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Lech Polkowski - One of the best experts on this subject based on the ideXlab platform.
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A Logic for Spatial Reasoning in the Framework of Rough Mereology
Transactions on Rough Sets XXI, 2019Co-Authors: Lech PolkowskiAbstract:Spatial reasoning concerns a language in which spatial objects are described and argued about. Within the plethora of approaches, we single out the one set in the framework of Mereology - the theory of concepts employing the notion of a part as the primitive one. Within Mereology, we can choose between the approach based on part as the basic notion or the approach based on the notion of a connection from which the notion of a part is defined. In this work, we choose the former approach modified to the rough Mereology version in which the notion of a part becomes ‘fuzzified’ to the notion of a part to a degree. The prevalence of this approach lies in the fact that it does allow for quantitative assessment of relations among spatial objects in distinction to only qualitative evaluation of those relations in case of other Mereology based approaches.
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IRC - Robot Navigation and Path Planning by Means of Rough Mereology
2018 Second IEEE International Conference on Robotic Computing (IRC), 2018Co-Authors: Lech Polkowski, Lukasz Zmudzinski, Piotr ArtiemjewAbstract:In this research contribution, authors advocate a new relational means for intelligent robot and robot teams control and navigation. The main underlying theory is that of Mereology and its extension rough Mereology augmented with new concepts transferred from geometry viz. betweenness, rendered in the mereological framework. Along with the theoretical proposition, we give results of experiments showing the usefulness of the method. The proposed method allows the user to switch among teams of robot configurations which opens the way to humancoordinated steering of team configurations depending on the environment and desired work aim.
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robot navigation and path planning by means of rough Mereology
2018 Second IEEE International Conference on Robotic Computing (IRC), 2018Co-Authors: Lech Polkowski, Lukasz Zmudzinski, Piotr ArtiemjewAbstract:In this research contribution, authors advocate a new relational means for intelligent robot and robot teams control and navigation. The main underlying theory is that of Mereology and its extension rough Mereology augmented with new concepts transferred from geometry viz. betweenness, rendered in the mereological framework. Along with the theoretical proposition, we give results of experiments showing the usefulness of the method. The proposed method allows the user to switch among teams of robot configurations which opens the way to humancoordinated steering of team configurations depending on the environment and desired work aim.
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IJCRS (2) - On Mereology as a Tool in Problems of Intelligent Control, Granular Computing, Data Analysis and Approximate and Spatial Reasoning
Rough Sets, 2017Co-Authors: Lech PolkowskiAbstract:Mereology is a theory of concepts using the notion of a part as its primitive notion. This notion is well suited for analysis and reasoning about mass concepts like solids, figures, swarms of things. We aim here at highlighting foundations of Mereology and its extension, rough Mereology in which the notion of a part undergoes a ‘fuzzification’ to the notion of a part to a degree, along with applications to problems of intelligent control of teams of intelligent agents, granular computing, spatial reasoning, data analysis and approximate reasoning about classification of data into decision classes.
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Mereology in Engineering and Computer Science
Mereology and the Sciences, 2014Co-Authors: Lech PolkowskiAbstract:Mereology as an alternative to naive/formal Set Theory, predominant in formalizations of mathematical and informatic theories, is especially suited to discussions of relations among mass things, e.g., collections of them or spatial objects like figures, solids, etc., but, it finds also essential applications in other areas of engineering and comp uter science like assembling and design, planning, data classification, reasoning by means of cognitive schemes and in many-agent systems. Our chapter aims at presenting specimens of the role Mereology plays in all of these areas of research. Out of a vast accumulated knowledge and of a plethora of applications, we strive to extract a skeleton of basic facts and exemplary applications in order to convey to the reader the elegance of solutions employing tools of Mereology. We begin with a discussion of principles of Mereology, by giving a fairly detailed account of the pioneering formalization by Stanislaw Lesniewski in Sect. 2, followed by an account of Mereology based on the notion of a connection in Sect. 3. These two sections give a foundation for further developments. An extension of Mereology called Rough Mereology, which may be regarded as Mereology fused in a sense with Fuzzy and Rough Set Theories, is discussed in Sect. 3. An important, both for theory and applications, topological ingredient of Mereology is brought to the reader attention in Sect. 4, and on it, the Part I, Foundations, closes. In Part II, devoted to applications, we discuss the notion of an artifact, along with artifact design and assembling, in Sect. 5 and Sect. 6 brings forth a discussion of the role of Mereology in Spatial Reasoning and its applications like descriptions of shape and orientation and spatial calculi like RCC. A related topic of Planning and Navigation by means of mereological tools is presented in Sect. 7 for autonomous mobile agents (robots), and, in Sect. 8 we give an account of applications of Mereology in Knowledge Engineering, centered on Mereological Granular Computing in synthesis of data classifiers. Finally, Sect. 9 gives an account of the mereological perceptron networks, reasoning in many-agent systems by mereological tools for fusion of knowledge, and an account of ideas for Mereological Granular Logics.
Aaron Cotnoir - One of the best experts on this subject based on the ideXlab platform.
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non wellfounded Mereology
Review of Symbolic Logic, 2012Co-Authors: Aaron Cotnoir, Andrew BaconAbstract:This paper is a systematic exploration of non-wellfounded Mereology. Motivations and applications suggested in the literature are considered. Some are exotic like Borges' ALEPH, and the TRINITY; other examples are less so, like TIME TRAVELING BRICKS, and even Geach's TIBBLES THE CAT. The authors point out that the transitivity of non-wellfounded parthood is inconsistent with extensionality. A non-wellfounded Mereology is developed with careful consideration paid to rival notions of supplementation and fusion. Two equivalent axiomatizations are given, and are compared to classical Mereology. We provide a class of models with respect to which the non-wellfounded Mereology is sound and complete. This paper explores the prospects of non-wellfounded Mereology. An order < (in this case proper parthood) on a domain is said to be wellfounded if every nonempty subset of that domain has a <-minimal element. We say that x is a <-minimal element of a set S if there is no y in S such that y < x. Wellfoundedness rules out any infinite descending <-chains. There are atomless mereologies, sometimes called gunky, in which proper parthood chains are all infinite. 1 This is one interesting and important case of a non- wellfounded Mereology. But notice, wellfoundedness also rules out structures in which for some x, x < x; likewise, it rules out cases in which there is some x and y such that x < y and y < x. That is, wellfoundedness rules out parthood loops. In this paper, we explore a non-wellfounded Mereology that allows for both these sorts of parthood loops. In §1, we briefly survey some applications for non-wellfounded Mereology that have been suggested in the literature. In §2, we consider difficulties with the classical definitions of parthood and proper parthood; we discuss extensionality principles in Mereology, and argue that extensionality is inconsistent with the transitivity of parthood in certain non- wellfounded scenarios. In §3, we examine supplementation principles and rival notions of fusion for non-wellfounded Mereology. §4 examines the relationship between classical Mereology and non-wellfounded Mereology. We show that the latter is a simple generaliza- tion of the former. Finally, we give a class of models for which non-wellfounded Mereology is sound and complete in §5.
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NON-WELLFOUNDED Mereology
Review of Symbolic Logic, 2011Co-Authors: Aaron Cotnoir, Andrew BaconAbstract:This paper is a systematic exploration of non-wellfounded Mereology. Motivations and applications suggested in the literature are considered. Some are exotic like Borges' ALEPH, and the TRINITY; other examples are less so, like TIME TRAVELING BRICKS, and even Geach's TIBBLES THE CAT. The authors point out that the transitivity of non-wellfounded parthood is inconsistent with extensionality. A non-wellfounded Mereology is developed with careful consideration paid to rival notions of supplementation and fusion. Two equivalent axiomatizations are given, and are compared to classical Mereology. We provide a class of models with respect to which the non-wellfounded Mereology is sound and complete. This paper explores the prospects of non-wellfounded Mereology. An order < (in this case proper parthood) on a domain is said to be wellfounded if every nonempty subset of that domain has a
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NON-WELLFOUNDED Mereology
The Review of Symbolic Logic, 2011Co-Authors: Aaron Cotnoir, Andrew BaconAbstract:This paper is a systematic exploration of non-wellfounded Mereology. Motivations and applications suggested in the literature are considered. Some are exotic like Borges’ Aleph, and the trinity; other examples are less so, like time traveling bricks, and even Geach’s Tibbles the Cat. The authors point out that the transitivity of non-wellfounded parthood is inconsistent with extensionality. A non-wellfounded Mereology is developed with careful consideration paid to rival notions of supplementation and fusion. Two equivalent axiomatizations are given, and are compared to classical Mereology. We provide a class of models with respect to which the non-wellfounded Mereology is sound and complete.
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anti symmetry and non extensional Mereology
The Philosophical Quarterly, 2010Co-Authors: Aaron CotnoirAbstract:I examine the link between extensionality principles of classical Mereology and the anti-symmetry of parthood. Varzi's most recent defence of extensionality depends crucially on assuming anti-symmetry. I examine the notions of proper parthood, weak supplementation and non-well-foundedness. By rejecting anti-symmetry, the anti-extensionalist has a unified, independently grounded response to Varzi's arguments. I give a formal construction of a non-extensional Mereology in which anti-symmetry fails. If the notion of ‘mereological equivalence’ is made explicit, this non-anti-symmetric Mereology recaptures all of the structure of classical Mereology.
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Anti‐Symmetry and Non‐Extensional Mereology
The Philosophical Quarterly, 2010Co-Authors: Aaron CotnoirAbstract:I examine the link between extensionality principles of classical Mereology and the anti-symmetry of parthood. Varzi's most recent defence of extensionality depends crucially on assuming anti-symmetry. I examine the notions of proper parthood, weak supplementation and non-well-foundedness. By rejecting anti-symmetry, the anti-extensionalist has a unified, independently grounded response to Varzi's arguments. I give a formal construction of a non-extensional Mereology in which anti-symmetry fails. If the notion of ‘mereological equivalence’ is made explicit, this non-anti-symmetric Mereology recaptures all of the structure of classical Mereology.
Rohan French - One of the best experts on this subject based on the ideXlab platform.
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An Argument for the Ontological Innocence of Mereology
Erkenntnis, 2016Co-Authors: Rohan FrenchAbstract:In Parts of Classes David Lewis argued that Mereology is ‘ontologically innocent’, mereological notions not incurring additional ontological commitments. Unfortunately, though, Lewis’s argument for this is not fully spelled out. Here we use some formal results concerning translations between formal languages to argue for the ontological innocence of Mereology directly.
Zaiyue Zhang - One of the best experts on this subject based on the ideXlab platform.
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RSFDGrC - Rough Mereology in knowledge representation
Lecture Notes in Computer Science, 2003Co-Authors: Zaiyue ZhangAbstract:The rough Mereology proposed by Polkowski and Skowron is used in complex systems, multi-agent systems, knowledge engineering and knowledge representation. The function µ makes the rough Mereology more like the fuzzy Mereology. A new rough Mereology is proposed, in which the rough inclusion is defined completely based on the upper and lower approximations of rough sets. The basic properties of the rough Mereology, and applications in the knowledge representation and knowledge engineering are discussed.
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rough Mereology in knowledge representation
Granular Computing, 2003Co-Authors: Cungen Cao, Yuefei Sui, Zaiyue ZhangAbstract:The rough Mereology proposed by Polkowski and Skowron is used in complex systems, multi-agent systems, knowledge engineering and knowledge representation. The function µ makes the rough Mereology more like the fuzzy Mereology. A new rough Mereology is proposed, in which the rough inclusion is defined completely based on the upper and lower approximations of rough sets. The basic properties of the rough Mereology, and applications in the knowledge representation and knowledge engineering are discussed.
Andrzej Skowron - One of the best experts on this subject based on the ideXlab platform.
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rough set theory
Wiley Encyclopedia of Computer Science and Engineering, 2007Co-Authors: Zdzislaw Pawlak, Lech Polkowski, Andrzej SkowronAbstract:In this article, basic concepts and different areas of research in rough set theory are presented. Keywords: indiscernibility; approximation space; concept approximation; rough set; rough Mereology
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Rough Mereology in information systems with applications to qualitative spatial reasoning
Fundamenta Informaticae, 2000Co-Authors: Lech Polkowski, Andrzej SkowronAbstract:Rough Mereology has been proposed as a paradigm for approximate reasoning in complex information systems. Its primitive notion is that of a predicate of rough inclusion which gives for any two entities of discourse the degree in which one of them is a part of the other. Rough Mereology may be regarded as an extension of Rough Set Theory as it proposes to argue in terms of similarity relations induced from a rough inclusion instead of reasoning in terms of more strict indiscernibility relations. Rough Mereology is also a generalization of Mereology i.e. a theory of reasoning based on the notion of a part. Classical languages of mathematics are of two-fold kind: the language of set theory (naive or formal) expressing classes of objects as sets consisting of ”elements”, ”points” etc. suitable for objects perceived as built of ”atoms” and applied to structures perceived as discrete and the language of part relations suitable for e.g. continuous objects like solids, regions, etc. where two objects are related to each other by saying that one of them is a part of the other. Mereological theories for reasoning about complex structures are at the heart of Qualitative Spatial Reasoning. In this paper, we study basic aspects of Rough Mereology in Information Systems. Mereology makes the distinction between entities perceived as individuals (singletons), to which the part predicate may be applied, and entities perceived as distributive classes (sets, lists, general names etc.) of entities. This distinction is made formal and precise within Ontology i.e. Theory of Being based on the primitive notion of the copula is which is also a basic ingredient of theories for Spatial Reasoning. The practical aim of Ontology is to elaborate a system of concepts (notions, names, sets of entities) about which the reasoning is carried out. Therefore, we begin our study with an analysis of a simple rough set-based Ontology (the template ontology) in Information Systems and in this setting we present our approach to Mereology in Information Systems. In this framework we introduce Rough Mereology and we present some ways for defining rough inclusions. We demonstrate applications of Rough Mereology to approximate reasoning taking as the case subject Qualitative Spatial Reasoning. We address here some of its mereo-topological as well as mereo-geometrical aspects.
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Rough Mereology in information systems. A case study: qualitative spatial reasoning
Rough Set Methods and Applications, 2000Co-Authors: Lech Polkowski, Andrzej SkowronAbstract:Rough Mereology has been proposed as a paradigm for approximate reasoning in complex information systems [65], [66], [67], [68], [76]. Its primitive notion is that of a rough inclusion functor which gives for any two entities of discourse the degree in which one of them is a part of the other. Rough Mereology may be regarded as an extension of Rough Set Theory as it proposes to argue in terms of similarity relations induced from a rough inclusion instead of reasoning in terms of indiscernibility relations (cf. Chapter 1); it also proposes an extension of Mereology as it replaces the mereological primitive functor of being a part with a more general functor of being a part in a degree. Rough Mereology has deep relations to Fuzzy Set Theory as it proposes to study the properties of partial containment which is also the fundamental subject of study for Fuzzy Set Theory.
