Trends in Contemporary Computer Science

Almost distributive lattices (ADL) are structures defined by Swamy and Rao in 1981 as the generalization of ordinary distributive lattices by removing certain conditions from well-known axiomatization of these. As distributive lattices are pretty well present in the Mizar Mathematical Library (MML), we decided to give also formal characterization of ADL in terms of Mizar attributes and clusters. Many of the lemmas and counterexamples can be obtained semiautomatically with the help of external provers (e.g. Prover9 and MACE), also internal Mizar utilities can improve human work in this area. We formalized crucial parts of the chosen papers of Rao (some of them are pretty recent), obtaining also the characterization of the class of generalized almost distributive lattices.

[1]  Jakub M. Tomczak,et al.  Advances in Systems Science , 2014 .

[2]  Ronny Kramer,et al.  Semantic Matching and Heuristic Search for a Dynamic Tour Guide , 2005, ENTER.

[3]  Marek R. Ogiela,et al.  Why Automatic Understanding? , 2007, ICANNGA.

[4]  Paul Milgrom,et al.  Putting Auction Theory to Work , 2004 .

[5]  Correctness of Dijkstra's Shortest Path and Prim's Minimum Spanning Tree Algorithms 1 , 2005 .

[6]  Piotr Rudnicki,et al.  On Equivalents of Well-Foundedness , 1999, Journal of Automated Reasoning.

[7]  Wojciech Penczek,et al.  Verifying epistemic properties of multi-agent systems via bounded model checking , 2002, AAMAS '03.

[8]  Paul R. McJones,et al.  Elements of Programming , 2009 .

[9]  Jesse Alama,et al.  Large Formal Wikis: Issues and Solutions , 2011, Calculemus/MKM.

[10]  Adam Naumowicz,et al.  Formal Mathematics for Mathematicians , 2012, Journal of Automated Reasoning.

[11]  Yatsuka Nakamura,et al.  An Extension of SCM , 1996 .

[12]  Konrad Raczkowski.  Real Function Differentiability 1 , 1990 .

[13]  Cezary Kaliszyk,et al.  PRocH: Proof Reconstruction for HOL Light , 2013, CADE.

[14]  J. Rotman.  An Introduction to the Theory of Groups , 1965 .

[15]  Roberto Montemanni,et al.  An ant colony system for team orienteering problems with time windows , 2023, 2305.07305.

[16]  Melquíades Pérez Pérez,et al.  A hybrid VNS–path relinking for the p-hub median problem , 2007 .

[17]  William McCune,et al.  Ivy: a preprocessor and proof checker for first-order logic , 2000 .

[18]  Marek R. Ogiela,et al.  Possible Uses of Information Technology (IT) in Anaesthesiology, Intensive Care and Emergency Medicine (eHealth). , 2006 .

[19]  V. V. Fedyurko,et al.  An algorithm for proving theorems in group theory , 1966 .

[20]  Josef Urban,et al.  MaLARea SG1- Machine Learner for Automated Reasoning with Semantic Guidance , 2008, IJCAR.

[21]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[22]  Ted Mau,et al.  Diagnostic evaluation and management of hoarseness. , 2010, The Medical clinics of North America.

[23]  Wojciech A. Trybulec.  Subgroup and Cosets of Subgroups , 1990 .

[24]  Peter Koepke,et al.  The Naproche Project: Controlled Natural Language Proof Checking of Mathematical Texts , 2009, CNL.

[25]  G. Sutcliffe.  The Design and Implementation of a Compositional Competition-Cooperation Parallel ATP System , 2001 .

[26]  Jasmin Christian Blanchette,et al.  Robust, Semi-Intelligible Isabelle Proofs from ATP Proofs , 2013, PxTP@CADE.

[27]  Adam Naumowicz,et al.  Mizar in a Nutshell , 2010, J. Formaliz. Reason..

[28]  Zdzislaw Pawlak,et al.  Information systems theoretical foundations , 1981, Inf. Syst..

[29]  Benjamin C. Paul,et al.  Hoarseness and laryngopharyngeal reflux: a survey of primary care physician practice patterns. , 2014, JAMA otolaryngology-- head & neck surgery.

[30]  Josef Urban,et al.  BliStr: The Blind Strategymaker , 2013, GCAI.

[31]  Zbigniew W. Ras,et al.  Action Rules Discovery without Pre-existing Classification Rules , 2008, RSCTC.

[32]  Dariusz Surowik,et al.  Cyclic Groups and Some of Their Properties - Part I , 1991 .

[33]  Piotr Rudnicki,et al.  Proving properties of Pascal programs in MIZAR 2 , 2004, Acta Informatica.

[34]  Andrzej Zbrzezny,et al.  On Boolean Encodings of Transition Relation for Parallel Compositions of Transition Systems , 2013, CS&P.

[35]  S. S. Shkilniak.  First-order logics of quasiary predicates , 2010 .

[36]  Josef Urban,et al.  XML-izing Mizar: Making Semantic Processing and Presentation of MML Easy , 2005, MKM.

[37]  Zbigniew W. Ras,et al.  Action-Rules: How to Increase Profit of a Company , 2000, PKDD.

[38]  Josef Urban,et al.  Escape to ATP for Mizar , 2011, PxTP.

[39]  Mariusz Rybnik,et al.  Querying in Spaces of Music Information , 2011, IUKM.

[40]  Jingchao Chen.  Dijkstra's Shortest Path Algorithm , 2003 .

[41]  Andrzej Zbrzezny,et al.  A New Translation from ECTL* to SAT , 2012, Fundam. Informaticae.

[42]  Piotr Rudnicki,et al.  Abian's Fixed Point Theorem , 2007 .

[43]  Artur Kornilowicz.  On Rewriting Rules in Mizar , 2012, Journal of Automated Reasoning.

[44]  Josef Urban,et al.  MizarMode - an integrated proof assistance tool for the Mizar way of formalizing mathematics , 2006, J. Appl. Log..

[45]  Alessio Lomuscio,et al.  Deontic Interpreted Systems , 2003, Stud Logica.

[46]  Zbigniew W. Ras,et al.  ARAS: Action Rules Discovery Based on Agglomerative Strategy , 2007, MCD.

[47]  Adam Grabowski,et al.  IMPROVING REPRESENTATION OF KNOWLEDGE WITHIN THE MIZAR LIBRARY , 2009 .

[48]  Mykola S. Nikitchenko,et al.  Composition-nominative aspects of address programming , 2009 .

[49]  Cezary Kaliszyk,et al.  Machine Learner for Automated Reasoning 0.4 and 0.5 , 2014, PAAR@IJCAR.

[50]  Jeffrey D. Ullman,et al.  Introduction to Automata Theory, Languages and Computation , 1979 .

[51]  Alexander V. Lyaletski,et al.  Evidence Algorithm and Sequent Logical Inference Search , 1999, LPAR.

[52]  Edmund M. Clarke,et al.  Model Checking , 1999, Handbook of Automated Reasoning.

[53]  Wladyslaw Homenda,et al.  Notes on Automatic Music Conversions , 2011, ISMIS.

[54]  Karol Pak.  Methods of Lemma Extraction in Natural Deduction Proofs , 2012, Journal of Automated Reasoning.

[55]  Geoff Sutcliffe,et al.  Smart Selective Competition Parallelism ATP , 1999, FLAIRS Conference.

[56]  Josef Urban,et al.  ATP-based Cross-Verification of Mizar Proofs: Method, Systems, and First Experiments , 2008, Math. Comput. Sci..

[57]  Thomas Hillenbrand.  Citius altius fortius: Lessons learned from the Theorem Prover WALDMEISTER , 2003, Electron. Notes Theor. Comput. Sci..

[58]  Joseph Y. Halpern,et al.  “Sometimes” and “not never” revisited: on branching versus linear time temporal logic , 1986, JACM.

[59]  J. Robinson.  An Overview of Mechanical Theorem Proving , 1970 .

[60]  Agnieszka Dardzinska.  Action Rules Mining , 2013, Studies in Computational Intelligence.

[61]  Andrzej Zbrzezny,et al.  SAT-Based Bounded Model Checking for Weighted Interpreted Systems and Weighted Linear Temporal Logic , 2013, PRIMA.

[62]  Josef Urban,et al.  Automated reasoning and presentation support for formalizing mathematics in Mizar , 2010, AISC'10/MKM'10/Calculemus'10.

[63]  Jerzy W. Grzymala-Busse,et al.  A New Version of the Rule Induction System LERS , 1997, Fundam. Informaticae.

[64]  G. Bancerek.  The Fundamental Properties of Natural Numbers , 1990 .

[65]  Boris Konev,et al.  Tableau Method with Free Variables for Intuitionistic Logic , 2006, Intelligent Information Systems.

[66]  Richard C. T. Lee,et al.  Symbolic logic and mechanical theorem proving , 1973, Computer science classics.

[67]  C. M. Sperberg-McQueen,et al.  Extensible markup language , 1997 .

[68]  Ronald Fagin,et al.  Reasoning about knowledge , 1995 .

[69]  Marius M. Solomon,et al.  Algorithms for the Vehicle Routing and Scheduling Problems with Time Window Constraints , 1987, Oper. Res..

[70]  N. Cowan.  Attention and Memory: An Integrated Framework , 1995 .

[71]  Jesse Alama,et al.  A wiki for Mizar: motivation, considerations, and initial prototype , 2010, AISC'10/MKM'10/Calculemus'10.

[72]  Andrei Voronkov,et al.  The design and implementation of VAMPIRE , 2002, AI Commun..

[73]  Grzegorz Bancerek,et al.  Program Algebra over an Algebra , 2012, Formaliz. Math..

[74]  Adam Grabowski,et al.  Revisions as an Essential Tool to Maintain Mathematical Repositories , 2007, Calculemus/MKM.

[75]  Konstantin Verchinine,et al.  Evidence algorithm and system for automated deduction: a retrospective view , 2010, AISC'10/MKM'10/Calculemus'10.

[76]  Larry Wos,et al.  Automated reasoning - 33 basic research problems , 1988 .

[77]  Manuel Laguna,et al.  Tabu Search , 1997 .

[78]  Paul A. Cairns,et al.  Using and Parsing the Mizar Language , 2004, Electron. Notes Theor. Comput. Sci..

[79]  Wladyslaw Homenda.  Automatic Data Understanding: A Necessity of Intelligent Communication , 2010, ICAISC.

[80]  Beata Madras,et al.  Basic Notation of Universal Algebra , 1992 .

[81]  Joanna Karbowska-Chilinska,et al.  Genetic Algorithm with Path Relinking for the Orienteering Problem with Time Windows , 2014, CS&P.

[82]  Alain Hertz,et al.  Metaheuristics for the team orienteering problem , 2005, J. Heuristics.

[83]  Alexander V. Lyaletski.  Sequent forms of Herbrand theorem and their applications , 2005, Annals of Mathematics and Artificial Intelligence.

[84]  Adam Naumowicz,et al.  A Brief Overview of Mizar , 2009, TPHOLs.

[85]  Colin Rowat,et al.  The ForMaRE Project - Formal Mathematical Reasoning in Economics , 2013, MKM/Calculemus/DML.

[86]  Andrzej Bargiela,et al.  Information structuring in natural language communication: Syntactical approach , 2006, J. Intell. Fuzzy Syst..

[87]  Jan Rauch,et al.  Action Rules and the GUHA Method: Preliminary Considerations and Results , 2009, ISMIS.

[88]  Michael Good,et al.  Extensible marckup language (XML) for music applications: an introduction , 2001 .

[89]  G. A. Miller.  THE PSYCHOLOGICAL REVIEW THE MAGICAL NUMBER SEVEN, PLUS OR MINUS TWO: SOME LIMITS ON OUR CAPACITY FOR PROCESSING INFORMATION 1 , 1956 .

[90]  Josef Urban,et al.  ATP and Presentation Service for Mizar Formalizations , 2011, Journal of Automated Reasoning.

[91]  Jerzy Tiuryn,et al.  Dynamic logic , 2001, SIGA.

[92]  Jamal Bentahar,et al.  Verifiable Semantic Model for Agent Interactions Using Social Commitments , 2009, LADS.

[93]  Adam Grabowski,et al.  On duplication in mathematical repositories , 2010, AISC'10/MKM'10/Calculemus'10.

[94]  Karol Pak.  THE ALGORITHMS FOR IMPROVING AND REORGANIZING NATURAL DEDUCTION PROOFS , 2010 .

[95]  Grzegorz Bancerek,et al.  On the structure of Mizar types , 2003, Mathematics, Logic and Computation @ ICALP.

[96]  Wojciech Penczek,et al.  BDD-versus SAT-based bounded model checking for the existential fragment of linear temporal logic with knowledge: algorithms and their performance , 2013, Autonomous Agents and Multi-Agent Systems.

[97]  N. Cowan.  The magical number 4 in short-term memory: A reconsideration of mental storage capacity , 2001, Behavioral and Brain Sciences.

[98]  Josef Urban,et al.  Evaluation of Automated Theorem Proving on the Mizar Mathematical Library , 2010, ICMS.

[99]  G. Laporte,et al.  A tabu search heuristic for periodic and multi-depot vehicle routing problems , 1997, Networks.

[100]  D. Wickens,et al.  Proactive inhibition and item similarity in short-term memory , 1963 .

[101]  Markus Wenzel,et al.  Efficient parallel programming in Poly/ML and Isabelle/ML , 2010, DAMP '10.

[102]  Yasunari Shidama,et al.  Isomorphisms of Direct Products of Finite Commutative Groups , 2013, Formaliz. Math..

[103]  M. Sirbu.  Credits and debits on the Internet , 1997 .

[104]  Keiichi Yasumoto,et al.  A Personal Navigation System for Sightseeing across Multiple days , 2006 .

[105]  Tobias Nipkow,et al.  Isabelle/HOL , 2002, Lecture Notes in Computer Science.

[106]  Wladyslaw Homenda.  Breaking accessibility barriers - computational intelligence in music processing for blind people , 2007, ICINCO-ICSO.

[107]  J. A. Robinson,et al.  Handbook of Automated Reasoning (in 2 volumes) , 2001 .

[108]  Joanna Karbowska-Chilinska,et al.  Genetic Algorithm Solving the Orienteering Problem with Time Windows , 2013, ICSS.

[109]  T. Tsiligirides,et al.  Heuristic Methods Applied to Orienteering , 1984 .

[110]  Martin D. Davis,et al.  Obvious Logical Inferences , 1981, IJCAI.

[111]  P. J. Cohen,et al.  THE INDEPENDENCE OF THE CONTINUUM HYPOTHESIS. , 1963, Proceedings of the National Academy of Sciences of the United States of America.

[112]  Dirk Van Oudheusden,et al.  The City Trip Planner: An expert system for tourists , 2011, Expert Syst. Appl..

[113]  Krassimir T. Atanassov,et al.  Intuitionistic fuzzy sets , 1986 .

[114]  E. Allen Emerson,et al.  Temporal and Modal Logic , 1991, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[115]  Lijun Wu,et al.  A concurrent dynamic logic of knowledge, belief and certainty for multi-agent systems , 2010, Knowl. Based Syst..

[116]  D. Landsittel,et al.  A novel scoring system to distinguish vocal cord dysfunction from asthma. , 2014, The journal of allergy and clinical immunology. In practice.

[117]  Yasunari Shidama,et al.  Isomorphisms of Direct Products of Cyclic Groups of Prime Power Order , 2013, Formaliz. Math..

[118]  Yatsuka Nakamura,et al.  A Mathematical Model of CPU , 1992 .

[119]  James H. Davenport,et al.  Intelligent Computer Mathematics, 10th International Conference, AISC 2010, 17th Symposium, Calculemus 2010, and 9th International Conference, MKM 2010, Paris, France, July 5-10, 2010. Proceedings , 2010, AISC/MKM/Calculemus.

[120]  Cezary Kaliszyk,et al.  MizAR 40 for Mizar 40 , 2013, Journal of Automated Reasoning.

[121]  C. A. R. Hoare,et al.  An axiomatic basis for computer programming , 1969, CACM.

[122]  Nikolaj S. Nikitchenko.  Abstract Computability of Non-deterministic Programs over Various Data Structures , 2001, Ershov Memorial Conference.

[123]  Andrzej Zbrzezny,et al.  SAT-Based Bounded Model Checking for Deontic Interleaved Interpreted Systems , 2012, KES-AMSTA.

[124]  Zbigniew W. Ras,et al.  Action Rules Discovery, a New Simplified Strategy , 2006, ISMIS.

[125]  Witold Kosinski,et al.  Metasets, Intuitionistic Fuzzy Sets and Uncertainty , 2013, ICAISC.

[126]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[127]  Mariusz Rybnik,et al.  Advanced Searching in Spaces of Music Information , 2012, ISMIS.

[128]  Jasmin Christian Blanchette,et al.  Redirecting Proofs by Contradiction , 2013, PxTP@CADE.

[129]  Donald W. Loveland,et al.  Mechanical Theorem-Proving by Model Elimination , 1968, JACM.

[130]  Stephan Schulz,et al.  E - a brainiac theorem prover , 2002, AI Commun..

[131]  Alexander V. Lyaletski,et al.  Literal Trees and Resolution Technique , 2005, Intelligent Information Systems.

[132]  Goldberg,et al.  Genetic algorithms , 1993, Robust Control Systems with Genetic Algorithms.

[133]  Munindar P. Singh.  A Social Semantics for Agent Communication Languages , 2000, Issues in Agent Communication.

[134]  R. H. Feierabend,et al.  Hoarseness in adults. , 2009, American family physician.

[135]  Josef Urban,et al.  MPTP 0.2: Design, Implementation, and Initial Experiments , 2006, Journal of Automated Reasoning.

[136]  Jerzy W. Grzymala-Busse,et al.  Rough Sets , 1995, Commun. ACM.

[137]  D. H. Mellor,et al.  Real time , 1981 .

[138]  Makarius Wenzel.  Parallel Proof Checking in Isabelle/Isar , 2009 .

[139]  Jesse Alama,et al.  Dependencies in Formal Mathematics: Applications and Extraction for Coq and Mizar , 2012, AISC/MKM/Calculemus.

[140]  Giuseppe Rosolini,et al.  Custom Automations in Mizar , 2012, Journal of Automated Reasoning.

[141]  Josef Urban,et al.  MaLARea: a Metasystem for Automated Reasoning in Large Theories , 2007, ESARLT.

[142]  Kenneth Kunen,et al.  Set Theory: An Introduction to Independence Proofs , 2010 .

[143]  Piotr Rudnicki.  Obvious inferences , 2004, Journal of Automated Reasoning.

[144]  R. Sataloff,et al.  Diagnosis and Treatment of Voice Disorders , 2014 .

[145]  Colin Rowat,et al.  A Qualitative Comparison of the Suitability of Four Theorem Provers for Basic Auction Theory , 2013, MKM/Calculemus/DML.

[146]  Mark Adams.  Introducing HOL Zero - (Extended Abstract) , 2010, ICMS.

[147]  Josef Urban.  MPTP – Motivation, Implementation, First Experiments , 2004, Journal of Automated Reasoning.