DOCSLIB.ORG

Trends in Contemporary Computer Science Podlasie 2014

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Trends in Contemporary Computer Science Podlasie 2014 Trends in Contemporary Computer Science Podlasie 2014 Edited by Anna Gomolińska, Adam Grabowski, Małgorzata Hryniewicka, Magdalena Kacprzak, and Ewa Schmeidel Białystok 2014 Editors of the Volume: Anna Gomolińska Adam Grabowski Małgorzata Hryniewicka Magdalena Kacprzak Ewa Schmeidel Editorial Advisory Board: Agnieszka Dardzińska-Głębocka Pauline Kawamoto Norman Megill Hiroyuki Okazaki Christoph Schwarzweller Yasunari Shidama Andrzej Szałas Josef Urban Hiroshi Yamazaki Bożena Woźna-Szcześniak Typesetting: Adam Grabowski Cover design: Anna Poskrobko Supported by the Polish Ministry of Science and Higher Education Distributed under the terms of Creative Commons CC-BY License Bialystok University of Technology Publishing Office Białystok 2014 ISBN 978-83-62582-58-7 Table of Contents Preface .......................................................... 5 I Computer-Assisted Formalization of Mathematics Formal Characterization of Almost Distributive Lattices ............... 11 Adam Grabowski Formalization of Fundamental Theorem of Finite Abelian Groups in Mizar 23 Kazuhisa Nakasho, Hiroyuki Okazaki, Hiroshi Yamazaki, and Yasunari Shidama Budget Imbalance Criteria for Auctions: A Formalized Theorem ........ 35 Marco B. Caminati, Manfred Kerber, and Colin Rowat Feasible Analysis of Algorithms with Mizar .......................... 45 Grzegorz Bancerek II Interactive Theorem Proving Equalities in Mizar ................................................ 59 Artur Korniłowicz Improving Legibility of Proof Scripts Based on Quantity of Introduced Labels ........................................................... 71 Karol Pąk On Logical and Semantic Investigations in Kyiv School of Automated Reasoning ........................................................ 83 Alexander Lyaletski and Mykola Nikitchenko Towards Standard Environments for Formalizing Mathematics .......... 99 Adam Grabowski and Christoph Schwarzweller Parallelizing Mizar ................................................ 109 Josef Urban 4 III Optimization Techniques and Decision-making Processes Optimization Problems and Methods Applicable in Intelligent Tourist Travel Planners ................................................... 127 Jolanta Koszelew Combining Genetic Algorithm and Path Relinking for Solving Orienteering Problem with Time Windows ........................... 135 Joanna Karbowska-Chilińska and Paweł Zabielski Comparison of Different Graph Weights Representations Used to Solve the Time-Dependent Orienteering Problem ........................... 147 Krzysztof Ostrowski An Approach to Making Decisions with Metasets ..................... 159 Magdalena Kacprzak and Bartłomiej Starosta IV Formal Methods and Data Mining On the SAT-based Verification of Communicative Commitments ........ 175 Bożena Woźna-Szcześniak Action Rules Mining in Laryngological Disorders ...................... 187 Agnieszka Dardzińska-Głębocka, Bożena Kosztyła-Hojna, and Anna Łobaczuk-Sitnik Similarity-based Searching in Structured Spaces of Music Information .. 195 Mariusz Rybnik and Władysław Homenda Author Index ................................................ 206 Preface This monograph presents the recent results obtained by the Podlasie com- puter scientists and their colleagues working among the wide world. The book consists of sixteen chapters and is divided into four parts. In Part I, comprising four chapters, some aspects of formalization of math- ematics are presented. In Chapter 1, almost distributive lattices (ADL) being structures defined by Swamy and Rao in 1981 as the generalization of ordinary distributive lattices by removing certain conditions from the well-known axioma- tization of these are considered. As distributive lattices are pretty well present in the Mizar Mathematical Library (MML), also formal characterization of ADL in terms of Mizar attributes and clusters are given. Many of the lemmas and coun- terexamples can be obtained semiautomatically with the help of external provers (e.g. Prover9 and MACE), and also internal Mizar utilities can improve human work in this area. A new formalization of crucial parts of the chosen results obtained by Rao is presented. The characterization of the class of generalized almost distributive lattices is obtained as well. The fundamental theorem of finite abelian groups, which describes the struc- ture of these groups, is formalized in Chapter 2. Since the theorem underlies the study of finite abelian groups, it is expected to become widely applied in formalizing fields such as number theory and cryptology as future Mizar results. In Chapter 3, an original theorem in auction theory is provided. It specifies general conditions under which the sum of the payments of all bidders is granted not to be identical to zero, and more generally – not to be constant. Moreover, it explicitly supplies a construction for a finite minimal set of possible bids on which such sum is not constant. In particular, the theorem presented applies to the important case of the second-price Vickrey auction, where it reduces itself to a basic result of which a novel, alternative proof is given. In order to enhance the confidence in this new theorem, it has been formalized in Isabelle/HOL: the main results and definitions of the formal proof are reproduced here in the common mathematical language, and accompanied with an informal discussion about the underlying ideas. Chapter 4 is devoted to the analysis of algorithms with Mizar. The approach proposed consists in the Mizar formalization of abstract concepts like algebra of instructions, execution function, termination, and their substantiation in a model with integers as the only data type and in models with abstract data types. The proof of correctness of the algorithm Exponentiation by Squaring is described. Part II is devoted to the memory of Andrzej Trybulec, a pioneer of computer– assisted formalization of mathematical problems. Over the last decades we wit- nessed a number of successful instances of such formalization. Research in this field has been boosted by the development of systems for practical formalization of mathematics (proof assistants), creation of large repositories of computer– verified formal mathematics, and integration of interactive and automated meth- 6 ods of theorem proving. Proof assistants provide a very useful teaching tool suit- able for undergraduate instruction, in particular for training beginning students in writing rigorous proofs. Thus, interactive theorem proving is the main subject of this part of the monograph. The part comprises five chapters. The usage of extensionality of sets, possibly satisfying some additional prop- erties, by proof checkers is presented in Chapter 5. In particular, it is shown how extensionality influences proof tactics and equational calculus. Short descrip- tions of Mizar constructions, having an impact on two basic Mizar modules: Reasoner for supporting definitional expansions and Equalizer for computing of the congruence closure of a given set of equalities, are collected. Chapter 6 is devoted to the formal proof checking systems such as Mizar and Isabelle/Isar. These systems can verify the correctness of proof scripts, both easily readable and obscure. However, for humans like those analysing of the main idea of a formal proof or redeveloping of fragments of reasoning to make them stronger, the legibility has a substantial significance. Furthermore, proof writers create still more and more complex deductions that cannot be shortened to several steps by any tools currently available. Therefore, it is important to understand better how we can facilitate the work of script readers modifying the order of independent deduction steps or how we can reorganize the proof structure by extracting lemmas that are obtained automatically. Experimental results are presented, obtained with a method that improves proof legibility and is based on human short-term memory. Chapter 7 is devoted to a brief description of the logical and semantic ap- proaches being developed in the Kyiv school of automated reasoning. This ap- proach can be traced back to 1970, when academician V. Glushkov initiated research on automated theorem proving in mathematics, which is known as the Evidence Algorithm programme (EA) having many common theses with the Polish Mizar project. A significant attention has been paid to the study and the development of logic and semantics as well as a technique for logical inference search. Carried out first at the Institute of Cybernetics of NASU, these investiga- tions moved in 1987 to the Faculty of Cybernetics of the National University of Kyiv, where now they are developed in two directions. The first direction is the traditional one, centered mainly on the construction of proof methods in various first-order logics. The second direction aims at developing of logics oriented on semantic models of programs. It is expected that the results obtained will give us a possibility to extend SAD with more expressive logical languages and more powerful reasoning tools. Though more and more advanced theorems have been formalized in proof systems, their presentation still lacks the elegance of the mathematical writing. The reason is that proof systems have to state much more details – a large number of which is usually omitted by mathematicians. In Chapter 8, the au- thors argue that proof languages should be improved into this direction to make proof systems more attractive and usable – the ultimate goal of course being a like-on-paper presentation. It has been shown that using advanced
Load more

Recommended publications
  • NDIGOZ016756.Pdf
    Trends in Contemporary Computer Science Podlasie 2014 Edited by Anna Gomolińska, Adam Grabowski, Małgorzata Hryniewicka, Magdalena Kacprzak, and Ewa Schmeidel Białystok 2014 Editors of the Volume: Anna Gomolińska Adam Grabowski Małgorzata Hryniewicka Magdalena Kacprzak Ewa Schmeidel Editorial Advisory Board: Agnieszka Dardzińska-Głębocka Pauline Kawamoto Norman Megill Hiroyuki Okazaki Christoph Schwarzweller Yasunari Shidama Andrzej Szałas Josef Urban Hiroshi Yamazaki Bożena Woźna-Szcześniak Typesetting: Adam Grabowski Cover design: Anna Poskrobko Supported by the Polish Ministry of Science and Higher Education Distributed under the terms of Creative Commons CC-BY License Bialystok University of Technology Publishing Office Białystok 2014 ISBN 978-83-62582-58-7 Table of Contents Preface .......................................................... 5 I Computer-Assisted Formalization of Mathematics Formal Characterization of Almost Distributive Lattices ............... 11 Adam Grabowski Formalization of Fundamental Theorem of Finite Abelian Groups in Mizar 23 Kazuhisa Nakasho, Hiroyuki Okazaki, Hiroshi Yamazaki, and Yasunari Shidama Budget Imbalance Criteria for Auctions: A Formalized Theorem ........ 35 Marco B. Caminati, Manfred Kerber, and Colin Rowat Feasible Analysis of Algorithms with Mizar .......................... 45 Grzegorz Bancerek II Interactive Theorem Proving Equalities in Mizar ................................................ 59 Artur Korniłowicz Improving Legibility of Proof Scripts Based on Quantity of Introduced Labels ..........................................................
    [Show full text]
  • On the History of Polish Logic
    1 ON POLISH LOGIC from a historical perspective Urszula Wybraniec-Skardowska, Poznań School of Banking, Faculty in Chorzów Autonomous Section of Applied Logic and Rhetoric, Chorzów, Poland http://main.chorzow.wsb.pl/~uwybraniec/ 29 May 2009, Department of Philosophy, Stanford University 1 In this talk, we will look at the development of Polish logic in the 20th century, and its main phases. There is no attempt at giving a complete history of this rich subject. This is a light introduction, from my personal perspective as a Polish student and professional logician over the last 40 years. But for a start, to understand Polish logic, you also need to understand a bit of Polish history. 1 Poland in the 20th century2 Polish logic and the logic of Poland’s history are tied together by a force that lifted the country from “decline” and “truncation” at times when national independence and freedom of thought and speech were inseparable. Take a glance at the maps that you see here: medieval Poland under the Jagiellonian dynasty in the 17th century, and 20th century Poland with its borders after the First World War (1918) and the Second World War (1945): 1 I would like to thank Johan van Benthem for his crucial help in preparing this text. 2 We rely heavily on Roman Marcinek, 2005. Poland. A Guide Book, Kluszczynski, Krakow. 2 A series of wars in the 17th c. led to territorial losses and economic disaster. Under the Wettin dynasty in the 18th c., Poland was a pawn in the hands of foreign rulers.
    [Show full text]
  • Wkład Logików Polskich W Światową Informatykę1
    Filozofia Nauki Rok XIV, 2006, Nr 3(55) Kazimierz Trzęsicki Wkład logików polskich w światową informatykę1 Kiedy słyszymy o sukcesach polskich studentów informatyki na Akademickich Mistrzostwach Świata w Programowaniu czy zwycięstwach w konkursach prac mło- dych naukowców Unii Europejskiej i o zajmowaniu przez Uniwersytet Warszawski czołowych pozycji w światowych rankingach studiów informatycznych, musimy za- pytać się, dlaczego tak jest, gdzie należy szukać źródeł tego sukcesu. Niewątpliwie sukcesy polskich studentów, nie tylko tych z Uniwersytetu Warszawskiego, są ich sukcesami osobistymi, wynikiem ich talentów, pracowitości i ambicji. Nie na wiele jednak by to się zdało, gdyby zabrakło dobrych nauczycieli, takich, którzy sami jako naukowcy wnoszą istotny i znaczący wkład w rozwój informatyki. Informatycy z Uniwersytetu Warszawskiego znajdują się w światowej czołówce. Komentując od- notowanie w 2003 roku Uniwersytetu Warszawskiego jako instytucji, skąd pochodzą publikacje znajdujące się na czołowym miejscu ze względu na liczbę cytowań, pro- fesor Damian Niwiński [Niwiński 2003] wskazuje na to, że na Uniwersytecie War- szawskim informatyka rozwija się systematycznie od 1960 roku. Przyczyny tego upatruje w postawach wielkich polskich matematyków2, spadkobierców polskiej szkoły matematycznej: Kazimierza Kuratowskiego, Stanisława Mazura, Wacława Sierpińskiego, Hugo Steinhausa3, Heleny Rasiowej4. Wskazuje przy tym na zasadni- 1 Pragnę podziękować anonimowemu recenzentowi za uwagi, które przyczyniły się do ulep- szenia artykułu. Praca została wykonana w ramach grantu KBN 3 T11F 01130. 2 W tym kontekście ważne są też dwa inne nazwiska: profesor Oskar Lange — ekonomista, profesor Janusz Groszkowski — dyrektor Państwowego Instytutu Telekomunikacyjnego, późniejszy zastępca przewodniczącego Rady Państwa PRL. 3 Początkowo pełnił funkcję wicedyrektora Grupy Aparatów Matematycznych ds. zastosowań. Później stanowisko to zajął prof. Stanisław Turski (1906-1986).
    [Show full text]
  • Polish Logic
    POLISH LOGIC some lines from a personal perspective Urszula Wybraniec-Skardowska, Poznań School of Banking, Faculty in Chorzów Autonomous Section of Applied Logic and Rhetoric, Chorzów, Poland http://main.chorzow.wsb.pl/~uwybraniec/ July 2009 Abstract Without aspiring to historical or systematic completeness, this paper presents an informal survey of some lines in 20th century Polish logic, together with some general historical background, and making special reference to the author’s environment in Opole, and the contributions by her teacher Jerzy Słupecki. Further published material can be found in the appended bibliography. 2 Contents Preface (Johan van Benthem)………………………………………………………………… 3 POLISH LOGIC, a few lines from a personal perspective…………………………………….4 1 Poland in the 20th century……………..……………………………………………….……… 4 2 How Polish logic started around 1900: the Lvov-Warsaw School………………………7 3 The Warsaw Logic School: its main figures and ideas……………………………...…… 8 Characteristics of the Warsaw School………………………………………….……. 11 Methodology of the sentential calculus and Tarski’s influence………………….13 A counterpoint: the work of Leśniewski………………………………………...… 13 The Warsaw School: further characteristics, and influence……..……….14 4 Polish Logic after the Second World War……………………………………………....... 15 The new Warsaw Centre…………………………………………………………….. 16 5 My teacher Jerzy Słupecki, his career and influence……………………………………17 Logic in Wrocław……………………………………………………………………. 18 My own environment: the Opole Centre……………………………………………19 Sentential calculi and methodological
    [Show full text]