We investigate the computational complexity of axiom pinpointing in Description Logics, which is the task of finding minimal subsets of a knowledge base that have a given consequence. We consider the problems of enumerating such subsets with and without order, and show hardness results that already hold for the propositional Horn fragment, or for the Description Logic EL. We show complexity results for several other related decision and enumeration problems for these fragments that extend to more expressive logics. In particular we show that hardness of these problems depends not only on expressivity of the fragment but also on the shape of the axioms used.

The least common subsumer (lcs) w.r.t general EL-TBoxes does not need to exists in general due to cyclic axioms. In this report we present an algorithm for computing role-depth bounded EL-lcs based on the completion algorithm for EL. We extend this computation algorithm to a recently introduced probabilistic variant of EL: Prob-EL⁰¹.

The aim is to present specific methodology of the austrian school with laying stress on prerequisits which determine its understanding of phenomena.

Axiom pinpointing has been introduced in description logics (DLs) to help the user to understand the reasons why consequences hold and to remove unwanted consequences by computing minimal (maximal) subsets of the knowledge base that have (do not have) the consequence in question. The pinpointing algorithms described in the DL literature are obtained as extensions of the standard tableau-based reasoning algorithms for computing consequences from DL knowledge bases. Although these extensions are based on similar ideas, they are all introduced for a particular tableau-based algorithm for a particular DL. The purpose of this paper is to develop a general approach for extending a tableau-based algorithm to a pinpointing algorithm. This approach is based on a general definition of „tableaux algorithms,' which captures many of the known tableau-based algorithms employed in DLs, but also other kinds of reasoning procedures.

The notion of a most specific consequence with respect to some terminological box is introduced, conditions for its existence in the description logic EL and its variants are provided, and means for its computation are developed. Algebraic properties of most specific consequences are explored. Furthermore, several applications that make use of this new notion are proposed and, in particular, it is shown how given terminological knowledge can be incorporated in existing approaches for the axiomatization of observations. For instance, a procedure for an incremental learning of concept inclusions from sequences of interpretations is developed.

Pastaruoju metu žiniomis grindžiamų informacinių sistemų kūrimui pradėtos naudoti ontologijos, tinkamos dalykinės srities žinioms vaizduoti ir sistemų mo-deliams kurti bei jiems įgyvendinti. Tačiau verslo taisyklių modeliavimas onto-logija grindžiamose informacinėse sistemose nėra pakankamai išnagrinėtas ir aiškiai aprašytas. Disertacijoje autorė siūlo metodą ontologijos aksiomoms trans-formuoti į verslo taisykles, kurios naudojamos tam tikriems dalykinės srities as-pektams apriboti arba nukreipti. Siūlomo metodo esmė – dalykinės srities aksio-mos, išreikštos pasirinkta kalba, transformuojamos į verslo taisykles, kurios įgyvendinamos informacinės sistemos programų vykdomosiomis taisyklėmis. Formaliam metodo aprašymui sukurti disertacijoje vartojama Z kalba, o MDA karkasas taikomas siūlomam metodui automatizuoti. Disertaciją sudaro įvadas, keturi skyriai ir išvados, naudotos literatūros ir au-toriaus publikacijų disertacijos tema sąrašai ir trys priedai. Įvadiniame skyriuje nagrinėjamas problemos aktualumas, formuluojamas darbo tikslas bei uždaviniai, aprašomas mokslinis darbo naujumas, pristatomi autorės pranešimai ir publikacijos, disertacijos struktūra. Pirmasis ir antrasis sky-riai skirti literatūros apžvalgai. Pirmajame skyriuje pateikta verslo taisyklės są-vokos analizė, nagrinėjami verslo taisyklių įgyvendinimo metodai ir kalbos. Ant-rajame skyriuje apžvelgiama ontologijos sąvoka, jos panaudojimo galimybės informacinėms sistemoms kurti. Pagrindinis dėmesys skiriamas... [toliau žr. visą tekstą] / Ontologies in nowadays are widely used in the process of development of modern information systems, since they are suitable to represent domain knowl-edge. However, the development of domain rules in ontology-based information systems is required to be analysed. In this dissertation, the author proposes a formal method of transforming ontology axioms to domain rules, making an im-portant and integral part of each domain and used to constrain or direct different aspects of a domain. Such rules can be consecutively transformed into executable form and implemented in a software system of an information system. The pro-posed method is formalised using the Z notation and the MDA framework is ap-plied to automate it. The dissertation consists of the introduction, four chapters, the conclusions, references, list of author’s publications and three annexes. The introduction overviews the main problem analysed in the dissertation and its importance. The aim and consequent objectives, scientific novelty and practical value of the research, methodology of the research, hypothesis of the research, scientific approval, contribution of the results and structure of the dis-sertation are formulated and presented in this chapter. The first and the second chapters cover analysis of existing publications re-lated with the problem of the dissertation. Therefore, the concept of the domain rule and the main problems of their modelling and implementing are analysed in the first chapter. The second... [to full text]

Working within the Zermelo-Frankel Axioms of set theory, we will introduce two important contradictory axioms: Axiom of Choice and Axiom of Determinacy. We will explore perfect polish spaces and games on these spaces to see that the Axiom of Determinacy is inconsistent with the Axiom of Choice. We will see some of the major consequences of accepting the Axiom of Determinacy and how some of these results change when accepting the Axiom of Choice. We will consider 2-player games of perfect information wherein we will see some powerful results having to do with properties of the real numbers. We will use a game to illustrate a weak proof of the continuum hypothesis.

The concept of social axiom represents generalized beliefs regarding individuals, agencies and other social institutions, and the spiritual world. The relationship between social axioms and social and mental well-being has not been widely investigated. The aim of this research is to consider the role of culture in four distinct areas of study: 1) The role of social axioms and their dimensions in predicting mental well-being (subjective and psychological well-being) as well as the mechanism of the relationship between social axioms and well-being through controlling the variables of Iranian and UK students and the big five personality factors. 2) The mediation role of mindfulness and perspective taking. 3) The scope of influence of one's attachment to national or ethnic identity on well-being. 4) The understanding of the participants of various social beliefs, especially of the concept of divine providence and its impact on one's well-being. As method, the first three goals were addressed by correlational studies while the fourth goal was investigated using grounded theory. The research sample for the first study consisted of 73 Iranian students (37 females and 36 males) residing in Iran and 66 students (45 females and 21 males) living in the UK. The sample for the second study included 72 Iranian students (34 females and 38 males) who reside in Iran, and in the third study the sample was composed of 66 Iranians (35 females and 31 males) who live in the UK. In the qualitative research (fourth study), the participants were 14 Iranians living in the UK for at least 3 years (4 male and 10 female). Instruments used were the Social Axiom Survey (SAS; Leung et al., 2002), Big Five Inventory (BFI; John, Donahue, & Kentle, 1991; John & Srivastava, 1999), Psychological Well-Being Scale (Ryff, 1989), Satisfaction With Life Scale (SWLS; Diener, Emmons, Larsen, & Griffin, 1985), Positive and Negative Affect Scale (Mroczek & Kolarz, 1998), the perspective taking subscale of the Empathy Questionnaire (Davis, 1980), the acceptance subscale of the Philadelphia Mindfulness Scale (Cardaciotto et al., 2008), Paullhus's Balanced Inventory of Desirable Responding (BIDR; Paulhus, 1984), and the Multigroup Ethnic Identity Measure-Revised (MEIM-R; Phinney & Ong, 2007). In the qualitative research, a structured interview was used. Results show that: 1) In both samples of students who live in the UK and in Iran iv social cynicism and fate control are related with well-being. Also, in the Iranian case reward for application, social complexity, and religiosity have significant relationships with well-being but in the UK based students this is not the case. Results also showed that social axioms can predict well-being over and above the role of country and personality traits. 2) The mediation role of mindful acceptance was not endorsed in the relationship between social cynicism and subjective well-being. It was found that the predictor (social cynicism) and the mediator (mindful acceptance) were not significantly correlated with the outcome (subjective well-being). However, the mediation role of perspective taking in the relationship between social complexity and psychological well-being was endorsed. 3) The moderation role of attachment to national identity in the relationship between social axioms and subjective well-being was endorsed. 4) The qualitative study indicated that Iranian immigrants have an indigenous strategy for attaining mental well-being in the face of complications and difficulties, relying on their national identity and religious background. This strategy is based on the concepts of free will and predestination of life events. Paying attention to negative events and ignoring positive events and inefficient problem-solving strategies can account for the relationship between social cynicism and low well-being and inattention to cultural elements. However, the Iranian collective culture, optimal coping style, and excessive insistence on religious elements as a cultural attribute can explain the relationship between religiosity, reward for application, and well-being in the Iranian sample. On the other hand, surrendering to divine will and the belief in divine will and predestination of life events along with the belief in human free will account for the role of attachment to national identity in the relationship between social axioms and well-being in the Iranian sample. In conclusion, it seems that though social axioms are related to well-being, different aspects of social axioms seem to be related to different aspects of well-being in different ways and this relationship is influenced by cultural attributes.

Submitted by ALINE CLARO DE FREITAS (aline_claro@yahoo.com.br) on 2016-02-16T18:44:15Z No. of bitstreams: 1 TCC versao final_ALine.pdf: 1602203 bytes, checksum: d62a761bc942b6ff65606a2498723090 (MD5) / Approved for entry into archive by Ana Paula Grisoto (grisotoana@reitoria.unesp.br) on 2016-02-17T16:12:02Z (GMT) No. of bitstreams: 1 freitas_ac_me_prud.pdf: 1602203 bytes, checksum: d62a761bc942b6ff65606a2498723090 (MD5) / Made available in DSpace on 2016-02-17T16:12:02Z (GMT). No. of bitstreams: 1 freitas_ac_me_prud.pdf: 1602203 bytes, checksum: d62a761bc942b6ff65606a2498723090 (MD5) Previous issue date: 2016-01-29 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Frente à realidade do ensino contemporâneo que demanda a necessidade de diversificar o uso de estratégias de ensino, pretendemos propor uma abordagem, por meio de material concreto e que pode tornar-se bastante significativa no ensino da matemática. Este trabalho discute sobre a história, aplicações clássicas e utilização do origami em sala de aula. Após uma breve apresentação histórica sobre o origami, apresentamos uma abordagem axiomática deste instrumento. Dois dos três famosos problemas matemáticos gregos da antiguidade que não podem ser solucionados através da régua e compasso: trissecção do ângulo e duplicação do cubo encontram uma solução por meio das técnicas de origami. Além disso, apresentamos sugestões de roteiros de aulas e a atividade aplicada em sala de aula que obteve resultado satisfatório. / Faced with the reality of contemporary teaching that demands the need to diversify the use of teaching strategies, we intend to propose an approach through concrete material and can become quite significant in mathematics education. This monograph discusses about the history, classic applications and use origami in the classroom. After a brief historical introduction about origami, we present an axiomatic approach of this instrument. Two of the three famous Greek mathematical problems of antiquity that can’t be solved by ruler and compass: trisection angle and doubling the cube find a solution through of origami techniques. In addition, we present suggestions classes scripts and the activitie applied in the classroom that obtained satisfactory result.

Submitted by Viviane Lima da Cunha (viviane@biblioteca.ufpb.br) on 2015-10-19T12:44:14Z No. of bitstreams: 1 arquivototal.pdf: 685310 bytes, checksum: c2f1ca276071e748c54644c3a47977f8 (MD5) / Approved for entry into archive by Maria Suzana Diniz (msuzanad@hotmail.com) on 2015-10-19T12:44:52Z (GMT) No. of bitstreams: 1 arquivototal.pdf: 685310 bytes, checksum: c2f1ca276071e748c54644c3a47977f8 (MD5) / Made available in DSpace on 2015-10-19T12:44:52Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 685310 bytes, checksum: c2f1ca276071e748c54644c3a47977f8 (MD5) Previous issue date: 2014-08-27 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The main objective of this work is showing the importance of systems axiomatic in mathematics. We will study some classic axioms, their equivalence and we will see some applications of them. / Este trabalho tem como objetivo fazer uma abordagem sobre a importância de sistemas axiomáticos na Matemática. Estudaremos alguns axiomas clássicos, suas equivalências e veremos algumas aplicações dos mesmos.