Logical machine
As a logical machines are or were - Refers to devices, handle and solve logical tasks - similar to the computing machine.
Ideally, examine arguments to their logical validity machines; in practice reach logical machines that goal more often indirectly, by identifying, what conclusions can be drawn from given premises at all. Machines that directly or indirectly verify the validity of syllogisms, but later especially those that automate the mechanical activities of propositional logic, such as the setting up of truth tables or the formation of normal forms were built Concretely first.
Mechanical logical machines
The idea of the logical machine is often attributed to Ramon Llull, who suggested various slide rule or mathematical calculating disk-like devices to form combinations of terms at the end of the 13th century. Mechanically similar to step, but of the logical foundations of systematic ago is the end of the 18th century, the Stanhope Demonstrator of Charles ( the third Earl ) Stanhope. As a first mechanical machine applies, however, the "Logical Piano", named for its piano keys keyboard similar to the 1869, so much later, designed by William Stanley Jevons.
Most previous logical machines work by the term logic, in which the variables are terms. If, for example, A for the term " pig" and B for the term " pink ", so sets can be formed from these terms such as "All A is B", that is, everything under the term " pig " falls, also falls under the term " pink " - in short, " All pigs are pink " Jevons used lowercase letters in order to" express " a term - " negation of a " thus means in our example, the term" non- pork ", under the. all things fall, do not fall (A) the term " pig".
In the machine of Jevons, any number of conceptual logical propositions enter as premises. The machine eliminates mechanical means all combinations of terms that are inconsistent with the premises entered. Are you, for example, a " All A are B", then closes the machine from the combination of " Down" ( "pig" and " not pink "). So finally remain only those combinations of terms that are consistent with all the input assumptions. The machine displays this combination - it is up to the users individual to draw from this information for them interesting conclusions.
Although Jevons machine and its underlying logical system are conceptual logical in nature, the machine can be already on propositional problems ( propositional logic ) apply if one interprets the uppercase set of characters ( statement letters) and lower case letters as its negation.
Allan Marquand, who already in the period 1874-1881 - a more precise dating is probably not possible - had developed a mechanical logical machine, suggested in 1885 planning to build an electric version of Jevons machine. While it is unknown or even questionable whether he could realize his electrical machine, but the idea to implement logical operations by electrical circuits, he seems to be the first to have had: Under the estate Marquand Alonzo Church found the wiring diagram of this machine. Wine Hart points out, however, that Jevons the suggestion to do so by his teacher, no one had received less than the American philosopher Charles Sanders Peirce. Ketner even of the opinion that this diagram could have been designed in truth Peirce himself. This conjecture he relies also on visual similarity of the labeling of the circuit diagram to Peircens handwriting. Although Ketners article has already been published in 1984 and handwriting comparisons are a common forensic practice, this similarity seems to have been scientifically studied to date, and is Ketners guess until today neither proved nor disproved.
Electrical logical machines
The first realized logical backed electric machine built Benjamin Burack in 1936. Thing after Buracks The machine is also understood logical in nature, however, they only classical syllogisms in the sense of Aristotle covers, so arguments with exactly two premises and a conclusion.
Were the early logical machines still dominated by the dominant since ancient term logic, happened in the 20th century - especially in the late 1940s, and with the spread of electrical / electronic circuits - a steady shift to propositional logic. The first logical machine of its designer himself viewed one or planned propositional terms, however, was still a mechanical device, which in 1910 filed for a patent machine of Charles P. R. Macaulay. Functional works too, so that it excludes not agree with this options for each input sentence, and finally displays the remaining variants.
A steady development of logical statements machines began in 1947 when Theodore A. Kalin and William Burkhart designed after attending a lecture at Willard Van Orman Quine, an electrical machine, which should relieve them of the manual setting up of truth tables. The device of Kalin and Burkhart is already characteristic of most of their following logical machines: It is calculated for a given statement with up to twelve different propositional variables the truth value for the evaluation of all possible assignments of truth values to the variables. In addition to setting up a complete table the device could also determine the assignments under which the complex statement is satisfied or refuted. The search for the assignments, however, is purely exhaustively ( " Brute Force " ), that is, it goes through as when setting up a truth table all possible assignments and stops when it encounters an affirmative or negative sentence assignment. For the through calculation of a complete truth table for a statement in twelve variables - the limit of the machine - it required 38 minutes.
From the resulting in downstream equipment fundamentally raises only one from: The resulting 1951 as one of several machines with the English manufacturer Ferranti " Feedback Logical Computor (sic) " This machine is designed for the fulfillment of a set of statements, ie. to find an assignment of truth values to the set of letters occurring in the statements, under which all of these statements are true. In contrast to all other known logic machines has become the center Logical Computor does not work "brute force " by all possible truth value assignments by running in an orderly fashion until he has found a verified; Rather, he tries to go a skillful way possible by the set of all possible truth value assignments. The procedure is described in detail in the original text of McCallum and Smith.
On most machines, the propositional input into Peano -Russell notation, one infix notation, or a form adapted to the machine variation is which: rotary switch at Kalin and Burkhart, patch cords about Johann Weipoltshammers " logistic Relais calculating machine ". Relatively early on it was recognized, however, that for automatic problem solving (whether in hardware or software), other spellings such as the Polish notation are better. The well-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 Munich from 1950 to 1951 by Friedrich Ludwig Bauer and completed in 1956. From the Operation ago Bauers Stanislaus is superior because the statement to be examined on a comfortable keyboard input while patch cords must be used when Burroughs device. However, the device of Burroughs allows up to ten variables, while the Stanislaus is limited to the five and only relatively short formulas of up to eleven characters allowed; it checks Stanislaus, whether the entered statement is syntactically well-formed, and rejects it otherwise. Functionally, both machines fall under the same category: you expect in a fixed order all truth value assignments through and keep on wishing upon reaching a certain result to.
The 1950s mark the culmination alike as the end of history logical machines. In general, this end is justified by the availability of programmable computer because let this all the tasks that are hard-wired to a logic machine, solve in software. This statement is indeed accurate, but can not be complete if one bears in mind that the same argument were correct on the calculator, but which is extinct at this time, not at all, but on the contrary only had their heyday before and in the form of is represented modern pocket calculator today. Rather, it seems to be such that the need for the solution of logical problems of this kind as they could be solved for a long time of logical machines, is only very small, or that where demand for the solution of such tasks is (simplification of statements, for example, circuit design ) the performance of contemporary art realizable logical machine was far from sufficient.