Results for 'granular partitions'

40 found
Order:
  1. A Theory of Granular Partitions.Thomas Bittner & Barry Smith - 2003 - In M. Duckham, M. F. Goodchild & M. F. Worboys (eds.), Foundations of Geographic Information Science. London: Taylor & Francis. pp. 117-151.
    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 (...)
    Download  
     
    Export citation  
     
    Bookmark   43 citations  
  2. Granular Partitions and Vagueness.Thomas Bittner & Barry Smith - 2003 - In Chris Welty & Barry Smith (eds.), Formal Ontology in Information Systems (FOIS). New York, USA: ACM Press. pp. 309-320.
    There are some who defend a view of vagueness according to which there are intrinsically vague objects or attributes in reality. Here, in contrast, we defend a view of vagueness as a semantic property of names and predicates. All entities are crisp, on this view, but there are, for each vague name, multiple portions of reality that are equally good candidates for being its referent, and, for each vague predicate, multiple classes of objects that are equally good candidates for being (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  3. A Taxonomy of Granular Partitions.Thomas E. Bittner & Barry Smith - 2001 - In Daniel Montello (ed.), Spatial Information Theory. Foundations of Geographic Information Science. Berlin: Springer. pp. 28-43.
    In this paper we propose a formal theory of partitions (ways of dividing up or sorting or mapping reality) and we show how the theory can be applied in the geospatial domain. We characterize partitions at two levels: as systems of cells (theory A), and in terms of their projective relation to reality (theory B). We lay down conditions of well-formedness for partitions and we define what it means for partitions to project truly onto reality. We (...)
    Download  
     
    Export citation  
     
    Bookmark   11 citations  
  4. Ontology for Task-Based Clinical Guidelines and the Theory of Granular Partitions.Anand Kumar & Barry Smith - 2003 - In Proceedings of 9th Conference on Artificial Intelligence in Medicine Europe (AIME 2003). Berlin: Springer. pp. 71-75.
    The theory of granular partitions (TGP) is a new approach to the understanding of ontologies and other classificatory systems. The paper explores the use of this new theory in the treatment of task-based clinical guidelines as a means for better understanding the relations between different clinical tasks, both within the framework of a single guideline and between related guidelines. We used as our starting point a DAML+OIL-based ontology for the WHO guideline for hypertension management, comparing this with related (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  5.  53
    Directly Depicting Granular Ontologies.Thomas Bittner & Barry Smith - 2004 - In IFOMIS Reports. pp. 117--151.
    Published in extended form as "Endurants and Perdurants in Directly Depicting Ontologies", -/- We propose an ontological theory that is powerful enough to describe both complex spatio-temporal processes and the enduring entities that participate in such processes. For this purpose we distinguish between ontologies and metaontology. Ontologies are based on very simple directly depicting languages and fall into two major categories: ontologies of type SPAN and ontologies of type SNAP. These represent two complementary perspectives on reality and result in distinct (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  6. A Unified Theory of Truth and Reference.Barry Smith & Berit Brogaard - 2000 - Logique Et Analyse 43 (169-170):49–93.
    The truthmaker theory rests on the thesis that the link between a true judgment and that in the world to which it corresponds is not a one-to-one but rather a one-to-many relation. An analogous thesis in relation to the link between a singular term and that in the world to which it refers is already widely accepted. This is the thesis to the effect that singular reference is marked by vagueness of a sort that is best understood in supervaluationist terms. (...)
    Download  
     
    Export citation  
     
    Bookmark   33 citations  
  7. Quantum Mereotopology.Barry Smith & Berit O. Brogaard - 2002 - Annals of Mathematics and Artificial Intelligence 36 (1):153-175.
    Mereotopology faces problems when its methods are extended to deal with time and change. We offer a new solution to these problems, based on a theory of partitions of reality which allows us to simulate (and also to generalize) aspects of set theory within a mereotopological framework. This theory is extended to a theory of coarse- and fine-grained histories (or finite sequences of partitions evolving over time), drawing on machinery developed within the framework of the so-called ‘consistent histories’ (...)
    Download  
     
    Export citation  
     
    Bookmark   22 citations  
  8. Vague Reference and Approximating Judgements.Thomas Bittner & Barry Smith - 2003 - Spatial Cognition and Computation 3 (2):137–156.
    We propose a new account of vagueness and approximation in terms of the theory of granular partitions. We distinguish different kinds of crisp and non-crisp granular partitions and we describe the relations between them, concentrating especially on spatial examples. We describe the practice whereby subjects use regular grid-like reference partitions as a means for tempering the vagueness of their judgments, and we demonstrate how the theory of reference partitions can yield a natural account of (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  9. The Unified Medical Language System and the Gene Ontology: Some Critical Reflections.Anand Kumar & Barry Smith - 2003 - In A. Günter, R. Kruse & B. Neumann (eds.), KI 2003: Advances in Artificial Intelligence. Berlin: Springer. pp. 135-148.
    The Unified Medical Language System and the Gene Ontology are among the most widely used terminology resources in the biomedical domain. However, when we evaluate them in the light of simple principles for wellconstructed ontologies we find a number of characteristic inadequacies. Employing the theory of granular partitions, a new approach to the understanding of ontologies and of the relationships ontologies bear to instances in reality, we provide an application of this theory in relation to an example drawn (...)
    Download  
     
    Export citation  
     
    Bookmark   9 citations  
  10.  52
    Carving Up Reality.Barry Smith - 2004 - In Michael Gorman & Jonathan Sanford (eds.), Categories: Historical and Systematic Essays. Catholic University of America Press. pp. 225-237.
    If Mont Blanc is a vague object, then its vagueness will depend on the context in which reference is made. In a geological context the mountain might include only rock, perhaps together with a certain amount of air in the crevices and tunnels which have been formed beneath its surface. In a context of soil chemistry we might include also a surrounding thin layer of organic matter. In a skiing context we might include some snow. This essay sketches in informal (...)
    Download  
     
    Export citation  
     
    Bookmark   5 citations  
  11. Une théorie unifiée de la vérité et de la référence.Barry Smith & Berit Brogaard - 2004 - In J. M. Monnoyer (ed.), La Structure du Monde: Objets, Propriétés, États du Choses. Paris: Vrin. pp. 141-184.
    The truthmaker theory rests on the thesis that the link between a true judgment and that in the world to which it corresponds is not a one-to-one but rather a one-to-many relation. An analogous thesis in relation to the link between a singular term and that in the world to which it refers is already widely accepted. This is the thesis to the effect that singular reference is marked by vagueness of a sort that is best understood in supervaluationist terms. (...)
    Download  
    Translate
     
     
    Export citation  
     
    Bookmark  
  12.  67
    A Unified Theory of Granularity, Vagueness and Approximation.Thomas Bittner & Barry Smith - 2001 - In COSIT Workshop on Spatial Vagueness, Uncertainty and Granularity. pp. 39.
    Abstract: We propose a view of vagueness as a semantic property of names and predicates. All entities are crisp, on this semantic view, but there are, for each vague name, multiple portions of reality that are equally good candidates for being its referent, and, for each vague predicate, multiple classes of objects that are equally good candidates for being its extension. We provide a new formulation of these ideas in terms of a theory of granular partitions. We show (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  13. Granular Spatio-Temporal Ontologies.Thomas Bittner & Barry Smith - 2003 - AAAI Symposium:12-17.
    We propose an ontological theory that is powerful enough to describe both complex spatio-temporal processes (occurrents) and the enduring entities (continuants) that participate therein. The theory is divided into two major categories of sub-theories: (sub-) theories of type SPAN and (sub-)theories of type SNAP. These theories represent two complementary perspectives on reality and result in distinct though compatible systems of categories. In SNAP we have enduring entities such as substances, qualities, roles, functions; in SPAN we have perduring entities such as (...)
    Download  
    Translate
     
     
    Export citation  
     
    Bookmark   2 citations  
  14. Giving Patients Granular Control of Personal Health Information: Using an Ethics ‘Points to Consider’ to Inform Informatics System Designers.Eric M. Meslin, Sheri A. Alpert, Aaron E. Carroll, Jere D. Odell, William M. Tierney & Peter H. Schwartz - 2013 - International Journal of Medical Informatics 82:1136-1143.
    Objective: There are benefits and risks of giving patients more granular control of their personal health information in electronic health record (EHR) systems. When designing EHR systems and policies, informaticists and system developers must balance these benefits and risks. Ethical considerations should be an explicit part of this balancing. Our objective was to develop a structured ethics framework to accomplish this. -/- Methods: We reviewed existing literature on the ethical and policy issues, developed an ethics framework called a “Points (...)
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  15. The Logic of Partitions: Introduction to the Dual of the Logic of Subsets: The Logic of Partitions.David Ellerman - 2010 - Review of Symbolic Logic 3 (2):287-350.
    Modern categorical logic as well as the Kripke and topological models of intuitionistic logic suggest that the interpretation of ordinary “propositional” logic should in general be the logic of subsets of a given universe set. Partitions on a set are dual to subsets of a set in the sense of the category-theoretic duality of epimorphisms and monomorphisms—which is reflected in the duality between quotient objects and subobjects throughout algebra. If “propositional” logic is thus seen as the logic of subsets (...)
    Download  
     
    Export citation  
     
    Bookmark   6 citations  
  16. How Bioethics Principles Can Aid Design of Electronic Health Records to Accommodate Patient Granular Control.Eric M. Meslin & Peter H. Schwartz - 2014 - Journal of General Internal Medicine 30 (1):3-6.
    Ethics should guide the design of electronic health records (EHR), and recognized principles of bioethics can play an important role. This approach was adopted recently by a team of informaticists designing and testing a system where patients exert granular control over who views their personal health information. While this method of building ethics in from the start of the design process has significant benefits, questions remain about how useful the application of bioethics principles can be in this process, especially (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  17. Partitions and Objective Indefiniteness.David Ellerman - manuscript
    Classical physics and quantum physics suggest two meta-physical types of reality: the classical notion of a objectively definite reality with properties "all the way down," and the quantum notion of an objectively indefinite type of reality. The problem of interpreting quantum mechanics (QM) is essentially the problem of making sense out of an objectively indefinite reality. These two types of reality can be respectively associated with the two mathematical concepts of subsets and quotient sets (or partitions) which are category-theoretically (...)
    Download  
     
    Export citation  
     
    Bookmark  
  18. The Ontology of Blood Pressure: A Case Study in Creating Ontological Partitions in Biomedicine.Anand Kumar & Barry Smith - 2003 - IFOMIS Reports.
    We provide a methodology for the creation of ontological partitions in biomedicine and we test the methodology via an application to the phenomenon of blood pressure. An ontology of blood pressure must do justice to the complex networks of intersecting pathways in the organism by which blood pressure is regulated. To this end it must deal not only with the anatomical structures and physiological processes involved in such regulation but also with the relations between these at different levels of (...)
    Download  
     
    Export citation  
     
    Bookmark  
  19. A Graph-Theoretic Method to Define Any Boolean Operation on Partitions.David Ellerman - 2019 - The Art of Discrete and Applied Mathematics 2 (2):1-9.
    The lattice operations of join and meet were defined for set partitions in the nineteenth century, but no new logical operations on partitions were defined and studied during the twentieth century. Yet there is a simple and natural graph-theoretic method presented here to define any n-ary Boolean operation on partitions. An equivalent closure-theoretic method is also defined. In closing, the question is addressed of why it took so long for all Boolean operations to be defined for (...). (shrink)
    Download  
     
    Export citation  
     
    Bookmark  
  20.  55
    Formalizing UMLS Relations Using Semantic Partitions in the Context of a Task-Based Clinical Guidelines Model.Anand Kumar, Matteo Piazza, Barry Smith, Silvana Quaglini & Mario Stefanelli - 2004 - In IFOMIS Reports. Saarbrücken: IFOMIS.
    An important part of the Unified Medical Language System (UMLS) is its Semantic Network, consisting of 134 Semantic Types connected to each other by edges formed by one or more of 54 distinct Relation Types. This Network is however for many purposes overcomplex, and various groups have thus made attempts at simplification. Here we take this work further by simplifying the relations which involve the three Semantic Types – Diagnostic Procedure, Laboratory Procedure and Therapeutic or Preventive Procedure. We define operators (...)
    Download  
     
    Export citation  
     
    Bookmark  
  21. An Introduction to Partition Logic.David Ellerman - 2014 - Logic Journal of the IGPL 22 (1):94-125.
    Classical logic is usually interpreted as the logic of propositions. But from Boole's original development up to modern categorical logic, there has always been the alternative interpretation of classical logic as the logic of subsets of any given (nonempty) universe set. Partitions on a universe set are dual to subsets of a universe set in the sense of the reverse-the-arrows category-theoretic duality--which is reflected in the duality between quotient objects and subobjects throughout algebra. Hence the idea arises of a (...)
    Download  
     
    Export citation  
     
    Bookmark   14 citations  
  22. Rethinking Boltzmannian Equilibrium.Charlotte Werndl & Roman Frigg - 2015 - Philosophy of Science 82 (5):1224-1235.
    Boltzmannian statistical mechanics partitions the phase space of a sys- tem into macro-regions, and the largest of these is identified with equilibrium. What justifies this identification? Common answers focus on Boltzmann’s combinatorial argument, the Maxwell-Boltzmann distribution, and maxi- mum entropy considerations. We argue that they fail and present a new answer. We characterise equilibrium as the macrostate in which a system spends most of its time and prove a new theorem establishing that equilib- rium thus defined corresponds to the (...)
    Download  
     
    Export citation  
     
    Bookmark   10 citations  
  23. The Principle of Indifference and Imprecise Probability.Susanna Rinard - 2014 - Thought: A Journal of Philosophy 3 (2):110-114.
    Sometimes different partitions of the same space each seem to divide that space into propositions that call for equal epistemic treatment. Famously, equal treatment in the form of equal point-valued credence leads to incoherence. Some have argued that equal treatment in the form of equal interval-valued credence solves the puzzle. This paper shows that, once we rule out intervals with extreme endpoints, this proposal also leads to incoherence.
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  24. On the Duality Between Existence and Information.David Ellerman - manuscript
    Recent developments in pure mathematics and in mathematical logic have uncovered a fundamental duality between "existence" and "information." In logic, the duality is between the Boolean logic of subsets and the logic of quotient sets, equivalence relations, or partitions. The analogue to an element of a subset is the notion of a distinction of a partition, and that leads to a whole stream of dualities or analogies--including the development of new logical foundations for information theory parallel to Boole's development (...)
    Download  
     
    Export citation  
     
    Bookmark  
  25. Cunoaștere și Informații.Nicolae Sfetcu - 2019 - Drobeta Turnu Severin: MultiMedia Publishing.
    Cunoașterea și informațiile (abordate în ansamblu sau în componentele lor distincte) sunt o preocupare majoră pentru tehnologia informației, sisteme de informații, știința informației și activitatea de informații în general. Procesul obţinerii, prelucrării şi analizei informaţiilor este o preocupare majoră pentru societatea actuală. În acest scop se folosesc procedee şi tehnici specifice pentru culegerea sau generarea de informaţii, prelucrarea acestora prin analiză şi sinteză, generarea de predicţii şi strategii, transmisia şi prezentarea informaţiilor factorilor de decizie, şi stocarea lor. Analiza informațiilor poate (...)
    Download  
    Translate
     
     
    Export citation  
     
    Bookmark   4 citations  
  26. Evidential Incomparability and the Principle of Indifference.Martin Smith - 2015 - Erkenntnis 80 (3):605-616.
    The _Principle of Indifference_ was once regarded as a linchpin of probabilistic reasoning, but has now fallen into disrepute as a result of the so-called _problem of multiple of partitions_. In ‘Evidential symmetry and mushy credence’ Roger White suggests that we have been too quick to jettison this principle and argues that the problem of multiple partitions rests on a mistake. In this paper I will criticise White’s attempt to revive POI. In so doing, I will argue that what (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  27. Counting Distinctions: On the Conceptual Foundations of Shannon’s Information Theory.David Ellerman - 2009 - Synthese 168 (1):119-149.
    Categorical logic has shown that modern logic is essentially the logic of subsets (or "subobjects"). Partitions are dual to subsets so there is a dual logic of partitions where a "distinction" [an ordered pair of distinct elements (u,u′) from the universe U ] is dual to an "element". An element being in a subset is analogous to a partition π on U making a distinction, i.e., if u and u′ were in different blocks of π. Subset logic leads (...)
    Download  
     
    Export citation  
     
    Bookmark   15 citations  
  28.  52
    Logical Entropy: Introduction to Classical and Quantum Logical Information Theory.David Ellerman - 2018 - Entropy 20 (9):679.
    Logical information theory is the quantitative version of the logic of partitions just as logical probability theory is the quantitative version of the dual Boolean logic of subsets. The resulting notion of information is about distinctions, differences and distinguishability and is formalized using the distinctions of a partition. All the definitions of simple, joint, conditional and mutual entropy of Shannon information theory are derived by a uniform transformation from the corresponding definitions at the logical level. The purpose of this (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  29. An Introduction to Logical Entropy and its Relation to Shannon Entropy.David Ellerman - 2013 - International Journal of Semantic Computing 7 (2):121-145.
    The logical basis for information theory is the newly developed logic of partitions that is dual to the usual Boolean logic of subsets. The key concept is a "distinction" of a partition, an ordered pair of elements in distinct blocks of the partition. The logical concept of entropy based on partition logic is the normalized counting measure of the set of distinctions of a partition on a finite set--just as the usual logical notion of probability based on the Boolean (...)
    Download  
     
    Export citation  
     
    Bookmark   5 citations  
  30. Praise, Blame, Obligation, and DWE: Toward a Framework for Classical Supererogation and Kin.Paul McNamara - 2011 - Journal of Applied Logic 9 (2):153-170.
    Continuing prior work by the author, a simple classical system for personal obligation is integrated with a fairly rich system for aretaic (agent-evaluative) appraisal. I then explore various relationships between definable aretaic statuses such as praiseworthiness and blameworthiness and deontic statuses such as obligatoriness and impermissibility. I focus on partitions of the normative statuses generated ("normative positions" but without explicit representation of agency). In addition to being able to model and explore fundamental questions in ethical theory about the connection (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  31. The Quantum Logic of Direct-Sum Decompositions: The Dual to the Quantum Logic of Subspaces.David Ellerman - 2017
    Since the pioneering work of Birkhoff and von Neumann, quantum logic has been interpreted as the logic of (closed) subspaces of a Hilbert space. There is a progression from the usual Boolean logic of subsets to the "quantum logic" of subspaces of a general vector space--which is then specialized to the closed subspaces of a Hilbert space. But there is a "dual" progression. The notion of a partition (or quotient set or equivalence relation) is dual (in a category-theoretic sense) to (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  32.  54
    Semantic Information G Theory and Logical Bayesian Inference for Machine Learning.Chenguang Lu - 2019 - Information 10 (8):261.
    An important problem with machine learning is that when label number n>2, it is very difficult to construct and optimize a group of learning functions, and we wish that optimized learning functions are still useful when prior distribution P(x) (where x is an instance) is changed. To resolve this problem, the semantic information G theory, Logical Bayesian Inference (LBI), and a group of Channel Matching (CM) algorithms together form a systematic solution. MultilabelMultilabel A semantic channel in the G theory consists (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  33.  86
    Content Aggregation, Visualization and Emergent Properties in Computer Simulations.Gordana Dodig-Crnkovic, Juan M. Durán & D. Slutej - 2010 - In Kai-Mikael Jää-Aro & Thomas Larsson (eds.), SIGRAD 2010 – Content aggregation and visualization. Linköping University Electronic Press. pp. 77-83.
    With the rapidly growing amounts of information, visualization is becoming increasingly important, as it allows users to easily explore and understand large amounts of information. However the field of information visualiza- tion currently lacks sufficient theoretical foundations. This article addresses foundational questions connecting information visualization with computing and philosophy studies. The idea of multiscale information granula- tion is described based on two fundamental concepts: information (structure) and computation (process). A new information processing paradigm of Granular Computing enables stepwise increase (...)
    Download  
     
    Export citation  
     
    Bookmark  
  34. Bridging the Gap Between Medical and Bioinformatics: An Ontological Case Study in Colon Carcinoma.Anand Kumar, Yum Lina Yip, Barry Smith & Pierre Grenon - 2006 - Computers in Biology and Medicine 36 (7):694--711.
    Ontological principles are needed in order to bridge the gap between medical and biological information in a robust and computable fashion. This is essential in order to draw inferences across the levels of granularity which span medicine and biology, an example of which include the understanding of the roles of tumor markers in the development and progress of carcinoma. Such information integration is also important for the integration of genomics information with the information contained in the electronic patient records in (...)
    Download  
     
    Export citation  
     
    Bookmark  
  35. Analytic Aesthetics and the Dilemma of Timelessness.Derek Allan - manuscript
    The paper highlights analytic aesthetics’ unacknowledged assumption that art is timeless, a view it inherited from Enlightenment thinkers such as Hume and Kant, who in turn inherited it from the Renaissance. This view, I contend, is no longer tenable because it is at odds with our experience of the art of the past. Analytic aesthetics bypasses this dilemma because it confines its attention to topics such as the nature of aesthetic pleasure, whether the appreciation of art should be disinterested and (...)
    Download  
     
    Export citation  
     
    Bookmark  
  36.  49
    MacColl’s Modes of Modalities.Fabien Schang - 2011 - Philosophia Scientiae 15:149-188.
    Hugh MacColl is commonly seen as a pioneer of modal and many-valued logic, given his introduction of modalities that go beyond plain truth and falsehood. But a closer examination shows that such a legacy is debatable and should take into account the way in which these modalities proceeded. We argue that, while MacColl devised a modal logic in the broad sense of the word, he did not give rise to a many-valued logic in the strict sense. Rather, his logic is (...)
    Download  
     
    Export citation  
     
    Bookmark  
  37.  54
    Minimizing the Threat of a Positive Majority Deficit in Two-Tier Voting Systems with Equipopulous Units.Claus Beisbart & Luc Bovens - 2013 - Public Choice 132 (1-2):75-94.
    The mean majority deficit in a two-tier voting system is a function of the partition of the population. We derive a new square-root rule: For odd-numbered population sizes and equipopulous units the mean majority deficit is maximal when the member size of the units in the partition is close to the square root of the population size. Furthermore, within the partitions into roughly equipopulous units, partitions with small even numbers of units or small even-sized units yield high mean (...)
    Download  
     
    Export citation  
     
    Bookmark  
  38. Epistemic Vs Ontic Classification of Quantum Entangled States?Michele Caponigro & Enrico Giannetto - 2012 - Discusiones Filosóficas 13 (20):137 - 145.
    In this brief paper, starting from recent works, we analyze from conceptual point of view this basic question: can be the nature of quantum entangled states interpreted ontologically or epistemologically? According some works, the degrees of freedom of quantum systems permit us to establish a possible classification between factorizables and entangled states. We suggest, that the "choice" of degree of freedom, even if mathematically justified introduces epistemic element, not only in the systems but also in their classification. We retain, instead, (...)
    Download  
     
    Export citation  
     
    Bookmark  
  39. Changing the Rules: Architecture and the New Millennium.David Kirsh - 2001 - Convergence 7 (2):113-125.
    Architecture is about to enter its first magical phase: a time when buildings actively co-operate with their inhabitants; when objects know what they are, where they are, what is near them; when social and physical space lose their type coupling; when wall and partitions change with mood and task. As engineers and scientists explore how to digitse the world around us, the classical constraints of design, ruled so long by the physics of space, time, and materials, are starting to (...)
    Download  
    Translate
     
     
    Export citation  
     
    Bookmark  
  40. On Classical and Quantum Logical Entropy.David Ellerman - manuscript
    The notion of a partition on a set is mathematically dual to the notion of a subset of a set, so there is a logic of partitions dual to Boole's logic of subsets (Boolean logic is usually mis-specified as "propositional" logic). The notion of an element of a subset has as its dual the notion of a distinction of a partition (a pair of elements in different blocks). Boole developed finite logical probability as the normalized counting measure on elements (...)
    Download  
    Translate
     
     
    Export citation  
     
    Bookmark