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  Subjects -> MATHEMATICS (Total: 1014 journals)
    - APPLIED MATHEMATICS (82 journals)
    - GEOMETRY AND TOPOLOGY (21 journals)
    - MATHEMATICS (751 journals)
    - MATHEMATICS (GENERAL) (41 journals)
    - NUMERICAL ANALYSIS (22 journals)
    - PROBABILITIES AND MATH STATISTICS (97 journals)

MATHEMATICS (751 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 4)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 4)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 7)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 15)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 3)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Hybrid Journal   (Followers: 35)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 13)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2)
Acta Mathematica Scientia     Full-text available via subscription   (Followers: 6)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 6)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 11)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 4)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 6)
Advances in Catalysis     Full-text available via subscription   (Followers: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 9)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 19)
Advances in Decision Sciences     Open Access   (Followers: 3)
Advances in Difference Equations     Open Access   (Followers: 3)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 17)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 6)
Advances in Materials Science     Open Access   (Followers: 15)
Advances in Mathematical Physics     Open Access   (Followers: 5)
Advances in Mathematics     Full-text available via subscription   (Followers: 11)
Advances in Nonlinear Analysis     Open Access  
Advances in Numerical Analysis     Open Access   (Followers: 7)
Advances in Operations Research     Open Access   (Followers: 12)
Advances in Porous Media     Full-text available via subscription   (Followers: 5)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 7)
Advances in Pure Mathematics     Open Access   (Followers: 7)
Advances in Science and Research (ASR)     Open Access   (Followers: 6)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 6)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 4)
Afrika Matematika     Hybrid Journal   (Followers: 1)
Air, Soil & Water Research     Open Access   (Followers: 14)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Al-Jabar : Jurnal Pendidikan Matematika     Open Access   (Followers: 1)
Algebra and Logic     Hybrid Journal   (Followers: 6)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Open Access   (Followers: 5)
Algorithms     Open Access   (Followers: 11)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 5)
American Journal of Mathematical Analysis     Open Access  
American Journal of Mathematics     Full-text available via subscription   (Followers: 6)
American Journal of Operations Research     Open Access   (Followers: 5)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 11)
Anadol University Journal of Science and Technology B : Theoritical Sciences     Open Access  
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access   (Followers: 1)
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 5)
Analysis Mathematica     Full-text available via subscription  
Analysis. International mathematical journal of analysis and its applications     Hybrid Journal   (Followers: 2)
Annales Mathematicae Silesianae     Open Access   (Followers: 1)
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica     Open Access   (Followers: 1)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica     Open Access  
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1)
Annals of Combinatorics     Hybrid Journal   (Followers: 4)
Annals of Data Science     Hybrid Journal   (Followers: 12)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 6)
Annals of Mathematics     Full-text available via subscription   (Followers: 1)
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 12)
Annals of Pure and Applied Logic     Open Access   (Followers: 4)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access  
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access  
Annals of West University of Timisoara - Mathematics and Computer Science     Open Access  
Annuaire du Collège de France     Open Access   (Followers: 6)
ANZIAM Journal     Open Access   (Followers: 1)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 2)
Applied Categorical Structures     Hybrid Journal   (Followers: 4)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 14)
Applied Mathematics     Open Access   (Followers: 3)
Applied Mathematics     Open Access   (Followers: 7)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 8)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 2)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access   (Followers: 3)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 7)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 4)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 3)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 6)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 6)
Arkiv för Matematik     Hybrid Journal   (Followers: 2)
Armenian Journal of Mathematics     Open Access  
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites     Open Access   (Followers: 21)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 2)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 6)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 4)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access   (Followers: 1)
Baltic International Yearbook of Cognition, Logic and Communication     Open Access   (Followers: 1)
Basin Research     Hybrid Journal   (Followers: 5)
BIBECHANA     Open Access   (Followers: 2)
Biomath     Open Access  
BIT Numerical Mathematics     Hybrid Journal  
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletim de Educação Matemática     Open Access  
Boletín de la Sociedad Matemática Mexicana     Hybrid Journal  
Bollettino dell'Unione Matematica Italiana     Full-text available via subscription   (Followers: 1)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 20)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 13)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 4)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 3)
Bulletin of Mathematical Sciences     Open Access   (Followers: 1)
Bulletin of Symbolic Logic     Full-text available via subscription   (Followers: 2)
Bulletin of the Australian Mathematical Society     Full-text available via subscription   (Followers: 1)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 4)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 19)
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal   (Followers: 2)
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
ChemSusChem     Hybrid Journal   (Followers: 7)
Chinese Annals of Mathematics, Series B     Hybrid Journal  
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 2)
Chinese Journal of Mathematics     Open Access  
Clean Air Journal     Full-text available via subscription   (Followers: 1)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 3)
Collectanea Mathematica     Hybrid Journal  
COMBINATORICA     Hybrid Journal  
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 4)
Combustion Theory and Modelling     Hybrid Journal   (Followers: 14)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Advanced Mathematical Sciences     Open Access  
Communications in Combinatorics and Optimization     Open Access  
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 2)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 3)
Complex Analysis and its Synergies     Open Access   (Followers: 2)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Composite Materials Series     Full-text available via subscription   (Followers: 8)
Compositio Mathematica     Full-text available via subscription   (Followers: 1)
Comptes Rendus Mathematique     Full-text available via subscription   (Followers: 1)
Computational and Applied Mathematics     Hybrid Journal   (Followers: 3)
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 2)
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 9)
Computational Mechanics     Hybrid Journal   (Followers: 5)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 8)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 9)
Concrete Operators     Open Access   (Followers: 5)
Confluentes Mathematici     Hybrid Journal  
Contributions to Game Theory and Management     Open Access  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 13)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Current Research in Biostatistics     Open Access   (Followers: 8)
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Demographic Research     Open Access   (Followers: 14)
Demonstratio Mathematica     Open Access  
Dependence Modeling     Open Access  
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 31)
Developments in Clay Science     Full-text available via subscription   (Followers: 1)
Developments in Mineral Processing     Full-text available via subscription   (Followers: 3)
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 4)
Differentsial'nye Uravneniya     Open Access  
Discrete Mathematics     Hybrid Journal   (Followers: 8)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae - General Algebra and Applications     Open Access  
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Diskretnaya Matematika     Full-text available via subscription  
Dnipropetrovsk University Mathematics Bulletin     Open Access  
Doklady Akademii Nauk     Open Access  
Doklady Mathematics     Hybrid Journal  
Duke Mathematical Journal     Full-text available via subscription   (Followers: 1)
Eco Matemático     Open Access  
Econometrics     Open Access   (Followers: 2)
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
Educação Matemática Debate     Open Access  
EduMatSains     Open Access  
Electronic Journal of Combinatorics     Open Access  

        1 2 3 4 | Last

Similar Journals
Journal Cover
Annals of Mathematics and Artificial Intelligence
Journal Prestige (SJR): 0.413
Citation Impact (citeScore): 1
Number of Followers: 12  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1573-7470 - ISSN (Online) 1012-2443
Published by Springer-Verlag Homepage  [2351 journals]
  • Rewriting input expressions in complex algebraic geometry provers
    • Authors: Z. Kovács; T. Recio; C. Sólyom-Gecse
      Pages: 73 - 87
      Abstract: We present an algorithm to help converting expressions having non-negative quantities (like distances) in Euclidean geometry theorems to be usable in a complex algebraic geometry prover. The algorithm helps in refining the output of an existing prover, therefore it supports immediate deployment in high level prover systems. We prove that the algorithm may take doubly exponential time to produce the output in polynomial form, but in many cases it is still computable and useful.
      PubDate: 2019-04-01
      DOI: 10.1007/s10472-018-9590-1
      Issue No: Vol. 85, No. 2-4 (2019)
       
  • From informal to formal proofs in Euclidean geometry
    • Authors: Sana Stojanović-Ðurđević
      Pages: 89 - 117
      Abstract: In this paper, we propose a new approach for automated verification of informal proofs in Euclidean geometry using a fragment of first-order logic called coherent logic and a corresponding proof representation. We use a TPTP inspired language to write a semi-formal proof of a theorem, that fairly accurately depicts a proof that can be found in mathematical textbooks. The semi-formal proof is verified by generating more detailed proof objects expressed in the coherent logic vernacular. Those proof objects can be easily transformed to Isabelle and Coq proof objects, and also in natural language proofs written in English and Serbian. This approach is tested on two sets of theorem proofs using classical axiomatic system for Euclidean geometry created by David Hilbert, and a modern axiomatic system E created by Jeremy Avigad, Edward Dean, and John Mumma.
      PubDate: 2019-04-01
      DOI: 10.1007/s10472-018-9597-7
      Issue No: Vol. 85, No. 2-4 (2019)
       
  • Portfolio theorem proving and prover runtime prediction for geometry
    • Authors: Mladen Nikolić; Vesna Marinković; Zoltán Kovács; Predrag Janičić
      Pages: 119 - 146
      Abstract: In recent years, portfolio problem solving found many applications in automated reasoning, primarily in SAT solving and in automated and interactive theorem proving. Portfolio problem solving is an approach in which for an individual instance of a specific problem, one particular, hopefully most appropriate, solving technique is automatically selected among several available ones and used. The selection usually employs machine learning methods. To our knowledge, this approach has not been used in automated theorem proving in geometry so far and it poses a number of new challenges. In this paper we propose a set of features which characterize a specific geometric theorem, so that machine learning techniques can be used in geometry. Relying on these features and using different machine learning techniques, we constructed several portfolios for theorem proving in geometry and also runtime prediction models for provers involved. The evaluation was performed on two corpora of geometric theorems: one coming from geometric construction problems and one from a benchmark set of the GeoGebra tool. The obtained results show that machine learning techniques can be useful in automated theorem proving in geometry, while there is still room for further progress.
      PubDate: 2019-04-01
      DOI: 10.1007/s10472-018-9598-6
      Issue No: Vol. 85, No. 2-4 (2019)
       
  • Towards a better integration of modelers and black box constraint solvers
           within the product design process
    • Authors: Jean-Philippe Pernot; Dominique Michelucci; Marc Daniel; Sebti Foufou
      Pages: 147 - 173
      Abstract: This paper presents a new way of interaction between modelers and solvers to support the Product Development Process (PDP). The proposed approach extends the functionalities and the power of the solvers by taking into account procedural constraints. A procedural constraint requires calling a procedure or a function of the modeler. This procedure performs a series of actions and geometric computations in a certain order. The modeler calls the solver for solving a main problem, the solver calls the modeler’s procedures, and similarly procedures of the modeler can call the solver for solving sub-problems. The features, specificities, advantages and drawbacks of the proposed approach are presented and discussed. Several examples are also provided to illustrate this approach.
      PubDate: 2019-04-01
      DOI: 10.1007/s10472-018-9599-5
      Issue No: Vol. 85, No. 2-4 (2019)
       
  • Implementing Euclid’s straightedge and compass constructions in type
           theory
    • Authors: Ariel Kellison; Mark Bickford; Robert Constable
      Pages: 175 - 192
      Abstract: Constructions are central to the methodology of geometry presented in the Elements. This theory therefore poses a unique challenge to those concerned with the practice of constructive mathematics: can the Elements be faithfully captured in a modern constructive framework' In this paper, we outline our implementation of Euclidean geometry based on straightedge and compass constructions in the intuitionistic type theory of the Nuprl proof assistant. A result of our intuitionistic treatment of Euclidean geometry is a proof of the second proposition from Book I of the Elements in its full generality; a result that differs from other formally constructive accounts of Euclidean geometry. Our formalization of the straightedge and compass utilizes a predicate for orientation, which enables a concise and intuitive expression of Euclid’s constructions.
      PubDate: 2019-04-01
      DOI: 10.1007/s10472-018-9603-0
      Issue No: Vol. 85, No. 2-4 (2019)
       
  • Competing hypotheses and abductive inference
    • Abstract: This paper explores the nature of competition between hypotheses and the effect of failing to model this relationship correctly when performing abductive inference. In terms of the nature of competition, the importance of the interplay between direct and indirect pathways, where the latter depends on the evidence under consideration, is investigated. Experimental results show that models which treat hypotheses as mutually exclusive or independent perform well in an abduction problem that requires identifying the most probable hypothesis, provided there is at least some positive degree of competition between the hypotheses. However, even in such cases a significant limitation of these models is their inability to identify a second hypothesis that may well also be true.
      PubDate: 2019-05-06
       
  • Guest editorial: special issue on answer set programming and other
           computing paradigms
    • PubDate: 2019-05-01
       
  • A review of the relations between logical argumentation and reasoning with
           maximal consistency
    • Abstract: This is a survey of some recent results relating Dung-style semantics for different types of logical argumentation frameworks and several forms of reasoning with maximally consistent sets (MCS) of premises. The related formalsims are also examined with respect to some rationality postulates and are carried on to corresponding proof systems for non-monotonic reasoning.
      PubDate: 2019-04-27
       
  • Digital forensics and investigations meet artificial intelligence
    • Abstract: In the frame of Digital Forensic (DF) and Digital Investigations (DI), the “Evidence Analysis” phase has the aim to provide objective data, and to perform suitable elaboration of these data so as to help in the formation of possible hypotheses, which could later be presented as elements of proof in court. The aim of our research is to explore the applicability of Artificial Intelligence (AI) along with computational logic tools – and in particular the Answer Set Programming (ASP) approach — to the automation of evidence analysis. We will show how significant complex investigations, hardly solvable for human experts, can be expressed as optimization problems belonging in many cases to the \(\mathbb {P}\) or \(\mathbb {N}\mathbb {P}\) complexity classes. All these problems can be expressed in ASP. As a proof of concept, in this paper we present the formalization of realistic investigative cases via simple ASP programs, and show how such a methodology can lead to the formulation of tangible investigative hypotheses. We also sketch a design for a feasible Decision Support System (DSS) especially meant for investigators, based on artificial intelligence tools.
      PubDate: 2019-04-24
       
  • A parallel memory-efficient epistemic logic program solver: harder,
           better, faster
    • Abstract: As the practical use of answer set programming (ASP) has grown with the development of efficient solvers, we expect a growing interest in extensions of ASP as their semantics stabilize and solvers supporting them mature. Epistemic Specifications, which adds modal operators K and M to the language of ASP, is one such extension. We call a program in this language an epistemic logic program (ELP). Solvers have thus far been practical for only the simplest ELPs due to exponential growth of the search space. We describe a solver that, at the time of its development (mid-2016), was able to solve harder problems better (e.g., without exponentially-growing memory needs w.r.t. K and M occurrences) and faster than any other known ELP solver.
      PubDate: 2019-04-23
       
  • Privacy stochastic games in distributed constraint reasoning
    • Abstract: In this work, we approach the issue of privacy in distributed constraint reasoning by studying how agents compromise solution quality for preserving privacy, using utility and game theory. We propose a utilitarian definition of privacy in the context of distributed constraint reasoning, detail its different implications, and present a model and solvers, as well as their properties. We then show how important steps in a distributed constraint optimization with privacy requirements can be modeled as a planning problem, and more specifically as a stochastic game. We present experiments validating the interest of our approach, according to several criteria.
      PubDate: 2019-04-11
       
  • Discovering state constraints for planning with conditional effects in
           Discoplan (part I)
    • Abstract: Discoplan is a durable and efficient system for inferring state constraints (invariants) in planning domains, specified in the PDDL language. It is exceptional in the range of constraint types it can discover and verify, and it directly allows for conditional effects in action operators. However, although various aspects of Discoplan have been previously described and its utility in planning demonstrated, the underlying methodology, the algorithms for the discovery and inductive verification of constraints, and the proofs of correctness of the algorithms and their complexity analysis have never been laid out in adequate detail. The purpose of this paper is to remedy these lacunae.
      PubDate: 2019-04-08
       
  • Complexity and approximability of the Euclidean generalized traveling
           salesman problem in grid clusters
    • Abstract: We consider the geometric version of the well-known Generalized Traveling Salesman Problem introduced in 2015 by Bhattacharya et al. that is called the Euclidean Generalized Traveling Salesman Problem in Grid Clusters (EGTSP-GC). They proved the intractability of the problem and proposed first polynomial time algorithms with fixed approximation factors. The extension of these results in the field of constructing the polynomial time approximation schemes (PTAS) and the description of non-trivial polynomial time solvable subclasses for the EGTSP-GC appear to be relevant in the light of the classic C. Papadimitriou result on the intractability of the Euclidean TSP and recent inapproximability results for the Traveling Salesman Problem with Neighborhoods (TSPN) in the case of discrete neighborhoods. In this paper, we propose Efficient Polynomial Time Approximation Schemes (EPTAS) for two special cases of the EGTSP-GC, when the number of clusters \(k=O(\log n)\) and \(k=n-O(\log n)\) . Also, we show that any time, when one of the grid dimensions (height or width) is fixed, the EGTSP-GC can be solved to optimality in polynomial time. As a consequence, we specify a novel non-trivial polynomially solvable subclass of the Euclidean TSP in the plane.
      PubDate: 2019-03-28
       
  • Knowledge representation analysis of graph mining
    • Abstract: This paper analyses the graph mining problem, and the frequent pattern mining task associated with it. In general, frequent pattern mining looks for a graph which occurs frequently within a network or, in the transactional setting, within a dataset of graphs. We discuss this task in the transactional setting, which is a problem of interest in many fields such as bioinformatics, chemoinformatics and social networks. We look at the graph mining problem from a Knowledge Representation point of view, hoping to learn something about support for higher-order logics in declarative languages and solvers. Graph mining is studied as a prototypical problem; it is easily expressible mathematically and exists in many variations. As such, it appears to be a prime candidate for a declarative approach; one would expect this allows for a clear, structured, statement of the problem combined with easy adaptation to changing requirements and variations. Current state-of-the-art KR languages such as IDP and ASP aspire to be practical solvers for such problems (Bruynooghe, Theory Practice Logic Program. (TPLP) 15(6), 783–817 2015). Nevertheless, expressing the graph mining problem in these languages requires unexpectedly complicated and unintuitive encoding techniques. These techniques are in contrast to the ease with which one can transform the mathematical definition of graph mining to a higher-order logic specification, and distract from the problem essentials, complicating possible future adaptation. In this paper, we argue that efforts should be made towards supporting higher-order logic specifications in modern specification languages, without unintuitive and complicated encoding techniques. We argue that this not only makes representation clearer and more susceptible to future adaptation, but might also allow for faster, more competitive solver techniques to be implemented.
      PubDate: 2019-03-28
       
  • An investigation of parametrized difference revision operators
    • Abstract: In this article, we provide the epistemic-entrenchment and partial-meet characterizations of a new, important class of concrete revision operators (all of which satisfy the AGM postulates for revision), called Parametrized Difference revision operators (PD operators, for short). PD operators are natural generalizations of Dalal’s revision operator, with a much greater range of applicability, hence, the epistemic-entrenchment and partial-meet characterizations of the latter are also provided, as a by-product. Lastly, we prove that PD operators satisfy the strong version of Parikh’s relevance-sensitive axiom for belief revision, showing that they are fully compatible with the notion of relevance.
      PubDate: 2019-03-26
       
  • Exact algorithms for two integer-valued problems of searching for the
           largest subset and longest subsequence
    • Abstract: The following two strongly NP-hard problems are considered. In the first problem, we need to find in the given finite set of points in Euclidean space the subset of largest size. The sum of squared distances between the elements of this subset and its unknown centroid (geometrical center) must not exceed a given value. This value is defined as percentage of the sum of squared distances between the elements of the input set and its centroid. In the second problem, the input is a sequence (not a set) and we have some additional constraints on the indices of the elements of the chosen subsequence. The restriction on the sum of squared distances is the same as in the first problem. Both problems can be treated as data editing problems aimed to find similar elements and removal of extraneous (dissimilar) elements. We propose exact algorithms for the cases of both problems in which the input points have integer-valued coordinates. If the space dimension is bounded by some constant, our algorithms run in a pseudopolynomial time. Some results of numerical experiments illustrating the performance of the algorithms are presented.
      PubDate: 2019-03-21
       
  • Foreword
    • Authors: Pascal Schreck; Tetsuo Ida; Laura Kovacs
      PubDate: 2019-01-26
      DOI: 10.1007/s10472-019-9617-2
       
  • Proof-checking Euclid
    • Authors: Michael Beeson; Julien Narboux; Freek Wiedijk
      Abstract: We used computer proof-checking methods to verify the correctness of our proofs of the propositions in Euclid Book I. We used axioms as close as possible to those of Euclid, in a language closely related to that used in Tarski’s formal geometry. We used proofs as close as possible to those given by Euclid, but filling Euclid’s gaps and correcting errors. Euclid Book I has 48 propositions; we proved 235 theorems. The extras were partly “Book Zero”, preliminaries of a very fundamental nature, partly propositions that Euclid omitted but were used implicitly, partly advanced theorems that we found necessary to fill Euclid’s gaps, and partly just variants of Euclid’s propositions. We wrote these proofs in a simple fragment of first-order logic corresponding to Euclid’s logic, debugged them using a custom software tool, and then checked them in the well-known and trusted proof checkers HOL Light and Coq.
      PubDate: 2019-01-10
      DOI: 10.1007/s10472-018-9606-x
       
  • Can one design a geometry engine'
    • Authors: Johann A. Makowsky
      Abstract: We survey the status of decidability of the first order consequences in various axiomatizations of Hilbert-style Euclidean geometry. We draw attention to a widely overlooked result by Martin Ziegler from 1980, which proves Tarski’s conjecture on the undecidability of finitely axiomatizable theories of fields. We elaborate on how to use Ziegler’s theorem to show that the consequence relations for the first order theory of the Hilbert plane and the Euclidean plane are undecidable. As new results we add: (A) The first order consequence relations for Wu’s orthogonal and metric geometries (Wen-Tsün Wu, 1984), and for the axiomatization of Origami geometry (J. Justin 1986, H. Huzita 1991) are undecidable. It was already known that the universal theory of Hilbert planes and Wu’s orthogonal geometry is decidable. We show here using elementary model theoretic tools that (B) the universal first order consequences of any geometric theory T of Pappian planes which is consistent with the analytic geometry of the reals is decidable. The techniques used were all known to experts in mathematical logic and geometry in the past but no detailed proofs are easily accessible for practitioners of symbolic computation or automated theorem proving.
      PubDate: 2018-12-12
      DOI: 10.1007/s10472-018-9610-1
       
  • Two cryptomorphic formalizations of projective incidence geometry
    • Authors: David Braun; Nicolas Magaud; Pascal Schreck
      Abstract: Incidence geometry is a well-established theory which captures the very basic properties of all geometries in terms of points belonging to lines, planes, etc. Moreover, projective incidence geometry leads to a simple framework where many properties can be studied. In this article, we consider two very different but complementary mathematical approaches formalizing this theory within the Coq proof assistant. The first one consists of the usual and synthetic geometric axiom system often encountered in the literature. The second one is more original and relies on combinatorial aspects through the notion of rank which is based on the matroid structure of incidence geometry. This paper mainly contributes to the field by proving the equivalence between these two approaches in both 2D and 3D. This result allows us to study the further automation of many proofs of projective geometry theorems. We give an overview of techniques that will be heavily used in the equivalence proof and are generic enough to be reused later in yet-to-be-written proofs. Finally, we discuss the possibilities of future automation that can be envisaged using the rank notion.
      PubDate: 2018-10-24
      DOI: 10.1007/s10472-018-9604-z
       
 
 
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