to a dolev yao model of intruders the result does not assume a limit on the size of messages and supports non atomic symmetric encryption keys we also prove that in order to build an attack with a fixed number of sessions the intruder needs only to forge messages of linear size provided that they are represented as dags

extension results for slice regular functions of a quaternionic variable in this paper we prove a new representation formula for slice regular functions which shows that the value of a slice regular function f at a point q x yi can be recovered by the values of f at the points q yj and q yk for any choice of imaginary units i j k this result allows us to extend the known properties of slice regular functions defined on balls centered on the real axis to a much larger class of domains called axially symmetric domains we show in particular that axially symmetric domains play for slice regular functions the role played by domains of holomorphy for holomorphic functions

k maxitive sugeno integrals as aggregation models for ordinal preferences we consider an order variant of k additivity so called k maxitivity and present an axiomatization of the class of k maxitive sugeno integrals over distributive lattices to this goal we characterize the class of lattice polynomial functions with degree at most k and show that k maxitive sugeno integrals coincide exactly with idempotent lattice polynomial functions whose degree is at most k we also discuss the use of this parametrized notion in preference aggregation and learning in particular we address the question of determining optimal values of k through a case study on empirical data

preference learning using the choquet integral the case of multipartite ranking we propose a novel method for preference learning or more specifically learning to rank where the task is to learn a ranking model that takes a subset of alternatives as input and produces a ranking of these alternatives as output just like in the case of conventional classifier learning training information is provided in the form of a set of labeled instances with labels or say preference degrees taken from an ordered categorical scale this setting is known as multipartite ranking in the literature our approach is based on the idea of using the discrete choquet integral as an underlying model for representing ranking functions being an established aggregation function in fields such as multiple criteria decision making and information fusion the choquet integral offers a number of interesting properties that make it attractive from a machine learning perspective too the learning problem itself comes down to properly specifying the fuzzy measure on which the choquet integral is defined this problem is formalized as a margin maximization problem and solved by means of a cutting plane algorithm the performance of our method is tested on a number of benchmark datasets

a new theory of regular functions of a quaternionic variable abstract in this paper we develop the fundamental elements and results of a new theory of regular functions of one quaternionic variable the theory we describe follows a classical idea of cullen but we use a more geometric formulation to show that it is possible to build a rather complete theory our theory allows us to extend some important results for polynomials in the quaternionic variable to the case of power series

fuzzy integral in multicriteria decision making abstract this paper presents a synthesis on the use of fuzzy integral as an aggregation operator in multicriteria decision making definitions essential properties are given and compared to those of usual aggregation operators a quick survey on applications is given

slice regular functions on real alternative algebras in this paper we develop a theory of slice regular functions on a real alternative algebra a our approach is based on a well known fueter s construction two recent function theories can be included in our general theory the one of slice regular functions of a quaternionic or octonionic variable and the theory of slice monogenic functions of a clifford variable our approach permits to extend the range of these function theories and to obtain new results in particular we get a strong form of the fundamental theorem of algebra for an ample class of polynomials with coefficients in a and we prove a cauchy integral formula for slice functions of class c 1

2 additive capacity identification methods from multicriteria correlation preference information the essential role of the particular families of capacities and the capacity identification methods is to help the decision maker to deal with the exponential complexity inherent in the construction process of the capacity the 2 additive capacities appear to be the most popular among the particular families of capacities since they permit to model interactions between criteria while preserving simplicity besides the preference with respect to the decision criteria most of the capacity identification methods also need to provide the desired overall evaluations of the decision alternatives in the learning set which is a time consuming task for the decision maker in this paper we propose some models to identify 2 additive capacities only from a kind of refined preference information with respect to the decision criteria called the multicriteria correlation preference information mccpi the mccpi is a group of 2 d preference information which can be described and obtained by the refined diamond diagram the common principle of the proposed models is to minimize the different kinds of deviations between the mccpi and the most desired 2 additive capacity ies a multicriteria decision making example is presented to show the feasibility of the proposed methods and a 2 d scale of the mccpi is also introduced in the further discussion of the illustrative example

a review of methods for capacity identification in choquet integral based multi attribute utility theory applications of the kappalab r package the application of multi attribute utility theory whose aggregation process is based on the choquet integral requires the prior identification of a capacity the main approaches to capacity identification proposed in the literature are reviewed and their advantages and inconveniences are discussed all the reviewed methods have been implemented within the kappalab r package their application is illustrated on a detailed example

k order additive discrete fuzzy measures and their representation abstract in order to face with the complexity of discrete fuzzy measures we propose the concept of k orderadditive fuzzy measure including usual additive measures and fuzzy measures every discrete fuzzy measure is a k order additive fuzzy measure for a unique k a related topic of the paper is to introduce an alternative representation of fuzzy measures called the interaction representation which sets and extends in a common framework the shapley value and the interaction index proposed by murofushi and soneda

learning choquet integral based metrics for semisupervised clustering we consider an application of fuzzy measures to the problem of metric learning in semisupervised clustering we investigate the necessary and sufficient conditions on the underlying fuzzy measure that make the discrete choquet integral suitable for defining a metric as a byproduct we can obtain the analogous conditions for the ordered weighted averaging owa operators which constitute a special case we then generalize these results for power based choquet and owa operators we show that this metric learning problem can be formulated as a linear programming problem and specify the required sets of linear constraints we present the results of numerical experiments on artificial and real world datasets which illustrate the potential usefulness and limitations of this construction

non additive robust ordinal regression a multiple criteria decision model based on the choquet integral abstract within the multicriteria aggregation disaggregation framework ordinal regression aims at inducing the parameters of a decision model for example those of a utility function which have to represent some holistic preference comparisons of a decision maker dm usually among the many utility functions representing the dm s preference information only one utility function is selected since such a choice is arbitrary to some extent recently robust ordinal regression has been proposed with the purpose of taking into account all the sets of parameters compatible with the dm s preference information until now robust ordinal regression has been implemented to additive utility functions under the assumption of criteria independence in this paper we propose a non additive robust ordinal regression on a set of alternatives a whose utility is evaluated in terms of the choquet integral which permits to represent the interaction among criteria modelled by the fuzzy measures parameterizing our approach in our methodology besides holistic pairwise preference comparisons of alternatives from a subset of reference alternatives a a the dm is also requested to express the intensity of preference on pairs of alternatives from a and to supply pairwise comparisons on the importance of criteria and the sign and intensity of interaction among pairs of criteria the output of our approach defines a set of fuzzy measures capacities such that the corresponding choquet integral is compatible with the dm s preference information moreover using linear programming our decision model establishes two preference relations for any a b a the necessary weak preference relation if for all compatible fuzzy measures the utility of a is not smaller than the utility of b and the possible weak preference relation if for at least one compatible fuzzy measure the utility of a is not smaller than the utility of b

data driven compression and efficient learning of the choquet integral the choquet integral chi is a parametric nonlinear aggregation function defined with respect to the fuzzy measure fm to date application of the chi has sadly been restricted to problems with relatively few numbers of inputs primarily as the fm has 2 n variables for n inputs and n 2 n 1 1 monotonicity constraints in return the community has turned to density based imputation e g sugeno lambda fm or the number of interactions fm variables are restricted e g k additivity herein we propose a new scalable data driven way to represent and learn the chi making learning computationally manageable for larger n first data supported variables are identified and used in optimization identification of these variables also allows us recognize future ill posed fusion scenarios chis involving variable subsets not supported by data second we outline an imputation function framework to address data unsupported variables third we present a lossless way to compress redundant variables and associated monotonicity constraints finally we outline a lossy approximation method to further compress the chi if when desired computational complexity analysis and experiments conducted on synthetic datasets with known fms demonstrate the effectiveness and efficiency of the proposed theory

singularities of slice regular functions over real alternative algebras abstract the main goal of this work is classifying the singularities of slice regular functions over a real alternative algebra a this function theory has been introduced in 2011 as a higher dimensional generalization of the classical theory of holomorphic complex functions of the theory of slice regular quaternionic functions launched by gentili and struppa in 2006 and of the theory of slice monogenic functions constructed by colombo sabadini and struppa since 2009 along with this generalization step the larger class of slice functions over a has been defined we introduce here a new type of series expansion near each singularity of a slice regular function this instrument which is new even in the quaternionic case leads to a complete classification of singularities this classification also relies on some recent developments of the theory concerning the algebraic structure and the zero sets of slice functions peculiar phenomena arise which were not present in the complex or quaternionic case and they are studied by means of new results on the topology of the zero sets of slice functions the analogs of meromorphic functions called slice semiregular functions are introduced and studied

symbolic protocol analysis for monoidal equational theories we are interested in the design of automated procedures for analyzing the in security of cryptographic protocols in the dolev yao model for a bounded number of sessions when we take into account some algebraic properties satisfied by the operators involved in the protocol this leads to a more realistic model in comparison to what we get under the perfect cryptography assumption but it implies that protocol analysis deals with terms modulo some equational theory instead of terms in a free algebra the main goal of this paper is to setup a general approach that works for a whole class of monoidal theories which contains many of the specific cases that have been considered so far in an ad hoc way e g exclusive or abelian groups exclusive or in combination with the homomorphism axiom we follow a classical schema for cryptographic protocol analysis which proves first a locality result and then reduces the insecurity problem to a symbolic constraint solving problem this approach strongly relies on the correspondence between a monoidal theory e and a semiring s e which we use to deal with the symbolic constraints we show that the well defined symbolic constraints that are generated by reasonable protocols can be solved provided that unification in the monoidal theory satisfies some additional properties the resolution process boils down to solving particular quadratic diophantine equations that are reduced to linear diophantine equations thanks to linear algebra results and the well definedness of the problem examples of theories that do not satisfy our additional properties appear to be undecidable which suggests that our characterization is reasonably tight

lexicographic preferences for predictive modeling of human decision making a new machine learning method with an application in accounting abstract lexicographic preferences on a set of attributes provide a cognitively plausible structure for modeling the behavior of human decision makers therefore the induction of corresponding models from revealed preferences or observed decisions constitutes an interesting problem from a machine learning point of view in this paper we introduce a learning algorithm for inducing generalized lexicographic preference models from a given set of training data which consists of pairwise comparisons between objects our approach generalizes simple lexicographic orders in the sense of allowing the model to consider several attributes simultaneously instead of looking at them one by one thereby significantly increasing the expressiveness of the model class in order to evaluate our method we present a case study of a highly complex real world problem namely the choice of the recognition method for actuarial gains and losses from occupational pension schemes using a unique sample of european companies this problem is well suited for demonstrating the effectiveness of our lexicographic ranker furthermore we conduct a series of experiments on benchmark data from the machine learning domain

intruder deduction for the equational theory of abelian groups with distributive encryption cryptographic protocols are small programs which involve a high level of concurrency and which are difficult to analyze by hand the most successful methods to verify such protocols are based on rewriting techniques and automated deduction in order to implement or mimic the process calculus describing the execution of a protocol we are interested in the intruder deduction problem that is vulnerability to passive attacks in presence of equational theories which model the protocol specification and properties of the cryptographic operators in the present paper we consider the case where the encryption distributes over the operator of an abelian group or over an exclusive or operator we prove decidability of the intruder deduction problem in both cases we obtain a ptime decision procedure in a restricted case the so called binary case these decision procedures are based on a careful analysis of the proof system modeling the deductive power of the intruder taking into account the algebraic properties of the equational theories under consideration the analysis of the deduction rules interacting with the equational theory relies on the manipulation of z modules in the general case and on results from prefix rewriting in the binary case

label ranking by learning pairwise preferences preference learning is an emerging topic that appears in different guises in the recent literature this work focuses on a particular learning scenario called label ranking where the problem is to learn a mapping from instances to rankings over a finite number of labels our approach for learning such a mapping called ranking by pairwise comparison rpc first induces a binary preference relation from suitable training data using a natural extension of pairwise classification a ranking is then derived from the preference relation thus obtained by means of a ranking procedure whereby different ranking methods can be used for minimizing different loss functions in particular we show that a simple weighted voting strategy minimizes risk with respect to the well known spearman rank correlation we compare rpc to existing label ranking methods which are based on scoring individual labels instead of comparing pairs of labels both empirically and theoretically it is shown that rpc is superior in terms of computational efficiency and at least competitive in terms of accuracy

an undecidability result for agh we present an undecidability result for the verification of security protocols since the perfect cryptography assumption is unrealistic for cryptographic primitives with visible algebraic properties several recent works relax this assumption allowing the intruder to exploit these properties we are interested in the abelian groups theory in combination with the homomorphism axiom we show that the security problem for a bounded number of sessions expressed by satisfiability of symbolic deductibility constraints is undecidable obtaining in this way the first undecidability result concerning a theory for which unification is known to be decidable f baader unification in commutative theories hilbert s basis theorem and grobner bases j acm 40 3 1993 477 503

compromise principle based methods of identifying capacities in the framework of multicriteria decision analysis abstract the basic aim of the compromise principle employed in this paper is to seek the capacity by which each alternative has a relatively equal chance to reach as close as possible to its highest reachable overall evaluation according to the compromise principle three types of capacity identification methods the simple arithmetic average based compromise method the least squares based compromise method and the linear programming based compromise method are proposed the input information required for the compromise principle based identification methods consists of the preference information with respect to the decision criteria and the partial evaluations of the alternatives provided by the decision maker an illustrative example is given to show the processes of the proposed methods and a comparison analysis with the maximum entropy principle based identification method is also presented