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  1. Tom Addis, Jan Townsend Addis, Dave Billinge, David Gooding & Bart-Floris Visscher (2008). The Abductive Loop: Tracking Irrational Sets. [REVIEW] Foundations of Science 13 (1):5-16.
    We argue from the Church-Turing thesis (Kleene Mathematical logic. New York: Wiley 1967) that a program can be considered as equivalent to a formal language similar to predicate calculus where predicates can be taken as functions. We can relate such a calculus to Wittgenstein’s first major work, the Tractatus, and use the Tractatus and its theses as a model of the formal classical definition of a computer program. However, Wittgenstein found flaws in his initial great work and he explored these (...)
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  2. Natasha Alechina, Piergiorgio Bertoli, Chiara Ghidini, Mark Jago, Brian Logan & Luciano Serafini (2007). Verifying Space and Time Requirements for Resource-Bounded Agents. In A. Lomuscio & S. Edelkamp (eds.), Model Checking and Artificial Intelligence. Springer
    The effective reasoning capability of an agent can be defined as its capability to infer, within a given space and time bound, facts that are logical consequences of its knowledge base. In this paper we show how to determine the effective reasoning capability of an agent with limited memory by encoding the agent as a transition system and automatically verifying whether a state where the agent believes a certain conclusion is reachable from the start state. We present experimental results using (...)
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  3. F. Alt & M. Ruminoff (eds.) (1965). Advances in Computers, Volume 6. Academic Press.
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  4. Mark A. Bedau, Richard Crandall & Michael J. Raven, Cryptographic Hash Functions Based on ALife. PSIpress.
    There is a long history of cryptographic hash functions, i.e. functions mapping variable-length strings to fixed-length strings, and such functions are also expected to enjoy certain security properties. Hash functions can be effected via modular arithmetic, permutation-based schemes, chaotic mixing, and so on. Herein we introduce the notion of an artificial-life (ALife) hash function (ALHF), whereby the requisite mixing action of a good hash function is accomplished via ALife rules that give rise to complex evolution of a given system. Various (...)
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  5. Thomas Bittner & Barry Smith (2003). A Theory of Granular Partitions. In Foundations of Geographic Information Science. Taylor & Francis
    We have a variety of different ways of dividing up, classifying, mapping, sorting and listing the objects in reality. The theory of granular partitions presented here seeks to provide a general and unified basis for understanding such phenomena in formal terms that is more realistic than existing alternatives. Our theory has two orthogonal parts: the first is a theory of classification; it provides an account of partitions as cells and subcells; the second is a theory of reference or intentionality; it (...)
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  6. Adam Bleckert & Rachel Ol Wong (2011). Identifying Roles for Neurotransmission in Circuit Assembly: Insights Gained From Multiple Model Systems and Experimental Approaches. Bioessays 33 (1):61-72.
  7. Robin Blume-Kohout, Carlton M. Caves & Ivan H. Deutsch (2002). Climbing Mount Scalable: Physical Resource Requirements for a Scalable Quantum Computer. [REVIEW] Foundations of Physics 32 (11):1641-1670.
    The primary resource for quantum computation is Hilbert-space dimension. Whereas Hilbert space itself is an abstract construction, the number of dimensions available to a system is a physical quantity that requires physical resources. Avoiding a demand for an exponential amount of these resources places a fundamental constraint on the systems that are suitable for scalable quantum computation. To be scalable, the effective number of degrees of freedom in the computer must grow nearly linearly with the number of qubits in an (...)
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  8. Gilles Brassard, Anne Broadbent & Alain Tapp (2005). Quantum Pseudo-Telepathy. Foundations of Physics 35 (11):1877-1907.
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  9. Michael Braund & Daniel Hambleton (2011). Dragonfly: An Ecological Approach to Digital Architectural Design. In J. M. Taron, V. Parlac, B. Kolarevic & J. S. Johnson (eds.), ACADIA: Integration through Computation.
    In his keynote address delivered to The American Society for Esthetics in 1976, James J. Gibson wrote, “Architecture and design do not have a satisfactory theoretical basis.” He then asked, “Can an ecological approach to the psychology of perception and behavior provide it?” (1976, p. 413) We believe that it can, at least in part. In this paper, we expand upon Gibson’s insights into the nature of perceptual experience by applying the concept of “affordances” to the design of architectural objects (...)
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  10. Cameron Buckner, Mathias Niepert & Colin Allen (2011). From Encyclopedia to Ontology: Toward Dynamic Representation of the Discipline of Philosophy. Synthese 182 (2):205-233.
    The application of digital humanities techniques to philosophy is changing the way scholars approach the discipline. This paper seeks to open a discussion about the difficulties, methods, opportunities, and dangers of creating and utilizing a formal representation of the discipline of philosophy. We review our current project, the Indiana Philosophy Ontology (InPhO) project, which uses a combination of automated methods and expert feedback to create a dynamic computational ontology for the discipline of philosophy. We argue that our distributed, expert-based approach (...)
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  11. M. W. Bunder & R. M. Rizkalla (2009). Proof-Finding Algorithms for Classical and Subclassical Propositional Logics. Notre Dame Journal of Formal Logic 50 (3):261-273.
    The formulas-as-types isomorphism tells us that every proof and theorem, in the intuitionistic implicational logic $H_\rightarrow$, corresponds to a lambda term or combinator and its type. The algorithms of Bunder very efficiently find a lambda term inhabitant, if any, of any given type of $H_\rightarrow$ and of many of its subsystems. In most cases the search procedure has a simple bound based roughly on the length of the formula involved. Computer implementations of some of these procedures were done in Dekker. (...)
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  12. Arthur Walter Burks & Jesse B. Wright, Sequence Generators, Graphs, and Formal Languages.
    A sequence generator is a finite graph, more general than, but akin to, the usual state diagram associated with a finite automaton. The nodes of a sequence generator represent complete states, and each node is labeled with an input and an output state. An element of the behavior of a sequence generator is obtained by taking the input and output states along an infinite path of the graph.Sequence generators may be associated with formulas of the monadic predicate calculus, in which (...)
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  13. S. B. Cooper & Andrea Sorbi (eds.) (2011). Computability in Context: Computation and Logic in the Real World. World Scientific.
    Recent new paradigms of computation, based on biological and physical models, address in a radically new way questions of efficiency and challenge assumptions ...
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  14. Michael E. Cuffaro (2014). Review Of: Christopher G. Timpson, Quantum Information Theory and the Foundations of Quantum Mechanics. [REVIEW] Philosophy of Science 81 (4):681-684,.
  15. U. Endriss & M. Baldoni (eds.) (2006). Declarative Agent Languages and Technologies 4. Springer.
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  16. Steven Ericsson-Zenith (forthcoming). Explaining Experience In Nature: The Foundations Of Logic And Apprehension. Institute for Advanced Science & Engineering.
    At its core this book is concerned with logic and computation with respect to the mathematical characterization of sentient biophysical structure and its behavior. -/- Three related theories are presented: The first of these provides an explanation of how sentient individuals come to be in the world. The second describes how these individuals operate. And the third proposes a method for reasoning about the behavior of individuals in groups. -/- These theories are based upon a new explanation of experience in (...)
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  17. William M. Farmer (1995). Reasoning About Partial Functions with the Aid of a Computer. Erkenntnis 43 (3):279 - 294.
    Partial functions are ubiquitous in both mathematics and computer science. Therefore, it is imperative that the underlying logical formalism for a general-purpose mechanized mathematics system provide strong support for reasoning about partial functions. Unfortunately, the common logical formalisms — first-order logic, type theory, and set theory — are usually only adequate for reasoning about partial functionsin theory. However, the approach to partial functions traditionally employed by mathematicians is quite adequatein practice. This paper shows how the traditional approach to partial functions (...)
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  18. Liping Gao & Wenfeng Tang (2015). High Efficient Consistency Maintenance Strategy of Real-Time String Text Editing Systems. International Journal of Hybrid Information Technology 8.
    Replicated architecture is widely used in the field of real-time collaborative text editor. The idea of address space transformation provides a new way for concurrency control. During concurrent processing, it retraces the document status back to the state when the operations are generated to maintain consistency. However the previous concurrency processes strategy is based on single characters, the transmission cost during processing is too high since every character is packaged and broadcasted to remote sites after they are created by local (...)
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  19. Liping Gao & Fangyu Yu (2015). Consistency Maintenance of Group/Ungroup Operations in Object-Based Collaborative Graphical Editing Systems. International Journal of Signal Processing, Image Processing and Pattern Recognition 8.
    In real-time collaborative graphical editing systems, Object-based Group/Ungroup operations are frequently accessible and practically useful. However, the existing research on these operations of the graphical editing is rare and defective. In this paper, based on Multi-Version strategy and Address Space Transformation method, a new MVSDR algorithm, which is not only applied to simple operations (such as Create, Delete, ChangeATT, etc.), but also suitable for Group/Ungroup ones, is proposed to solve the consistency maintenance problem. The proposed algorithm abandons previous attempts to (...)
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  20. Kyriaki G. Giota (2014). Mental Health Apps: Innovations, Risks and Ethical Considerations. E-Health Telecommunication Systems and Networks 3:19-23.
    The purpose of this article is to briefly review some of the innovations that mobile mental health apps present to consumers and mental health practitioners. Particular attention was given to understanding some of the important risks and the potential ethical dilemmas which may arise for counselors and psychologists who embrace them in their practice. Key considerations of issues pertinent to regulations, privacy concerns, and research are being discussed.
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  21. Brent Gregory, Sue Gregory, Bogdanovych A., Jacobson Michael, Newstead Anne & Simeon Simoff and Many Others (2011). How Are Australian Higher Education Institutions Contributing to Innovative Teaching and Learning Through Virtual Worlds? In Gregory Sue (ed.), Proceedings of Ascilite 2011 (Australian Society of Computers in Tertiary Education). Ascilite
    Over the past decade, teaching and learning in virtual worlds has been at the forefront of many higher education institutions around the world. The DEHub Virtual Worlds Working Group (VWWG) consisting of Australian and New Zealand higher education academics was formed in 2009. These educators are investigating the role that virtual worlds play in the future of education and actively changing the direction of their own teaching practice and curricula. 47 academics reporting on 28 Australian higher education institutions present an (...)
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  22. Stan Gudder (2006). Quantum Mechanics on Finite Groups. Foundations of Physics 36 (8):1160-1192.
    Although a few new results are presented, this is mainly a review article on the relationship between finite-dimensional quantum mechanics and finite groups. The main motivation for this discussion is the hidden subgroup problem of quantum computation theory. A unifying role is played by a mathematical structure that we call a Hilbert *-algebra. After reviewing material on unitary representations of finite groups we discuss a generalized quantum Fourier transform. We close with a presentation concerning position-momentum measurements in this framework.
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  23. Peter Hucklenbroich (1988). Problems of Nomenclature and Classification in Medical Expert Systems. Theoretical Medicine and Bioethics 9 (2).
    Medical expert systems (MES) are knowledge-based computer programs that are designed for advising physicians on diagnostical and therapeutical decision-making. They use heuristic methods developed by Artificial Intelligence researchers in order to retrieve from large knowledge-bases information needed in the situation. Constructing the knowledge-base of a MES embraces the problem of explicating and fixing the conceptual, causal and epistemic relations between a lot of medical objects. There is a number of preconditions which any adequate representation of such knowledge must fulfil, among (...)
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  24. Michael J. Jacobson, Charlotte Taylor, Anne Newstead, Wai Yat Wong, Deborah Richards, Meredith Taylor, Porte John, Kartiko Iwan, Kapur Manu & Hu Chun (2011). Collaborative Virtual Worlds and Productive Failure. In Proceedings of the CSCL (Computer Supported Cognition and Learning) III. University of Hong Kong
    This paper reports on an ongoing ARC Discovery Project that is conducting design research into learning in collaborative virtual worlds (CVW).The paper will describe three design components of the project: (a) pedagogical design, (b)technical and graphics design, and (c) learning research design. The perspectives of each design team will be discussed and how the three teams worked together to produce the CVW. The development of productive failure learning activities for the CVW will be discussed and there will be an interactive (...)
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  25. Michael J. Jacobson, Charlotte Taylor, Anne Newstead, Wai Yat Wong, Deborah Richards, Meredith Taylor, Porte John, Kartiko Iwan, Kapur Manu & Hu Chun (2011). Proceedings of the CSCL (Computer Supported Cognition and Learning) III. University of Hong Kong.
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  26. Mark Jago (2006). Resource-Bounded Belief Revision and Contraction. In P. Torroni, U. Endriss, M. Baldoni & A. Omicini (eds.), Declarative Agent Languages and Technologies III. Springer 141--154.
    Agents need to be able to change their beliefs; in particular, they should be able to contract or remove a certain belief in order to restore consistency to their set of beliefs, and revise their beliefs by incorporating a new belief which may be inconsistent with their previous beliefs. An influential theory of belief change proposed by Alchourron, G¨ardenfors and Makinson (AGM) [1] describes postulates which a rational belief revision and contraction operations should satisfy. The AGM postulates have been perceived (...)
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  27. Fred Johnson (1995). Apodeictic Syllogisms: Deductions and Decision Procedures. History and Philosophy of Logic 16 (1):1-18.
    One semantic and two syntactic decision procedures are given for determining the validity of Aristotelian assertoric and apodeictic syllogisms. Results are obtained by using the Aristotelian deductions that necessarily have an even number of premises.
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  28. Nane Kratzke (2014). Lightweight Virtualization Cluster How to Overcome Cloud Vendor Lock-In. JCC 2:1-7.
    To overcome vendor lock-in obstacles in public cloud computing, the capability to define transferable cloud-based services is crucial but has not yet been solved satisfactorily. This is especially true for small and medium sized enterprises being typically not able to operate a vast staff of cloud service and IT experts. Actual state of the art cloud service design does not systematically deal with how to define, deploy and operate cross-platform capable cloud services. This is mainly due to inherent complexity of (...)
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  29. Leonardo Lana de Carvalho, Franck Varenne & Elayne de Moura Bragra (2014). Ontologias para a Modelagem Multiagente de Sistemas Complexos em Ciências Cognitivas. Ciências and Cognição 19 (1):58-75.
    Cognitive sciences as an interdisciplinary field, involving scientific disciplines (such as computer science, linguistics, psychology, neuroscience, economics, etc.), philosophical disciplines (philosophy of language, philosophy of mind, analytic philosophy, etc.) and engineering (notably knowledge engineering), have a vast theoretical and practical content, some even conflicting. In this interdisciplinary context and on computational modeling, ontologies play a crucial role in communication between disciplines and also in a process of innovation of theories, models and experiments in cognitive sciences. We propose a model for (...)
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  30. Catherine Legg & Samuel Sarjant (2012). Bill Gates is Not a Parking Meter: Philosophical Quality Control in Automated Ontology Building. Proceedings of the Symposium on Computational Philosophy, AISB/IACAP World Congress 2012 (Birmingham, England, July 2-6).
    The somewhat old-fashioned concept of philosophical categories is revived and put to work in automated ontology building. We describe a project harvesting knowledge from Wikipedia’s category network in which the principled ontological structure of Cyc was leveraged to furnish an extra layer of accuracy-checking over and above more usual corrections which draw on automated measures of semantic relatedness.
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  31. Antonio Lieto & Marco Cruciani (eds.) (2013). Artificial Intelligence and Cognition. Proceedings of the First International Workshop AIC 2013. CEUR Workshop Proceedings.
  32. Gregory Linshiz, Alex Goldberg, Tania Konry & Nathan J. Hillson (2013). The Fusion of Biology, Computer Science, and Engineering: Towards Efficient and Successful Synthetic Biology. Perspectives in Biology and Medicine 55 (4):503-520.
    The integration of computer science, biology, and engineering has resulted in the emergence of rapidly growing interdisciplinary fields such as bioinformatics, bioengineering, DNA computing, and systems and synthetic biology. Ideas derived from computer science and engineering can provide innovative solutions to biological problems and advance research in new directions. Although interdisciplinary research has become increasingly prevalent in recent years, the scientists contributing to these efforts largely remain specialists in their original disciplines and are not fully capable of covering the many (...)
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  33. Hong Liu, Bin Hu & Philip Moore (2015). HCI Model with Learning Mechanism for Cooperative Design in Pervasive Computing Environment. Journal of Internet Technology 16.
    This paper presents a human-computer interaction model with a three layers learning mechanism in a pervasive environment. We begin with a discussion around a number of important issues related to human-computer interaction followed by a description of the architecture for a multi-agent cooperative design system for pervasive computing environment. We present our proposed three- layer HCI model and introduce the group formation algorithm, which is predicated on a dynamic sharing niche technology. Finally, we explore the cooperative reinforcement learning and fusion (...)
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  34. Brian Logan, Mark Jago & Natasha Alechina (2006). Modelling Communicating Agents in Timed Reasoning Logics. In U. Endriss & M. Baldoni (eds.), Declarative Agent Languages and Technologies 4. Springer
    Practical reasoners are resource-bounded—in particular they require time to derive consequences of their knowledge. Building on the Timed Reasoning Logics (TRL) framework introduced in [1], we show how to represent the time required by an agent to reach a given conclusion. TRL allows us to model the kinds of rule application and conflict resolution strategies commonly found in rule-based agents, and we show how the choice of strategy can influence the information an agent can take into account when making decisions (...)
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  35. A. Lomuscio & S. Edelkamp (eds.) (2007). Model Checking and Artificial Intelligence. Springer.
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  36. Olena Medelyan & Catherine Legg (2008). Integrating Cyc and Wikipedia: Folksonomy Meets Rigorously Defined Common-Sense. Proceedings of Wikipedia and AI Workshop at the AAAI-08 Conference. Chicago, US, July 12 2008.
    Integration of ontologies begins with establishing mappings between their concept entries. We map categories from the largest manually-built ontology, Cyc, onto Wikipedia articles describing corresponding concepts. Our method draws both on Wikipedia’s rich but chaotic hyperlink structure and Cyc’s carefully defined taxonomic and common-sense knowledge. On 9,333 manual alignments by one person, we achieve an F-measure of 90%; on 100 alignments by six human subjects the average agreement of the method with the subject is close to their agreement with each (...)
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  37. Paolo Milazzo (2014). Membrane Computing: From Biology to Computation and Back. Isonomia: Online Philosophical Journal of the University of Urbino:1-15.
    Natural Computing is a field of research in Computer Science aimed at reinterpreting biological phenomena as computing mechanisms. This allows unconventional computing architectures to be proposed in which computations are performed by atoms, DNA strands, cells, insects or other biological elements. Membrane Computing is a branch of Natural Computing in which biological phenomena of interest are related with interactions between molecules inside cells. The research in Membrane Computing has lead to very important theoretical results that show how, in principle, cells (...)
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  38. David Milne, Catherine Legg, Medelyan Olena & Witten Ian (2009). Mining Meaning From Wikipedia. International Journal of Human-Computer Interactions 67 (9):716-754.
    Wikipedia is a goldmine of information; not just for its many readers, but also for the growing community of researchers who recognize it as a resource of exceptional scale and utility. It represents a vast investment of manual effort and judgment: a huge, constantly evolving tapestry of concepts and relations that is being applied to a host of tasks. This article provides a comprehensive description of this work. It focuses on research that extracts and makes use of the concepts, relations, (...)
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  39. Indraneel Mukhopadhyay (2014). Hardware Realization of Artificial Neural Network Based Intrusion Detection & Prevention System. JIS 5:154-165.
    In the 21st century with the exponential growth of the Internet, the vulnerability of the network which connects us is on the rise at a very fast pace. Today organizations are spending millions of dollars to protect their sensitive data from different vulnerabilities that they face every day. In this paper, a new methodology towards implementing an Intrusion Detection & Prevention System (IDPS) based on Artificial Neural Network (ANN) onto Field Programmable Gate Array (FPGA) is proposed. This system not only (...)
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  40. Matthias Müller-Hannemann & Stefan Schirra (eds.) (2010). Algorithm Engineering: Bridging the Gap Between Algorithm Theory and Practice. Springer.
    Driven by concrete applications, Algorithm Engineering complements theory by the benefits of experimentation and puts equal emphasis on all aspects arising during a cyclic solution process ranging from realistic modeling, design, analysis, ...
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  41. Anne Newstead & Michael J. Jacobson, Collaborative Virtual Worlds for Enhanced Scientific Understanding.
    This is a copy of the presentation given at the Workshop on Agency and Distributed Cognition at Macquarie University, March 2012.
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  42. Antje Nowack (2005). A Guarded Fragment for Abstract State Machines. Journal of Logic, Language and Information 14 (3):345-368.
    Abstract State Machines (ASMs) provide a formal method for transparent design and specification of complex dynamic systems. They combine advantages of informal and formal methods. Applications of this method motivate a number of computability and decidability problems connected to ASMs. Such problems result for example from the area of verifying properties of ASMs. Their high expressive power leads rather directly to undecidability respectively uncomputability results for most interesting problems in the case of unrestricted ASMs. Consequently, it is rather natural to (...)
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  43. Peter Purgathofer (2006). Is Informatics a Design Discipline? Poiesis and Praxis 4 (4):303-314.
    The article discusses the theory and practice of software development in the light of design theory. It tries to show that the design process cannot be forced into a predefined operational sequence. To underline this, the history of design methods is retraced, showing that such approaches were abolished not only in practice, but also the theory of design. The essay then discusses the cognitive framework of contemporary design theory and closes with the proposal that informatics should redefine itself as a (...)
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  44. Deborah Richards, Jacobson Michael, Taylor Charlotte, Taylor Meredith, Porte John, Newstead Anne & Hanna Nader, Evaluating the Models and Behaviour of 3D Intelligent Virtual Animals in a Predator-Prey Relationship. AAMAS 2012: 79-86. Proceedings of the Eleventh International Conference on Agent and Multiagent Systems (AAMAS).
    This paper presents the intelligent virtual animals that inhabit Omosa, a virtual learning environment to help secondary school students learn how to conduct scientific inquiry and gain concepts from biology. Omosa supports multiple agents, including animals, plants, and human hunters, which live in groups of varying sizes and in a predator-prey relationship with other agent types (species). In this paper we present our generic agent architecture and the algorithms that drive all animals. We concentrate on two of our animals to (...)
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  45. Robert J. Rovetto, An Ontological Architecture for Orbital Debris Data.
    The orbital debris problem presents an opportunity for inter-agency and international cooperation toward the mutually beneficial goals of debris prevention, mitigation, remediation, and improved space situational awareness (SSA). Achieving these goals requires sharing orbital debris and other SSA data. Toward this, I present an ontological architecture for the orbital debris and broader SSA domain, taking steps in the creation of an orbital debris ontology (ODO). The purpose of this ontological system is to (I) represent general orbital debris and SSA domain (...)
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  46. Yehoshua Sagiv (1979). An Algorithm for Inferring Multivalued Dependencies That Works Also for a Subclass of Propositional Logic. Dept. Of Computer Science, University of Illinois at Urbana-Champaign.
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  47. Samuel Sarjant, Catherine Legg, Olena Medelyan & Michael Robinson (2009). “All You Can Eat” Ontology-Building: Feeding Wikipedia to Cyc. IEEE/WIC/ACM International Conference on Web Intelligence (WI-09), 15 – 18 September 2009 Università Degli Studi di Milano Bicocca, Milano, Italy.
    In order to achieve genuine web intelligence, building some kind of large general machine-readable conceptual scheme (i.e. ontology) seems inescapable. Yet the past 20 years have shown that manual ontology-building is not practicable. The recent explosion of free user-supplied knowledge on the Web has led to great strides in automatic ontology building, but quality-control is still a major issue. Ideally one should automatically build onto an already intelligent base. We suggest that the long-running Cyc project is able to assist here. (...)
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  48. Jörg R. J. Schirra (2005). Foundation of Computational Visualistics. Deutscher Universitätsverlag.
    Images in Computer Science: Clarifications Required. The Age of the Images Images take a rather prominent place in contemporary life in the western ...
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  49. Yaroslav Sergeyev (2010). Lagrange Lecture: Methodology of Numerical Computations with Infinities and Infinitesimals. Rendiconti Del Seminario Matematico dell'Università E Del Politecnico di Torino 68 (2):95–113.
    A recently developed computational methodology for executing numerical calculations with infinities and infinitesimals is described in this paper. The approach developed has a pronounced applied character and is based on the principle “The part is less than the whole” introduced by the ancient Greeks. This principle is applied to all numbers (finite, infinite, and infinitesimal) and to all sets and processes (finite and infinite). The point of view on infinities and infinitesimals (and in general, on Mathematics) presented in this paper (...)
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  50. Yaroslav Sergeyev (2010). Counting Systems and the First Hilbert Problem. Nonlinear Analysis Series A 72 (3-4):1701-1708.
    The First Hilbert problem is studied in this paper by applying two instruments: a new methodology distinguishing between mathematical objects and mathematical languages used to describe these objects; and a new numeral system allowing one to express different infinite numbers and to use these numbers for measuring infinite sets. Several counting systems are taken into consideration. It is emphasized in the paper that different mathematical languages can describe mathematical objects (in particular, sets and the number of their elements) with different (...)
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