Logical machine

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"Logical Piano" by William Stanley Jevons from 1869

As a logical machines are or were - like the abacus - Refers to devices that treat the logical tasks and solve.

Ideally, logical machines should examine arguments for their validity; In practice, logical machines more often achieve this goal indirectly by determining which conclusions can be drawn from given premises . In concrete terms, machines were initially built that directly or indirectly check the validity of syllogisms , but later mainly those that automate the mechanical activities of propositional logic , for example the setting up of truth tables or the formation of normal forms .

Mechanical logical machines

The idea of ​​the logical machine is often attributed to the Mallorcan philosopher, logician and Franciscan theologian Ramon Llull (approx. 1232-1316), who proposed various slide rules or disk-like devices for the formation of concept combinations as early as the end of the 13th century . Mechanically on a similar level, but more systematic in terms of the logical basis, is the Stanhope demonstrator by Charles (the third Earl) Stanhope at the end of the 18th century . The first mechanical machine, however, is considered to be the “logical piano”, so called because of its keyboard-like keyboard, which was constructed in 1869, significantly later, by William Stanley Jevons .

Most earlier logical machines used conceptual logic , in which the variables represent concepts . Is z. B. A for the term “pig” and B for the term “pink”, then sentences like “Everything A is also B” can be formed from these terms. H. Everything that falls under the term “pig” also falls under the term “pink” - in short: “All pigs are pink.” Jevons uses lowercase letters to express the “negation” of a term - “a” means in our example the term “not pig”, which includes all things that do not come under the term “pig” (A).

With the Jevons machine, any number of conceptual logical sentences can be entered as premises. The machine mechanically eliminates all combinations of terms that are inconsistent with the premises entered. Is z. B. an “All A are B”, then the machine excludes the combination “Ab” (“Pig” and “Not pink”). In the end, only those term combinations remain that are consistent with all of the entered premises. The machine displays these combinations - it is up to the user to draw conclusions that are of interest to her from this information.

Although Jevon's machine and its underlying logical system are of a conceptual logic nature, the machine can already be applied to propositional logic questions ( propositional logic ) if the uppercase letters are interpreted as sentence letters ( statement letters ) and the lowercase letters as their negation.

Allan Marquand , who had already developed a mechanical logic machine between 1874 and 1881 - a more precise dating is probably not possible - suggested in 1885 that an electrical version of Jevon's machine be built. Although it is unknown or even questionable whether he was able to realize his electrical machine, he seems to have been the first to have the idea of ​​realizing logical operations through electrical circuits: Alonzo Church found the circuit diagram of this machine under the estate of Marquand . Weinhart points out, however, that Jevons received the suggestion for this from his teacher, none other than the American philosopher Charles Sanders Peirce . Ketner is even of the opinion that this circuit diagram could actually have been designed by Peirce himself. He bases this assumption, among other things, on the visual similarities between the inscriptions on the circuit diagram and Peircen's handwriting. Although Ketner's article was published in 1984 and handwriting comparisons are a common forensic practice, this similarity does not seem to have been scientifically investigated and Ketner's conjecture has not been proven or disproved.

Electrical logical machines

Benjamin Burack built the first reliably realized electrical logical machine in 1936. In terms of its nature, Burack's machine is also of a conceptual logic, although it only covers the classical syllogisms in the sense of Aristotle , i.e. arguments with exactly two premises and one conclusion.

While the early logical machines were still dominated by the conceptual logic that had dominated since antiquity, in the 20th century - especially in the late 1940s and with the spread of electrical / electronic circuits - there was a constant shift towards propositional logic. The first logical machine with a logical proposition seen or planned by its designer himself was, however, still a mechanical device, the machine submitted for patenting in 1910 by Charles P. R. Macaulay. Functionally, it also works in such a way that for each sentence entered it excludes the possibilities that are incompatible with this sentence and finally displays the remaining variants.

A steady development of propositional logic machines began in 1947: After attending a lecture with Willard Van Orman Quine, Theodore A. Kalin and William Burkhart designed an electrical machine that was supposed to relieve them of the manual setting up of truth tables. The device by Kalin and Burkhart is already characteristic of most of their following logical machines: For a given statement with up to twelve different proposition variables, it calculates the truth value for the evaluation among all possible assignments of truth values ​​to the variables. In addition to setting up a complete table, the device was also able to determine the assignments under which the complex statement is fulfilled or refuted. The search for the occupancy is, however, purely exhaustive (" brute force "), i. That is, it runs through all possible assignments as when setting up a truth table and stops as soon as it encounters an assignment that is affirmative or negative for the sentence. It takes 38 minutes to calculate a complete truth table for a statement in twelve variables - the limit of the machine.

Of the machines that followed, only one is fundamentally different: The "Feedback Logical Computor (sic!)", Which was created in 1951 as one of several machines at the English manufacturer Ferranti . This machine is designed to fulfill a number of statements, i. H. to search for an assignment of truth values ​​to the sentence letters occurring in the statements under which all these statements are true. In contrast to all other known logical machines, the Feedback Logical Computor does not work “brute force”, in that it runs through all possible truth value assignments in an orderly order until it has found a verifying one; rather, he tries to find the most skilful way possible through the set of all possible truth value assignments. The procedure is described in detail in the original text by McCallum and Smith.

Most propositional machines are entered in Peano-Russell notation, an infix notation , or a variation of it adapted to the machine: rotary switches in Kalin and Burkhart, patch cords in Johann Weipoltshammer's “ logistic relay calculator ”. However, it was recognized relatively early that other spellings, such as the Polish notation, are better suited for machine problem solving (whether in hardware or software) . The best-known machines that use Polish notation are the Burroughs Truth Function Evaluator, built in 1956 by William Miehle at Burroughs , and the Stanislaus, designed in 1950–1951 by Friedrich Ludwig Bauer in Munich and completed in 1956. In terms of operation, Bauers is superior to Stanislaus because the statement to be examined can be entered on a comfortable keyboard, whereas patch cords have to be used with the Burroughs device. Burroughs' device allows up to ten variables, while Stanislaus is limited to five and only allows relatively short formulas of up to eleven characters in length; To do this, Stanislaus checks whether the statement entered is syntactically well-formed, and rejects it otherwise. Functionally, both machines fall under the same category: They calculate all truth value assignments in a fixed order and stop when a certain result is reached if desired.

The 1950s marked both the climax and the end of the history of logical machines. As a rule, this end is justified with the availability of programmable computers, because all tasks that are hardwired to a logical machine can be solved in software on them. Although this explanation is factually correct, it cannot be complete if one realizes that the same argument applies to the calculating machine , which, however, was by no means extinct at that time, but on the contrary only had its heyday ahead of it and in the form of the modern pocket calculator is still represented today. Rather, it seems to be the case that the need to solve logical problems of the kind that could be solved by logical machines for a long time is only very small, or that where there is a need to solve such problems (simplification of Statements e.g. in circuit design) the performance of logical machines realizable with contemporary technology was by far not sufficient.

See also

literature

Secondary literature

  • Edmund C. Berkeley: Giant Brains or Machines that Think , New York: John Wiley and Sons 1949 (7th ed. 1963)
  • BV Bowden: Faster Than Thought , London: Sir Isaac Pitman 1953
  • Martin Gardner : Logic Machines and Diagrams , New York: McGraw-Hill 1958
  • Karl Weinhart (ed.): Computer science and automation. Guide through the exhibition , Munich: Deutsches Museum 1990 ISBN 3-924183-14-7
  • William Kneale, Martha Kneale: The Development of Logic , Oxford: Oxford University Press 1962 (1984) ISBN 0-19-824773-7
  • Kenneth Lane Ketner, AF Stewart: The Early History of Computer Design: CS Peirce and Marquand's Logical Machines, Princeton University Library Chronicle 1984 XLV 3, pp. 187-224
  • Christian Gottschall: Logical notations and their processing on electronic computers from a theoretical, practical and historical point of view (diploma thesis), Vienna: 2005

swell

  • B. Burack, An Electrical Logic Machine , Science, Vol. 109, June 17, 1949, p. 610
  • R. Harley, The Stanhope Demonstrator , Mind, Vol. 4, April, 1879
  • William Stanley Jevons: On the Mechanical Performance of Logical Inference , Philosophical Transactions of the Royal Society, Vol. 160, 1870, pp. 497-518
  • Charles P. R. Macaulay: U.S. Patent 1,079,504, dated November 25, 1913
  • Wolfe Mays, DG Prinz: A Relay Machine for the Demonstration of Symbolic Logic , Nature, Vol. 165, February 4, 1950, p. 197
  • Wolfe Mays: The First Circuit for an Electrical Logic-Machine , Science, New Series, Vol. 118, No. 3062, September 4, 1953, page 281 ff.
  • DM McCallum, JB Smith: Feedback Logical Computors (sic!) , Electronic Engineering, Vol. 23, December 1951, pp. 458-461
  • DM McCallum, JB Smith: Mechanized Reasoning. Logical Computers and Their Design , Electronic Engineering, April 1951, pages 126-133
  • William Miehle: Burroughs Truth Function Evaluator , Journal of the ACM (JACM), Vol. 4, Issue 2, April 1957, pp 189-192
  • Johann Weipoltshammer: The logistic relay calculating machine LRR1 , Vienna: 1954 (diploma thesis)
  • FL Bauer: The Formula-Controlled Logical Computer "Stanislaus" , Math. Tabl. Aids Comp. 14 (1960) pp. 64-67.

Web links

Individual evidence

  1. ^ Martin Gardner: Logic Machines and Diagrams , New York: McGraw-Hill 1958, pp. 9ff.
  2. ^ R. Harley, The Stanhope Demonstrator , Mind, Vol. 4, April, 1879
  3. ^ Martin Gardner: Logic Machines and Diagrams , New York: McGraw-Hill 1958, pp. 80ff.
  4. ^ William Kneale , Martha Kneale : The Development of Logic , Oxford: Oxford University Press 1962, p. 421
  5. ^ William Stanley Jevons: On the Mechanical Performance of Logical Inference , Philosophical Transactions of the Royal Society, Vol. 160, 1870, pp. 497-518
  6. ^ Martin Gardner: Logic Machines and Diagrams , New York: McGraw-Hill 1958, pp. 95ff.
  7. ↑ Wolfe Mays: The First Circuit for an Electrical Logic-Machine , Science, New Series, Vol. 118, No. 3062, September 4, 1953, page 281ff.
  8. ^ Karl Weinhart (ed.): Computer science and automation. Guide through the exhibition , Munich: Deutsches Museum 1990, page 113
  9. ↑ Kenneth Lane Ketner, AF Stewart: The Early History of Computer Design: CS Peirce and Marquand's Logical Machines, Princeton University Library Chronicle 1984 XLV 3, pp. 187-224
  10. ↑ Martin Gardner: Logic Machines and Diagrams , New York: McGraw-Hill 1958; B. Burack, An Electrical Logic Machine , Science, Vol. 109, June 17, 1949, p. 610
  11. ^ Martin Gardner: Logic Machines and Diagrams , New York: McGraw-Hill 1958, p. 113
  12. ^ Martin Gardner: Logic Machines and Diagrams , New York: McGraw-Hill 1958, p. 128
  13. ↑ Edmund C. Berkeley: Giant Brains or Machines that Think , New York: John Wiley and Sons 1949 (7th ed. 1963), pp. 144ff.
  14. ^ DM McCallum, JB Smith: Feedback Logical Computors (sic!) , Electronic Engineering, Vol. 23, December 1951, pp. 458-461
  15. ^ Karl Weinhart (ed.): Computer science and automation. Guide through the exhibition , Munich: Deutsches Museum 1990, page 114