Mauro Bertani

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Bibliography on the mathematics behind the facet classification

From the birth of logic through late nineteenth-century mathematics, towards the faceted classification of S.R. Ranganathan

This is a work born from a research group of ISKO Italy on the mathematical structure of facet classifications. The link to the web resource is http://www.iskoi.org/penumbra/. It is a bibliography developed during the research space, starting from the book of Prolegomena S.R.Ranganathan and developing from works by Charles Sanders Peirce, to first order logic and propositional calculus, up to boundary logic. It ends with Derek Austin's work on PRECIS and John Sowa's work on conceptual graphs. In the repository it is possible to find some source code in javascript on the material treated in the bibliography. From a BTree implementation, to a rule Engine, to an advanced conditional probability calculator.

There are 5 tracks:

Track 1

An in-depth study of chapter Q, R and S of the prolegomena of S.R.Ranganathan in which he explains the APUPA arrangement. The work began from the writing of Miksa Francis. In addition to dealing with filling curves, it also covers the axiomatic aspect of subject heading, a subject very dear to S.R.Ranganathan.

  • Bertani's draft

    • Bertani Mauro & Luca Giusti, Draft_ranganatan_v2.1, (2019-2020), link

  • Ranganathan's book

    • Ranganathan S. R., "Prolegomena to Library Classification, 3rd edi-tion by SR Ranganathan assisted by M. A. Gopinath.", Chapter Q,R,S Asia Publish-ing House (1967), link.
    • Ranganathan S. R., Depth Classification and Reference Service & Reference Material, Indian Library Association, 1953.
    • Ranganathan S. R., Postulation approach to facetd classification: depth classification 29, Annals of Library Science & Documentation, Volume 5(2); 1958; p. 33-51; Reprinted with permission from NISCAIR

  • Math, space filling curve

    • Butz Arthur R., "Space filling curves and mathematical programming.", Information and control 12.4 (1968): 314-330, link
    • Peano Giuseppe, "Sur une courbe, qui remplit toute une aire plane.", Mathematische Annalen 36.1 (1890): 157-160, link
    • Russell Bertrand, "Mathematical logic as based on the theory of types.", American journal of mathematics 30.3 (1908): 222-262, link
    • Grossi Davide & Dignum Frank & Meyer John-jules, Contextual Taxonomies, (2004). 33-51. 10.1007/11533092_3, link

  • Postulational method

    • Peirce Charles S, "On the logic of number." American Journal of Mathematics 4.1 (1881): 85-95, link
    • Peano Giuseppe, Arithmetices principia: Nova methodo exposita, Fratres Bocca, 1889, link
    • Peano Giuseppe, Calcolo geometrico secondo l'Ausdehnungslehre di H. Grassmann: preceduto dalla operazioni della logica deduttiva, Vol. 3. Fratelli Bocca, 1888, link.

  • Micksa

    • Miksa Francis, The influence of mathematics on the classificatory thought of SR Ranganathan, (1997)
    • Thomas M. Dousa, Intellection and Intuition: On the Epistemology of S.R. Ranganathan, NASKO. Vol. 7. 149-173, (2019), link
    • Ranganathan, Shiyali Ramamrita. "Micro thought and its service." (1957), link
    • Broughton, V. (2006), "The need for a faceted classification as the basis of all methods of information retrieval", Aslib Proceedings, Vol. 58 No. 1/2, pp. 49-72, link
    • Bianchini Carlo & Luca Giusti & Claudio Gnoli, "The APUPA bell curve.", Les cahiers du numérique 13.1, (2017), 49-68, link.
    • Broughton Vanda, "Notational expressivity; the case for and against the representation of internal subject structure in notational coding.", KO KNOWLEDGE ORGANIZATION 26.3, (1999), 140-148, link.

  • History of math

    • Boyer Carl B. & Uta C. Merzbach, A history of mathematics (chapter XXVI), John Wiley & Sons, (2011).
    • La Barre, Kathryn. (2006). The use of faceted analytico-synethic theory as revealed in the practice and construction of website design, link
    • Van den Heuvel Charles, "Multidimensional classifications: Past and future conceptualizations and visualizations.", KO KNOWLEDGE ORGANIZATION 39.6, (2012), 446-460, link

Track 2

From a second trace proposed by Luca Giusti, the relationships between the work of Charles Sanders Pierce and the structuring of the subject indexing of S.R.Ranganthan are investigated. The birth of logic from Boole's work to De Morgan's work is discussed. The axiom of Zermelo's choice. Benjamin Pierce's works on linear algebras and the birth of group theory.

  • Math at time of C.S:Peirce

    • Riche Jacques, "From universal algebra to universal logic.", Perspectives on Universal Logic. Itália: Polimetrica Publisher (2007), 3-39. , link
    • Boole George, The mathematical analysis of logic. Philosophical Library, 1847 , link
    • Cayley Arthur, “A Memoir on the Theory of Matrices.”, Philosophical Transactions of the Royal Society of London, vol. 148, The Royal Society, 1858, pp. 17–37 , link
    • Codd Edgar F., Relational completeness of data base sublanguages. IBM Corporation, 1972. , link
    • Cayley Arthur, "On the theory of Determinants", Transaction of the Cambrige philosofical society, vol. 8, 1849, link
    • Boole George, A question in logic, Notes and Queries, Second series vol. 9, Junuary-June, 1860 , p. 184, link
    • De Morgan Augustus, "On the Syllogism, No. iii. And on Logic In General.", Transaction of the Cambridge philosofical society, vol. 9, 1864,p. 173-230 link
    • Wikipedia en , "Eigenvalues and eigenvectors", (2022) link
    • Frege Gottlob, "Philosophical Writings of Gottlob Frege.", chapter Function and Concept, Trans. Peter Geach and Max Black. 2nd edn. Oxford: Blackwell (1960)
    • Grätzer George, Universal Algebra, U.S. Naval Academy, Annapolis, Md.Volume: 173-210, (1966) link
    • Peirce Charles Sanders, "Description of a Notation for the Logic of Relatives, Resulting from an Amplification of the Conceptions of Boole's Calculus of Logic", Memoirs of the American Academy of Arts and Sciences , 1873, New Series, Vol. 9, No. 2 (1873), pp. 317-378 link
    • Hosseini Giv Hossein, The Axiom of Choice, Well-Ordering, and Well-Classification, American Mathematical Monthly, 122. 10.4169/amer.math.monthly.122.01.56. , (2015) link
    • Zermelo Ernst, Investigations in the foundations of set theory I. 1908. [transl. in From Frege to G¨odel, van Heijenoort, Harvard Univ. Press, 1971.]
    • De Morgan Augustus, "Syllabus of a proposed system of logic", Wanton and Maberly, 1860 link
    • Dijkstra Edsger W. , "Predicate calculus: The unification of three calculi", EDW1123, link
    • Dijkstra Edsger W. , "Predicate calculus: How subtypes should enter the picture", EDW1160, link
    • Dijkstra Edsger W. , "Predicate calculus: Our book’s omission on quantification over scalar subtypes", EDW1184, link
    • Peirce Benjamin, "Linear Associative Algebra", American Journal of Mathematics , 1881, Vol. 4, No. 1 (1881), pp. 97-229 link
    • Peirce Charles Sanders , "On the Algebra of Logic", American Journal of Mathematics , Mar., 1880, Vol. 3, No. 1 (Mar., 1880), pp. 15-57 link
    • Peirce Charles Sanders , "On the Algebra of Logic: A Contribution to the Philosophy of Notation", American Journal of Mathematics , Jan., 1885, Vol. 7, No. 2 (Jan., 1885), pp. 180-196 , link
    • Peirce Charles Sanders , "On the Algebra of Logic [Continued]" , American Journal of Mathematics , Apr., 1885, Vol. 7, No. 3 (Apr., 1885), pp. 197-202 link
    • Sylvester J. J. , "Lectures on the Principles of Universal Algebra", American Journal of Mathematics , 1883 - 1884, Vol. 6, No. 1 (1883 - 1884), pp. 270-286 link

Ontolog

In this trace the propositional calculus linked to the cellular automata rule numbers is dealt with. A significant part of the material concerns the work of Awbrey Jon.

  • Propositional calculus

    • Wikipedia en, "Hilbert system" , (2022) , link
    • Wikipedia en, "List of Hilbert system" , (2022) link
    • Wikipedia en, "Propositional calculus" , (2022) link
    • Wikipedia en, "Syllogism" , (2022) link
    • Burgess John P., "Kripke models.", Saul Kripke (2011), 119-140, link
    • Roberts Don D., "The existential graphs of Charles S. Peirce" , De Gruyter Mouton, 2009 , link
    • Wolfram Stephen, "Statistical mechanics of cellular automata", Reviews of modern physics 55.3, (1983): 601 , link
    • Wolfram Stephen, "Cellular automata as simple self-organizing system" , Caltrech preprint CALT , (1982), pp. 68-938link
    • Zeman Jay J. , "The graphical logic of C. S. Peirce", Ph. D. Dissertation, Department of Philosophy, University of Chicago
    • OpenLogicProject , Github repository, (2022) link
    • OpenLociaProject, "Arithmetization" , rev: e729305 (2022-02-16) link
    • OpenLogicProject, "Arithmetization of syntax", rev: e729305 (2022-02-16) , link
    • Łukasiewicz Jan, "The shortest axiom of the implicational calculus of propositions.", Proceedings of the Royal Irish Academy, Section A: Mathematical and Physical Sciences, Vol. 52, Royal Irish Academy, 1948 , link
    • Wadler Philips , "Proposition as a type",Commun. ACM 58, 12 (December 2015), 75–84, link
    • Nicod Jean, "A Reduction in the number of the Primitive Propositions of Logic", Proceedings of the Cambridge Philosophical Society 19 (1917–1920), 32–41 link
    • Scharle Thomas W., "Axiomatization of propositional calculus with Sheffer functors", Notre Dame Journal of Formal Logic, 6.3, (1965), 209-217, link
    • Sheffer Henry Maurice, "A set of five independent postulates for Boolean algebras, with application to logical constants", Transactions of the American mathematical society, 14.4, (1913), 481-488, link

  • Awbrey Jon's work

    • Awbrey Jon , "Cactus Language", Oeiswiki, visited 2022 link
    • Awbrey Jon , "Logical Graph", Oeiswiki, visited 2022 , link
    • Awbrey Jon , "Propositional Equation Reasoning Systems", Oeiswiki, visited 2022 , link
    • Awbrey Jon , "Exploratory Qualitative Analysis of Sequential Observation Data", Oeiswiki, visited 2022 , link

Laws of form

The syllogism and adjacency matrices are treated in relation to the logic of the first and second order. The concept of relation and function are treated and therefore the quantifiers.

  • laws of form book

    • Bricken Williams , "Boundary logic from the biginning", 2001 link
    • Conrad Leon , "laws of form - laws of logic", link
    • Bertani Mauro , "Difference", 2021, link
    • Etter Tom , "Membership and Identity", Interval Reasearch Corporation, 2006link
    • Etter Tom , "Link Theory: Part I", Interval Reasearch Corporation, 1998 link
    • Etter Tom , "Link Theory: Part II", Interval Reasearch Corporation, 1998 link
    • Etter Tom , "Relational arithmetic revived, Boundary Istitute , 2000, link
    • Floyd Robert W., "Assigning meanings to programs.", Program Verification, Springer, Dordrecht, 1993. 65-81. link
    • Hilbert David & Bernays Paul , "Grundlagen der Mathematik vol 1", Traslation by Mueller Ian [Foundation of mathematic, vol 1], (1934)link
    • Kauffman Louis, Knot Logic: Logical Connection and Topological Connection, (2015), link
    • Kauffman Louis, "Laws of form, an exploration in Mathematic and foundation" , link
    • Kolmogorov A. N. , "Foundations of probability theory", Traslation by Natan Morrison, Chealsy Publishing Company, New York, 1950
    • Mingers John, "Can the Laws of Form Represent Syllogisms?", Cybernetics & Human Knowing, 21.4, (2014), 9-30.link
    • Oeis.org , "Relation composition", visited 2022 , link
    • Oeis.org , "Relation reduction" , visited 2022 , link
    • Oeis.org , "Reletion construction" , visited 2022 , link
    • Rao Anup , "Turing Machine and boolean circuit: Lecture 2", link
    • Rao Anup , "Dianagolization: Lecture 4" , link
    • Corcoran John et al, “String Theory.” The Journal of Symbolic Logic, vol. 39, no. 4, [Association for Symbolic Logic, Cambridge University Press], 1974, pp. 625–37, https://doi.org/10.2307/2272846 , link
    • Dedekind Richard, "Essays on the Theory of Numbers", traslated by Wooster Woodruf Beman, (1901) [eBook 21016]link
    • Solomonoff Ray J., "A formal theory of inductive inference. Part I", Information and control, 7.1, (1964), 1-22. , link
    • Solomonoff Ray J., "A formal theory of inductive inference. Part II", Information and control, 7.2, (1964), 224-254. , link

Conceptual Graph

This trace discusses the functions of action, agent. And the rules for linking the sentences of the text. An important work on subject heading and the birth of theasuri is Derek Austin's Precis.

  • Conceptual Graph

    • Frege Gottlob, "Begriffsschrift, a formula language, modeled upon that of arithmetic, for pure thought", From Frege to Gödel: A source book in mathematical logic 1931, (1879), 1-82 , link
    • Sowa John , "Peirce’s Tutorial on Existential Graphs", VivoMind Intelligence, Inc., link
    • Awbrey Jon , "Logical Graph", Oeis Foundation, visited 2022 , link
    • Awbrey Jon , "Propositional Equation Reasoning Systems", Oeis Foundation, visited 2022 , link
    • Awbrey Jon , "Propositions as_Types of Analogy", Oeis Foundation, visited 2022 , link
    • Awbrey Jon , "Differential propositional calculus Part 1", Oeis Foundation, visited 2022 , , link
    • Feng Justin C., "The poor man’s introduction to tensors", The University of Texas, Physics (2017) , link
    • Awbrey Jon , "Mathematical notes", Oeis Foundation, visited 2022, link
    • Awbrey Jon , "Prospects for Inquiry Driven Systems", Oeis Foundation, visited 2022 , link
    • FOM mailing list , "C.S. Peirce on 'General' and 'Vague'" link
    • Cohen Paul J., "The independence of the continuum hypothesis", Proceedings of the National Academy of Sciences of the United States of America, 50.6, (1963), 1143 , link
    • FOM mailing list , "Some questions regarding irrational numbers" , link
    • Miller Justin, "On the independence of Goodstein’s theorem", University of Arizona, Tucson, AZ, USA, (2001) , link
    • FOM mailing list , "Who was the first to accept undefinable individuals in mathematics?" link
    • McCulloch Warren S., "What is a number, that a man may know it, and a man, that he may know a number", General Semantics Bulletin, 26.27, (1961), 7-18 , link
    • RDF logic mailinglist , "Conceptual Graphs, N3, RDF, Semantic Web" link
    • Paris Jeff, "A mathematical incompleteness in Peano arithmetic", Studies in Logic and the Foundations of Mathematics, Vol. 90, Elsevier, 1977, 1133-1142 , link
    • Mathias Adrian RD, "The ignorance of Bourbaki", Mathematical Intelligencer, 14.3, (1992), 4-13 , link
    • Sowa John , "A Dynamic Theory of Ontology", VivoMind Intelligence Inc. link
    • Sowa John , "From Existential Graphs to Conceptual Graphs", VivoMind Intelligence Inc., link
    • Sowa John , "The Role of Logic and Ontology In Language and Reasoning", VivoMind Intelligence Inc., link
    • Sowa John , "Signs, Processes, and Language Games: Foundations for Ontology", VivoMind Intelligence Inc., link
    • Geurts Bart, "Discourse Representation Theory", Stanford Encyclopedia of Philosophy link

  • Precis

    • Higgins Peter , "the rise and fall of precis as indexing system", 1991link
    • Curwen Anthony G., "A decade of PRECIS, 1974-84", Journal of librarianship, 17.4, (1985), 244-267, link
    • McIlwaine Ia C., "Indexing and the Classification Research Group", Indexer, 23.4, (2003), 204-209, link
    • Petrucciani Alberto , "PRECIS un sistema di indicizzazione in sperimentazione in Italia", L'indicizzazione, Anno 2, n. 1, 1987
    • Petrucciani Alberto, "Le prospettive di lavoro del Gruppo di ricerca sull'indicizzazione per soggetto" ,Bollettino AIB, ISSN 1121-1490, voi. 32 n. 4 (dicembre 1992), p. 419-43
    • Fabbrizzi Andrea , "Guida all'indicizzazione per soggetto", AIB, 2001link
    • Devadason F. J., "Online construction of Alphabetic Classaurus", Pergamon Press, Information Processing and Menagment, 21,1985, vol 1, pag. 11-26, link
    • Chatterjee Amitabha , "Preserved Context Indexing System (PRECIS)", Encyclopedia of Knowledge Organization, 2022, link