Thesis (Dr. rer. nat.)--Technische Universität München, 2000. / "Infix"--Cover. Includes bibliographical references (p. [164]-175) and index.

Univ., Diss.--Cambridge, 1991. / Literaturverz. S. [133] - 138.

Thesis (Ph.D.) - University of Queensland, 2006. / Includes bibliography.

Τα «Συστήματα Αυτόματης Απόδειξης Θεωρημάτων-ΣΑΑΘ» (Automatic Theorem Proving Systems-ATP Systems) είναι συστήματα βασισμένα στη λογική πρώτης τάξεως, τα οποία μπορούν από ένα σύνολο λογικών προτάσεων να συνάγουν την αλήθεια μιας δεδομένης λογικής πρότασης με αυτόματο τρόπο. Η διαδικασία της απόδειξης στα περισσότερα ΣΑΑΘ στηρίζεται στην αρχή της επίλυσης, τον ισχυρότερο κανόνα λογικής εξαγωγής συμπερασμάτων, και την αντίφαση της επίλυσης, μια διαδικασία που εξασφαλίζει την ορθότητα των συμπερασμάτων. Ο ACT-P είναι ένα ΣΑΑΘ που στηρίζεται στην αρχή της επίλυσης και την αντίφαση της επίλυσης, γραμμένο στο εργαλείο GCLISP Developer 5.0 της Gold-Hill, και διαθέτει μια βιβλιοθήκη γνωστών στρατηγικών ελέγχου της διαδικασίας απόδειξης, προσφέροντας τη δυνατότητα στον χρήστη να ορίσει κάθε φορά ένα (κατάλληλο) συνδυασμό στρατηγικών. Στην εργασία αυτή έγινε κατ’ αρχήν μεταφορά του ACT-P σε LispWorks, ένα δυναμικότερο εργαλείο ανάπτυξης εφαρμογών σε Lisp. Επιπλέον, ο χρήστης μέσω του νέου παραθυρικού περιβάλλοντος μπορεί να βλέπει δυο διαφορετικές λύσεις του ίδιου προβλήματος, τη συνοπτική και αναλυτική λύση. Στη συνέχεια, έγινε έλεγχος της καλής λειτουργίας του ACT-P και των στρατηγικών του μέσω δοκιμών με προβλήματα που προέρχονται από την TPTP (Thousands of Problems for Theorem Provers), μια γνωστή βιβλιοθήκη προβλημάτων για ΣΣΑΘ συστήματα στο Διαδίκτυο, και έγιναν οι απαραίτητες διορθώσεις έτσι ώστε να επιλύει προβλήματα από διάφορες κατηγορίες προβλημάτων της βιβλιοθήκης TPTP. Τέλος, έγινε μια μελέτη χρήσης διαφόρων συνδυασμών στρατηγικών ελέγχου για διάφορα προβλήματα της TPTP και εξήχθησαν χρήσιμα συμπεράσματα για την καταλληλότητά τους και την αποδοτικότητά τους σε σχέση με το είδος των προβλημάτων. / Automatic Theorem Proving Systems (ATP Systems) are based on First Order Logic (FOL) and are able to automatically prove the truth of logical sentence. The proof procedure in most ATP Systems uses the resolution principle which is the strongest existing inference rule, and the resolution refutation process which ensure soundeness of the conclusion. The ACT-P is an ATP System which uses the resolution principle and the resolution refutation and it is written in GCLISP Developer 5.0 of Gold-Hill. ACT-P has a library of strategies to control the proof process, and gives users the ability to assign to specify a suitable combination of strategies. In this dissertation a new window based interface is developed for ACTP in Lispworks, which is a powerful tool for developing Lisp applications. The interface gives to the user a more thorough view of the solving process. Moreover, the user can see two different solutions of the problem, the brief and the analytic one. In addition, the functionality and the strategies of ACTP were tested on problems from the TPTP (Thousands of Problems for Theorem Provers) which is a known library of problems for ATP Systems on the web. ACTP has been improved so as to solve problems from various categories of the TPTP library. Finally, different strategy combinations for solving problems from various categories of TPTP library were studied, leading to useful conclusions about the suitability and the performance of the different combinations depending on the problems.

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Capes / A partir dos teoremas encontrados na publicação Geometriae Pars Universalis de 1668 são apresentadas, pela primeira vez em português, as demonstrações dos teoremas de Pappus para os sólidos de revolução. Essa publicação, escrita originalmente em latim, foi feita pelo matemático escocês James Gregory (1638-1675) e é anterior ao desenvolvimento do Cálculo. Além disso, alguns conceitos de Cálculo e de centro de gravidade são revistos a fim de também apresentarumademonstraçãodessesteoremasapartirdessasferramentas. Ainda são feitas algumas aplicações dos teoremas de Pappus para os casos diretos, onde o eixo de rotação ou revolução é representado por um dos eixos coordenados ou ainda, por uma reta paralela a eles. Também são mostrados casos onde o eixo de rotação é dado por uma reta inclinada no plano cartesiano, deixando claro a abrangência, eficiência e a relativa simplicidade de aplicação desses teoremas. / From the theorems found in the publication Geometriae Pars Universalisof 1668 are presented, for the first time in portuguese, the proof of Pappus’s theorems for solids of revolution. This publication , originally written in latin, is due to the scottish mathematician James Gregory (1638-1675) and is prior to the development of Calculus. Furthermore some concepts of Calculus and center of gravity are also revised to present a proof of these theorems from these tools. Some direct cases for Pappus’s theorems are presented, where the axis of rotation or revolution is represented by one of the coordinate axes or by a straight line parallel to them. Also shown are cases where the axis of rotation is given by a straight tilted in the cartesian plane, showing the scope, efficiency and relative simplicity of applying these theorems.

With the widely use of software technique in everyday applications, the correctness of software becomes more and more important. Formal verification is an important method to improve the correctness of software. However, it mainly takes formal languages as its modeling languages, which are based on mathematical logic, automata or graph theory, hard for learning and domain description. That hinders the applications of formal verification in industry. This dissertation investigates the design and practice of domain modeling and verification language EDOLA, to possess all the features of the usability for domain description, reusability and automatic verification. It proposes a three-level design method with the domain knowledge level, the common module level and the verification support level. The main contributions are summarized as follows: 1. In the domain knowledge level, the extraction and representation methods of the domain knowledge on both job-shop scheduling and PLC control software are proposed. It defines domain-specific operators of the job-shop scheduling problem, timed Petri net, etc. for the job-shop scheduling description. It also defines the operators of the scan cycle pattern, the complete environment pattern and five kinds of verification requests for the PLC domain description. It presents the formal semantics of the defined domain-specific operators, for the further EDOLA definition and its automatic verification. 2. In the common module level, the method to define common operators is presented with real-time as an example for common knowledge. It proposes two kinds of basic time operators and four advanced ones, which help EDOLA to describe real-time features easily and make the reusability of EDOLA design among time-sensitive domains possible. 3. In the verification support level, it presents a properties-oriented abstraction strategy, which reduces the state space and exploring space during automatic verifi- cation. It then formulates the encoding rules from EDOLA to first-order logic, thus implements the verification of the models with infinite states, with the help of first-order logic automatic theorem provers. 4. A prototype of the PLC domain modeling and verification language: EDOLA-PLC are developed and its tools are implemented. The tools provide an EDOLA-PLC editor and a compiler with the functionalities like syntax checking, semantics checking and translation-based automatic verification. 5. A case study of the EDOLA-PLC language on a dock fire-fighting control system is presented. It indicates that EDOLA-PLC is easy to describe both the PLC domain knowledge and the properties to be verified; is easy to describe the common knowledge: real-time and can be verified automatically. The results show that the abstraction strategy adopted in the verification support level of EDOLA-PLC improves the efficiency of automatic verification.

CAPES / Organizou-se esta dissertação a partir da constatação de que teoremas de matemáticos como Matthew Stewart e Heron são pouco empregados nas aulas de matemática do ensino fundamental e médio. As contribuições desses matemáticos no cálculo das cevianas e da área de triângulos podem simplificar a solução de muitos problemas. Como ponto de partida, elaborou-se uma atividade extraclasse contendo quatro questões centradas no Teorema de Stewart e aplicou-se a mesma a três turmas do ensino m´edio do CPM-PR. A partir da análise dos resultados dessa atividade, definiu-se a pesquisa bibliográfica, a estrutura do texto e a organização de uma coleção de problemas aplicados. / This dissertation was organized from the observation that mathematical theorems as Stewart’s theorem and Heron’s theorem are rarely used in mathematics classes in middle and high schools. The contributions of these mathematicians in calculating cevians and area of triangles can simplify the solution of many problems. As a starting point, we prepared one extracurricular activity containing four questions centered on Stewart’s theorem and applied the same in three high school classes of CPM-PR. From the analysis of the results of this activity, we defined the literature, the text structure and organization of a collection of applied problems.

"Feature-oriented programming is a way of designing a program around the features it performs, rather than the objects or files it manipulates. This should lead to an extensible and flexible "product-line" architecture that allows custom systems to be assembled with particular features included or excluded as needed. Composing these features together modularly, while leading to flexibility in the feature-set of the finished product, can also lead to unexpected interactions that occur between features. Robert Hall presented a manual methodology for locating these interactions and has used it to search for feature interactions in email. Li et al. performed automatic verification of Hall's system using model-checking verifications tools. Model-checking verification is state-based, and is not well-suited for verifying recursive data structures, an area where theorem-proving verification tools excel. In this thesis, we propose a methodology for using formal theorem-proving tools for modularly verifying feature-oriented systems. The methodology presented captures the essential steps for using modular techniques for modeling and verifying a system. This enables verification of individual modules, without examining the source code of the other modules in the system. We have used Hall's email system as a test case for validating the methodology."

Based on the author's Ph. D. thesis, University of California, Berkeley, 1993. / Includes bibliographical references (p. [73]-78) and index. Also issued online.