Introduction to Logical Access Control
1. Anil Nerode of logical access controlAnil Nerode (born 1932) is an American mathematician. He received his undergraduate education and a Ph.D. in mathematics from the University of Chicago, the latter under the directions of Saunders Mac Lane. He enrolled in the Hutchins College at the University of Chicago in 1947 at the age of 15, and received his Ph.D. in 1956. His Ph.D. thesis was on an algebraic abstract formulation of substitution in many-sorted free algebras and its relation to equational definitions of the partial recursive functions.While in graduate school, beginning in 1954, he worked at Professor Walter Bartky's Institute for Air Weapons Research, which did classified work for the US Air Force. He continued to work there following the completion of his Ph.D., from 1956 to 1957. In the summer of 1957 he attended the Cornell NSF Summer 1957 Institute in Logic. In 1958 to 1959 he went to the Institute for Advanced Study in Princeton, New Jersey, where he worked with Kurt Gdel. He also did post-graduate work at University of California, Berkeley.When in 1959 he got an unsolicited offer of a faculty position at Cornell University, he accepted, in part because on his previous visit to the campus he had thought "it was the prettiest place I'd ever seen". Nerode is Goldwin Smith Professor of Mathematics at Cornell, having been named to that chair in 1991. His interests are in mathematical logic, the theory of automata, computability and complexity theory, the calculus of variations, and distributed systems. With John Myhill, Nerode proved the MyhillNerode theorem specifying necessary and sufficient conditions for a formal language to be regular.The academic year 201920 saw Nerode's 60th year as an active faculty member at Cornell, which the university said was its longest such tenure ever.Nerode is an Editorial Board member of the journals Annals of Mathematics and Artificial Intelligence, Mathematical and Computer Modelling, Documenta Mathematica and others.In 2012 he became a fellow of the American Mathematical Society.------2. Publications of logical access controlHolland authored a number of books about complex adaptive systems, including:Adaptation in Natural and Artificial Systems (1975, MIT Press)Hidden Order: How Adaptation Builds Complexity (1995, Basic Books)Emergence: From Chaos to Order (1998, Basic Books)Signals and Boundaries: Building Blocks for Complex Adaptive Systems (2012, MIT Press)Complexity: A Very Short Introduction (2014, Oxford University Press)Articles, a selection:"A universal computer capable of executing an arbitrary number of subprograms simultaneously", in: Proc. Eastern Joint Comp. Conf. (1959), pp.108112"Iterative circuit computers", in: Proc. Western Joint Comp. Conf. (1960), pp.259265"Outline for a logical theory of adaptive systems", in: JACM, Vol 9 (1962), no. 3, pp.279314"Hierarchical descriptions, universal spaces, and adaptive systems", in: Arthur W. Burks, editor. Essays on Cellular Automata (1970). University of Illinois Press"Using Classifier Systems to Study Adaptive Nonlinear Networks", in: Daniel L. Stein, editor. Lectures in the Sciences of Complexity (1989). Addison Wesley"Concerning the Emergence of Tag-Mediated Lookahead in Classifier Systems", in: Stephanie Forrest, editor. Emergent Computation: self-organizing, collective, and cooperative phenomena in natural and computing networks (1990). MIT Press"The Royal Road for Genetic Algorithms: Fitness Landscapes and GA Performance", in: Francisco J. Varela, Paul Bourgine, editors. Toward a Practice of Autonomous Systems: proceedings of the first European conference on Artificial Life (1992). MIT Press"Echoing Emergence: objectives, rough definitions, and speculations for ECHO-class models", in: George A. Cowan, David Pines, David Meltzer, editors. Complexity: metaphors, models, and reality (1994), Addison-Wesley"Can There Be A Unified Theory of Complex Adaptive Systems?", in: Harold J. Morowitz, Jerome L. Singer, editors. The Mind, The Brain, and Complex Adaptive Systems (1995). Addison-Wesley"Board Games", in: John Brockman, editor. The Greatest Inventions of the Past 2000 Years (2000). Phoenix"What is to Come and How to Predict It.", in: John Brockman, editor. The Next Fifty Years: science in the first half of the twenty-first century (2002). Weidenfeld & Nicolson------3. Major ideas of logical access controlThe imagination of reason or systematic imagination in philosophy. This, in Unger's thinking, is a basic tool in any philosophical enquiry into the world of being into reality beyond experience. Speaking of the latter, Unger writes: "The matter of the world as a whole is not an empirical object, although it is unquestionable real" ('The Living and the Divine' Ch.1). In this essay Unger explains how, in order to apprehend that reality and other, like concepts, such as being or consciousness, we require the imagination of reason. Not unlike astronomers who research heavenly constellations of which they have only a partial direct experience and who then need to complement their experience by using a reasoning imagination to access the aspect that is beyond their direct experience.Myth. The imagination of reason is also in evidence in Unger's views on the function of myth in religion. His book, 'Wirklichkeit, Mythos, Erkenntnis' ('Reality, Myth and Cognition') is an early work, yet his preoccupation with myth is still seen in a later essay: 'The Natural Order of Miracles', the English version of which appeared in The Journal of Jewish Thought and Philosophy. Here Unger writes: "A genuine myth handles one unit: religion, science, politics, social every day life and extends and is constrained by the concepts of order and apprehension of natural experience. This is the source of its rational aspect. As distinct from this, the poetic myth is either pure art or, at least, half religion, half art".Unger's views on Judaism are wide ranging. He notes with regret the gradual shrinking of Jewish culture to the 'mere religion' that it is today and suggests that, in order to revitalise Judaism, it must once again inspire and underpin our society. This does not mean that there is such a thing as 'Jewish' science or 'Jewish' technology. But Judaism may have views in other areas, in philosophy, sociology or politics, on topics such as Immortality or a specific Jewish ethical stand in political matters (cf. 'A Restatement of Judaism' in the journal Shofar).------4. Influence of logical access controlSchrder's influence on the early development of the predicate calculus, mainly by popularising C.S. Peirce's work on quantification, is at least as great as that of Frege or Peano. For an example of the influence of Schrder's work on English-speaking logicians of the early 20th century, see Clarence Irving Lewis (1918). The relational concepts that pervade Principia Mathematica are very much owed to the Vorlesungen, cited in Principia's Preface and in Bertrand Russell's Principles of Mathematics.Frege (1960) dismissed Schrder's work, and admiration for Frege's pioneering role has dominated subsequent historical discussion. Contrasting Frege with Schrder and C.S. Peirce, however, Hilary Putnam (1982) writes:When I started to trace the later development of logic, the first thing I did was to look at Schrder's Vorlesungen ber die Algebra der Logik, ...whose third volume is on the logic of relations (Algebra und Logik der Relative, 1895). The three volumes immediately became the best-known advanced logic text, and embody what any mathematician interested in the study of logic should have known, or at least have been acquainted with, in the 1890s.While, to my knowledge, no one except Frege ever published a single paper in Frege's notation, many famous logicians adopted Peirce-Schrder notation, and famous results and systems were published in it. Lwenheim stated and proved the Lwenheim theorem (later reproved and strengthened by Thoralf Skolem, whose name became attached to it together with Lwenheim's) in Peircian notation. In fact, there is no reference in Lwenheim's paper to any logic other than Peirce's. To cite another example, Zermelo presented his axioms for set theory in Peirce-Schrder notation, and not, as one might have expected, in Russell-Whitehead notation.One can sum up these simple facts (which anyone can quickly verify) as follows: Frege certainly discovered the quantifier first (four years before Oscar Howard Mitchell, going by publication dates, which are all we have as far as I know). But Leif Ericson probably discovered America "first" (forgive me for not counting the native Americans, who of course really discovered it "first"). If the effective discoverer, from a European point of view, is Christopher Columbus, that is because he discovered it so that it stayed discovered (by Europeans, that is), so that the discovery became known (by Europeans). Frege did "discover" the quantifier in the sense of having the rightful claim to priority; but Peirce and his students discovered it in the effective sense. The fact is that until Russell appreciated what he had done, Frege was relatively obscure, and it was Peirce who seems to have been known to the entire world logical community. How many of the people who think that "Frege invented logic" are aware of these facts?------5. Work of logical access controlSchrder's early work on formal algebra and logic was written in ignorance of the British logicians George Boole and Augustus De Morgan. Instead, his sources were texts by Ohm, Hankel, Hermann Grassmann, and Robert Grassmann (Peckhaus 1997: 233296). In 1873, Schrder learned of Boole's and De Morgan's work on logic. To their work he subsequently added several important concepts due to Charles Sanders Peirce, including subsumption and quantification.Schrder also made original contributions to algebra, set theory, lattice theory, ordered sets and ordinal numbers. Along with Georg Cantor, he codiscovered the CantorBernsteinSchrder theorem, although Schrder's proof (1898) is flawed. Felix Bernstein (18781956) subsequently corrected the proof as part of his Ph.D. dissertation.Schrder (1877) was a concise exposition of Boole's ideas on algebra and logic, which did much to introduce Boole's work to continental readers. The influence of the Grassmanns, especially Robert's little-known Formenlehre, is clear. Unlike Boole, Schrder fully appreciated duality. John Venn and Christine Ladd-Franklin both warmly cited this short book of Schrder's, and Charles Sanders Peirce used it as a text while teaching at Johns Hopkins University.Schrder's masterwork, his Vorlesungen ber die Algebra der Logik, was published in three volumes between 1890 and 1905, at the author's expense. Vol. 2 is in two parts, the second published posthumously, edited by Eugen Mller. The Vorlesungen was a comprehensive and scholarly survey of "algebraic" (today we would say "symbolic") logic up to the end of the 19th century, one that had a considerable influence on the emergence of mathematical logic in the 20th century. The Vorlesungen is a prolix affair, only a small part of which has been translated into English. That part, along with an extended discussion of the entire Vorlesungen, is in Brady (2000). Also see Grattan-Guinness (2000: 15976).Schrder said his aim was:...to design logic as a calculating discipline, especially to give access to the exact handling of relative concepts, and, from then on, by emancipation from the routine claims of natural language, to withdraw any fertile soil from "clich" in the field of philosophy as well. This should prepare the ground for a scientific universal language that looks more like a sign language than like a sound language.