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In order to think the simultaneously idealist and realist qualities of the thought of Giambattista Vico, this article considers the axioms of Book I of the Scienza nuova (1730) in the context of literatures on aphorism. It surveys the motley array of eclectic axioms that Vico collects in the first book of his masterpiece, and runs some of those scripts conceptually in order to see them as both found-object stand-ins for realism and as exempla-turned-rules that begin the poetic-logical work of ideation. The essay affirms that aphorisms are phenomena that are essentially collectible and collected. The author of this essay thus articulates five principles of the aphoristic machines produced in the course of such collecting. The essay concludes with the hypothesis that the ideated incompleteness of the aphorism and the cornucopia of inferential potentials that is characteristic of the collection of aphorisms combine to enable us to think realism and idealism together as copious particularity and case-into-rule extrapolations. [ABSTRACT FROM AUTHOR]

The classes of non-commutative cylindric algebras and weakened cylindric algebras were shown, by Istv'an N'emeti, to have decidable equational theories. In this article, we give new proof for this result and we give an answer to the open problem, posed by N'emetin 1985, addressing the atomicity of the finitely generated free algebras of these classes. We prove that the free algebras of these classes are not atomic. [ABSTRACT FROM AUTHOR]

The occurrence of nonresponse is very much plebeian in surveys, which troubles the analysis, and hence, an inappropriate inference is left out. To counterbalance the sour effects of the incompleteness, fresh imputation techniques have been proposed with the aid of multi-auxiliary variates for the estimation of population mean on successive waves. Properties of the proposed estimators have been elaborated, and they have been compared with the work of Priyanka et al. (2015). Detailed simulation study is carried out to substantiate the empirical and theoretical results. Several possible cases have been addressed in which nonresponse can occur. [ABSTRACT FROM AUTHOR]

Big data have revealed unexpected and statistically significant correlations along with intractable propositions. In order to address this development, an algorithm is introduced that is consistent with Ramsey's theorem for pairs and G¨odel's incompleteness theorem. The algorithm assigns one of three truth values to a fuzzy proposition in order to update automatic theorem proving. A unique feature of the algorithm is an AI module that selects the multiple axiom sets needed for a proof. A metric for the AI module is the probability that the database of axiom sets is inadequate for the context. The importance of context is illustrated by a simple analog electrical circuit applied to Fermat's last theorem as contrasted with a similar exponential equation having positive real numbers for bases. Another algorithm or decision tree is introduced to differentiate risk factors from necessary conditions. A failure to recognize this distinction has impaired the public health sector for centuries and continues to do so. The second algorithm introduced here represents an effort to conserve science in general. The risk that big data pose for science is the misuse of positive, statistically significant correlations to infer causality when the correlations actually reflect risk factors or even rare coincidences. [ABSTRACT FROM AUTHOR]

The obsessive-compulsive core dimensions model posits that compulsions are driven by harm avoidance, or to counteract a sense of incompleteness, known as ‘not just right experiences’ (NJREs). Evidence suggests NJREs are associated with obsessive-compulsive disorder (OCD) symptoms and maladaptive perfectionism. However, manipulations of NJREs have focused on the visual system, and have not been examined in the context of arousal fears associated with anxiety sensitivity (AS). This study examined the relationship between OC symptoms, perfectionism, and AS using in vivo manipulations of NJREs across visual, auditory, and tactile sensory modalities. Using a 2 (NJRE vs. JRE) × 2 (AS vs. no AS) between-subjects design, participants (N = 132) completed behavioural tasks designed to elicit NJREs and assess task discomfort and urge to counteract sensory-specific stimuli. Strong relationships were observed between task ratings and self-report measures of NJREs, incompleteness, OCD symptoms, maladaptive perfectionism, and AS. Those in the NJRE conditions gave significantly higher task ratings compared to JRE conditions; however, there was no main effect for AS. While maladaptive perfectionism and AS were significant predictors of task performance, there was no interaction between the two. The results confirm and extend research suggesting a strong association between NJREs and incompleteness motivations, as well as sensory-affective disturbance in OCD. [ABSTRACT FROM AUTHOR]

This paper is concerned with some recursive relations of the derivatives of the Gamma function Γ(a) and incomplete Gamma function Γ(a,z) for the complex value of. In particular, dnΓ/dan(-m)(n,m = 0,1,2...) can be expressed as linear forms in djΓ/daj(1)(j = 0,1,....n + 1) while ∂nΓ/∂an(-m,n) can be represented as the combination of ∂jΓ/∂aj(1,z)(j = 0,1,...,n+1) and the elementary functions. With the aid of these results, we can establish the closed forms of some special integrals associated with Γ(a) and Γ(a,z), which can be expressed by the Riemann zeta functions and some special constants. [ABSTRACT FROM AUTHOR]

We present the Stackelberg model with linear demand and cost functions for the agents where the leader agent and follower agents have imprecise initial information regarding the marginal costs of competitors. Agents dynamically refine their perceptions and actions based on observing the actions other agents. We obtain necessary and sufficient conditions of the event that the dynamic converges to a Stackelberg equilibrium with true values of marginal costs. We also clarify the situations when agents cannot come to an equilibrium. [ABSTRACT FROM AUTHOR]

Gödel-Rosser's Incompleteness Theorem is generalized by showing Πn+1-incompleteness of any ∑n+1-definable extension of Peano Arithmetic which is either ∑n-sound or n-consistent. The optimality of this result is proved by presenting a complete, ∑n+1-definable, ∑n-1-sound, and (n-1)consistent theory for any n>0. Though the proof of the incompleteness theorem for ∑n+1-definable theories using the ∑n-soundness assumption is constructive, it is shown that there is no constructive proof for the Incompleteness Theorem for ∑n+1-definable theories using the n-consistency assumption, when n>2. [ABSTRACT FROM AUTHOR]

Mapping functional requirements first to specifications and then to code is one of the most challenging tasks in software development. Since requirements are commonly written in natural language, they can be prone to ambiguity, incompleteness and inconsistency. Structured semantic representations allow requirements to be translated to formal models, which can be used to detect problems at an early stage of the development process through validation. Storing and querying such models can also facilitate software reuse. Several approaches constrain the input format of requirements to produce specifications, however they usually require considerable human effort in order to adopt domain-specific heuristics and/or controlled languages. We propose a mechanism that automates the mapping of requirements to formal representations using semantic role labeling. We describe the first publicly available dataset for this task, employ a hierarchical framework that allows requirements concepts to be annotated, and discuss how semantic role labeling can be adapted for parsing software requirements. [ABSTRACT FROM AUTHOR]

We study the long-time behavior of the Einstein flow coupled to matter on 2-dimensional surfaces. We consider massless matter models such as collisionless matter composed of massless particles, massless scalar fields and radiation fluids and show that the maximal globally hyperbolic development of homogeneous and isotropic initial data on the 2-sphere is geodesically incomplete in both time directions, i.e. the spacetime recollapses. This behavior also holds for open sets of initial data. In particular, we construct classes of recollapsing 2+1-dimensional spacetimes with spherical spatial topology which provide evidence for a closed universe recollapse conjecture for massless matter models in 2+1 dimensions. Furthermore, we construct solutions with toroidal and higher genus topology for the massless matter fields, which in both cases are future complete. The spacetimes with toroidal topology are 2+1-dimensional analogies of the Einstein-de Sitter model. In addition, we point out a general relation between the energy-momentum tensor and the Kretschmann scalar in 2+1 dimensions and use it to infer strong cosmic censorship for all these models. In view of this relation, we also recall corresponding models containing massive particles, constructed in a previous work and determine the nature of their initial singularities. We conclude that the global structure of non-vacuum cosmological spacetimes in 2+1 dimensions is determined by the mass of particles and-in the homogeneous and isotropic setting studied here-verifies strong cosmic censorship. [ABSTRACT FROM AUTHOR]

In set theory, a maximality principle is a principle that asserts some maximality property of the universe of sets or some part thereof. Set theorists have formulated a variety of maximality principles in order to settle statements left undecided by current standard set theory. In addition, philosophers of mathematics have explored maximality principles whilst attempting to prove categoricity theorems for set theory or providing criteria for selecting foundational theories. This article reviews recent work concerned with the formulation, investigation and justification of maximality principles. [ABSTRACT FROM AUTHOR]

Human age estimation is an important research topic and has found its applications in such scenarios as commodity recommendation and security monitoring. The design of existing estimators generally follows a same pipeline, i.e., an estimator is built from a given training dataset and then evaluated on a holdout testing set from the same dataset to display its effectiveness. In doing so, an implicit assumption is that both training and testing sets should share the same age distribution and feature representation, consequently-meaning that (1) once the age of a face image to be tested is outside the age range of training set, a mis-estimation is naturally inevitable; (2) an estimator built on a specific dataset usually cannot be directly applied to make evaluations on other datasets, because the dimensions and types of their feature representations are usually different (i.e., these datasets are heterogeneous). That is, existing methods can not be directly employed to perform cross-heterogeneous-dataset age estimation. To the best of our knowledge, the age distributions of existing aging datasets are usually not consistent but complementary to each other. Motivated by such a complementarity characteristic of different datasets in age distributions, we develop a so-called correlation component manifold space learning (CCMSL) to first learn a common feature space by capturing the correlations between the heterogeneous databases, and then in the resulting space establish a single age estimator across such heterogeneous datasets through correlation representation learning (CRL). As a result, not only can the age-distribution-incompleteness of individual aging datasets be compensated, but also the discriminating ability of the estimator be reinforced. Finally, experimental results demonstrate the superiority of the proposed methods. [ABSTRACT FROM AUTHOR]

By using the restricted and associated Stirling numbers of the first kind, we define the generalized restricted and associated poly-Cauchy polynomials. By using the restricted and associated Stirling numbers of the second kind, we define the generalized restricted and associated poly-Bernoulli polynomials. These polynomials are generalizations of original poly-Cauchy polynomials and original poly-Bernoulli polynomials, respectively. We also study their characteristic and combinatorial properties. [ABSTRACT FROM AUTHOR]

This paper addresses the question: given some theory T that we accept, is there some natural, generally applicable way of extending T to a theory S that can prove a range of things about what it itself (i.e., S) can prove, including a range of things about what it cannot prove, such as claims to the effect that it cannot prove certain particular sentences (e.g., 0 = 1), or the claim that it is consistent? Typical characterizations of Gödel’s second incompleteness theorem, and its significance, would lead us to believe that the answer is ‘no’. But the present paper explores a positive answer. The general approach is to follow the lead of recent (and not so recent) approaches to truth and the Liar paradox. [ABSTRACT FROM PUBLISHER]

The question that is the subject of this article is not intended to be a sociological or statistical question about the practice of today's mathematicians, but a philosophical question about the nature of mathematics, and specifically the method of mathematics. Since antiquity, saying that mathematics is problem solving has been an expression of the view that the method of mathematics is the analytic method, while saying that mathematics is theorem proving has been an expression of the view that the method of mathematics is the axiomatic method. In this article it is argued that these two views of the mathematical method are really opposed. In order to answer the question whether mathematics is problem solving or theorem proving, the article retraces the Greek origins of the question and Hilbert's answer. Then it argues that, by Gödel's incompleteness results and other reasons, only the view that mathematics is problem solving is tenable. [ABSTRACT FROM AUTHOR]

Gödel introduced the original provability predicate in the proofs of Gödel’s incompleteness theorems, and Rosser defined a new one. They are equivalent in the standard model ${\mathbb N}$ of arithmetic or any nonstandard model of ${\rm PA} + {\rm Con_{PA}} $, but the behavior of Rosser’s provability predicate is different from the original one in nonstandard models of ${\rm PA} + \neg {\rm Con_{PA}} $. In this paper, we investigate several properties of the derivability conditions for Rosser provability predicates, and prove the existence of a Rosser provability predicate with which we can define any consistent complete extension of ${\rm PA}$ in some nonstandard model of ${\rm PA} + \neg {\rm Con_{PA}} $. We call it a universal Rosser predicate. It follows from the theorem that the true arithmetic ${\rm TA}$ can be defined as the set of theorems of ${\rm PA}$ in terms of a universal Rosser predicate in some nonstandard model of ${\rm PA} + \neg {\rm Con_{PA}} $. By using this theorem, we also give a new proof of a theorem that there is a nonstandard model M of ${\rm PA} + \neg {\rm Con_{PA}} $ such that if N is an initial segment of M which is a model of ${\rm PA} + {\rm Con_{PA}} $ then every theorem of ${\rm PA}$ in N is a theorem of $\rm PA$ in ${\mathbb N}$. In addition, we prove that there is a Rosser provability predicate such that the set of theorems of $\rm PA$ in terms of the Rosser provability predicate is inconsistent in any nonstandard model of ${\rm PA} + \neg {\rm Con_{PA}} $. [ABSTRACT FROM PUBLISHER]

We investigate the violation factor of the Bell-Mermin inequality. Until now, we use an assumption that the results of measurement are ±1. In this case, the maximum violation factor is 2. The quantum predictions by n-partite Greenberger-Horne-Zeilinger (GHZ) state violate the Bell-Mermin inequality by an amount that grows exponentially with n. Recently, a new measurement theory based on the truth values is proposed (Nagata and Nakamura, Int. J. Theor. Phys. 55:3616, 2016). The values of measurement outcome are either +1 or 0. Here we use the new measurement theory. We consider multipartite GHZ state. It turns out that the Bell-Mermin inequality is violated by the amount of 2. The measurement theory based on the truth values provides the maximum violation of the Bell-Mermin inequality. [ABSTRACT FROM AUTHOR]

Obsessive-compulsive disorder (OCD) is a heterogeneous illness and evidence suggests that different clinical characteristics may relate to varying treatment outcomes. This study was designed to identify subgroups based on core motivational domains in a clinical sample of individuals with OCD, and to compare groups on clinical characteristics. Cluster analyses identified four subgroups including groups with relatively high or low levels of both harm avoidance (HA) and incompleteness (INC) motivations. A subgroup was identified that demonstrated a “traditional profile” marked by high motivation to avoid harm, and elevated levels of beliefs about responsibility/overestimation of threat. The model also contained a subgroup characterized by high incompleteness, low motivation to avoid harm, and higher levels of perfectionistic beliefs and intolerance of uncertainty. Findings reemphasize that current cognitive and behavioral models of OCD may be enhanced by integrating incompleteness/NJREs. [ABSTRACT FROM AUTHOR]

The theory of graphs are very useful tool in solving the combinatorial problems in different areas of computer science and computational intelligence systems. In this paper, we present a frame work to handle m-polar fuzzy information by combining the theory of m-polar fuzzy sets with graphs. We introduce the notion of weak self complement m-polar fuzzy graphs and establish a necessary condition for m-polar fuzzy graph to be weak self complement. Some properties of self complement and weak self complement m-polar fuzzy graphs are discussed. The order, size, busy vertices and free vertices of an m-polar fuzzy graphs are also defined and proved that isomorphic m-polar fuzzy graphs have same order, size and degree. Also, we have presented some results of busy vertices in isomorphic and weak isomorphic m-polar fuzzy graphs. Finally, a relative study of complement and operations on m-polar fuzzy graphs have been made. Applications of m-polar fuzzy graph are also given at the end. [ABSTRACT FROM AUTHOR]

We give a meaning to the expression ψ ( n ) ( − m ) in neutrix setting. Further the incomplete gamma type function γ ⁎ ( α , x − ) is introduced for negative values of α . [ABSTRACT FROM AUTHOR]

Gödel' incompleteness theorems play a key role in a lot of logical and philosophical arguments, two of them being prominent in the contemporary debates: the thesis that meaning transcends use and the Argument Lucas/Penrose. But, these arguments derive some consequences much stronger than those allowed by Godel'sresults. Aswe show below, Godel himself adoptsa more moderateview and that his cautions as to the philosophical interpretations of the incompleteness theorems are wholly justified. [ABSTRACT FROM AUTHOR]

This paper surveys the interactions between Russell and Gödel, both personal and intellectual. After a description of Russell’s influence on Gödel, it concludes with a discussion of Russell’s reaction to the incompleteness theorems. [ABSTRACT FROM AUTHOR]

D numbers theory is an appropriate method to deal with the information of uncertainty and incompleteness when making a reasonable decision. Previous D numbers theory provides a rule to combine multiple D numbers. However, the commutative law is not satisfied in the rule of combining multiple D numbers. In this paper, a modified method for multiple D numbers combination is proposed. The proposed method defines a new function for multiple D numbers combination which is mainly determined by the original value of D numbers. Then the proposed combination rule is applied to environmental impact assessment (EIA); our results show that the proposed method is efficient for multiple D numbers combination and it is useful when dealing with uncertainty and incompleteness. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of maximization of the expected value of the sum of the utility of the terminal wealth and the utility of the consumption, in a case where some sudden jumps in the risk-free interest rate create incompleteness. To solve the problem we use the dual approach. We characterize the value function of the dual problem by a BSDE and the duality between the primal and the dual value functions is exploited to study the BSDE associated to the primal problem. [ABSTRACT FROM AUTHOR]

Efficient matching of incoming mass events to persistent queries is fundamental to complex event processing systems. Event matching based on pattern rule is an important feature of complex event processing engine. However, the intrinsic uncertainty in pattern rules which are predecided by experts increases the difficulties of effective complex event processing. It inevitably involves various types of the intrinsic uncertainty, such as imprecision, fuzziness, and incompleteness, due to the inability of human beings subjective judgment. Nevertheless, D numbers is a new mathematic tool to model uncertainty, since it ignores the condition that elements on the frame must be mutually exclusive. To address the above issues, an intelligent complex event processing method with D numbers under fuzzy environment is proposed based on the Technique for Order Preferences by Similarity to an Ideal Solution (TOPSIS) method. The novel method can fully support decision making in complex event processing systems. Finally, a numerical example is provided to evaluate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

This article focuses on issues related to improving an argument about minds and machines given by Kurt Gödel in 1951, in a prominent lecture. Roughly, Gödel's argument supported the conjecture that either the human mind is not algorithmic, or there is a particular arithmetical truth impossible for the human mind to master, or both. A well-known weakness in his argument is crucial reliance on the assumption that, if the deductive capability of the human mind is equivalent to that of a formal system, then that system must be consistent. Such a consistency assumption is a strong infallibility assumption about human reasoning, since a formal system having even the slightest inconsistency allows deduction of all statements expressible within the formal system, including all falsehoods expressible within the system. We investigate how that weakness and some of the other problematic aspects of Gödel's argument can be eliminated or reduced. [ABSTRACT FROM AUTHOR]

By using a provability predicate of PA, we define ThmPA(M) as the set of theorems of PA in a model M of PA. We say a model M of PA is (1) illusory if ThmPA(M) ⊈ ThmPA(ℕ), (2) heterodox if ThmPA(M) ⊈ TA, (3) sane if M ⊨ ConPA, and insane if it is not sane, (4) maximally sane if it is sane and ThmPA(M) ⊆ ThmPA(N) implies ThmPA(M) = ThmPA(N) for every sane model N of PA. We firstly show that M is heterodox if and only if it is illusory, and that ThmPA(M) ∩ TA ≠ ThmPA(ℕ) for any illusory model M. Then we show that there exists a maximally sane model, every maximally sane model satisfies ¬ConPA+ConPA, and there exists a sane model of ¬ConPA+ConPA which is not maximally sane. We define that an insane model is (5) illusory by nature if its every initial segment being a nonstandard model of PA is illusory, and (6) going insane suddenly if its every initial segment being a sane model of PA is not illusory. We show that there exists a model of PA which is illusory by nature, and we prove the existence of a model of PA which is going insane suddenly. [ABSTRACT FROM PUBLISHER]

Hybrid multi-granularity approach is a data processing mode in rough set theory. Taking the incomplete information system as the research object, variable precision rough set method and hybrid multi-granulation rough set method is fused. And this paper proposes a hybrid multi-granulation rough sets based on variable precision tolerance relations and discusses two other hybrid multi-granulation rough sets of variable precision based on similarity relation and limited tolerance relation. Basic properties of hybrid multi-granularity rough set of variable precision are discussed, which provides a new approach to deal with the incomplete information system. [ABSTRACT FROM AUTHOR]

Many properties of gamma functions are known. In this paper, we extend similar properties to incomplete gamma functions. In particular, it is known that . In this paper we find similar results for products of incomplete gamma functions. Since the error functions are a special case of the incomplete gamma functions, we extend these results to these functions. Also, we prove an interesting relation between the error functions and the Laplace transform. [ABSTRACT FROM AUTHOR]

We define a liar-type paradox as a consistent proposition in propositional modal logic which is obtained by attaching boxes to several subformulas of an inconsistent proposition in classical propositional logic, and show several famous paradoxes are liar-type. Then we show that we can generate a liar-type paradox from any inconsistent proposition in classical propositional logic and that undecidable sentences in arithmetic can be obtained from the existence of a liar-type paradox. We extend these results to predicate logic and discuss Yablo's Paradox in this framework. Furthermore, we define explicit and implicit self-reference in paradoxes in the incompleteness phenomena. [ABSTRACT FROM AUTHOR]

By using the restricted Stirling numbers and associated Stirling numbers, we introduce two kinds of incomplete Cauchy numbers, which are generalizations that of the classical Cauchy numbers. We also study several arithmetical and combinatorial properties. [ABSTRACT FROM AUTHOR]

Charles Darwin's empirical research in palaeontology, especially on fossil invertebrates, has been relatively neglected as a source of insight into his thinking, other than to note that he viewed the fossil record as very incomplete. During theBeaglevoyage, Darwin gained extensive experience with a wide diversity of fossil taxa, and he thought deeply about the nature of the fossil record. That record was, for him, a major source of evidence for large-scale transmutation, but much less so for natural selection or single lineages. Darwin's interpretation of the fossil record has been criticised for its focus on incompleteness, but the record as he knew itwasextremely incomplete. He was compelled to address this in arguing for descent with modification, which was likely his primary goal. Darwin's gradualism has been both misrepresented and exaggerated, and has distracted us from the importance of the fossil record in his thinking, which should be viewed in the context of the multiple, sometimes competing demands of the multifaceted argument he presented in theOrigin of Species. [ABSTRACT FROM AUTHOR]

Multigranulation rough sets are desirable features in the field of rough set, where this concept is approximated by multiple granular structures. In this study, we employ belief and plausibility functions from evidence theory to characterize the set approximations and attribute reductions in multigranulation rough set theory. First, we show that in an incomplete information system, the pessimistic multigranulation approximations can be measured by belief and plausibility functions, whereas the optimistic multigranulation approximations do not possess this characteristic in general. We also give a sufficient and necessary condition for the numerical measurement of optimistic multigranulation approximations by belief and plausibility functions. Second, in an incomplete decision system, the pessimistic multigranulation approximations are also measured by belief and plausibility functions. In the end, an attribute reduction algorithm for multigranulation rough sets is proposed based on evidence theory, and its efficiency is examined by an example. Thus, belief and plausibility functions can be employed to numerically characterize the attribute reductions and to construct an attribute reduction algorithm for multigranulation rough sets. [ABSTRACT FROM AUTHOR]

Conditional Preference Networks (CP-nets) are widely used to express qualitative preferences. As users are sometimes reluctant or unable to specify complete CP-nets, it prohibits personalized search from being effectively conducted. In this article, we present an approach to perform personalized search using incomplete CP-nets. We propose a preference recommendation scheme for complementing a user’s CP-nets, so as to improve the accuracy of personalized search. We have conducted extensive simulation and user study to demonstrate the effectiveness of our approach. [ABSTRACT FROM AUTHOR]

A substantial number of indefinite integrals are presented for the incomplete elliptic integrals of the first and second kinds. The number of new results presented is about three times the total number to be found in the current literature. These integrals were obtained with a Lagrangian method based on the differential equations which these functions obey. All results have been checked numerically with Mathematica. Similar results for the incomplete elliptic integral of the third kind will be presented separately. [ABSTRACT FROM AUTHOR]

This paper proposes a novel approach for modelling complex interconnected systems by means of Mamdani fuzzy networks with feedforward rule bases. The nodes in these networks are rule bases connected in a feedforward manner whereby outputs from some rule bases are fed as inputs to subsequent rule bases. The approach allows any fuzzy network of this type to be presented as an equivalent Mamdani fuzzy system by linguistic composition of its nodes. The composition process makes use of formal models for fuzzy networks, basic operations in such networks, their properties and advanced operations. These models, operations and properties are used for defining several types of networks with single or multiple horizontal levels and vertical layers. The proposed approach facilitates the understanding of complex interconnected systems by improving the transparency of their models. [ABSTRACT FROM AUTHOR]

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Determining right model of business process from event log is the purpose of process discovery. However some problems i.e the inability to discover OR, noise and event log incompleteness are emmerged while determining right model of business process. First, OR relation is often discovered as AND relation. Second, noise problem is occured when there are truncated and low frequency traces in event log. Thus control-flow pattern is used to solve issues of same noise relation frequency hence it discovers relation based on transaction function of activity. Consequently, it can refine non noise relation in business process model. Third, incompleteness leads to incorrect discovery of parallel process model; therefore we used Timed-based Process Mining which utilized non-linear dependence to solve the incompleteness. Finally this paper proposed combination of Timed-based Process Mining and control-flow pattern to discover OR and handle same frequency noise and incompleteness. From the experiment in section 3, this proposed method manages to get right process model from event log. [ABSTRACT FROM AUTHOR]

A special class of preferences, given by a directed acyclic graph, is considered. They are represented by incomplete pairwise comparison matrices as only partial information is available: for some pairs no comparison is given in the graph. A weighting method satisfies the linear order preservation property if it always results in a ranking such that an alternative directly preferred to another does not have a lower rank. We study whether two procedures, the EigenvectorMethod and the Logarithmic Least SquaresMethod meet this axiom. Both weighting methods break linear order preservation, moreover, the ranking according to the EigenvectorMethod depends on the incomplete pairwise comparison representation chosen. [ABSTRACT FROM AUTHOR]

The implicit content associated with incomplete definite descriptions is contributed in the form of definite descriptions of situations. A definite description of this kind is contributed by a small structure in the syntax, which is interpreted, in general terms, as 'the situation that bears R to s'. [ABSTRACT FROM AUTHOR]