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History of logic | A Wisdom Archive on History of logic | | History of logic A selection of articles related to History of logic | |
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History of logic
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| ARTICLES RELATED TO History of logic | | | | | |  History of logic: Encyclopedia II - Mathematical logic - Topics in mathematical logicThe main areas of mathematical logic include model theory, proof theory and recursion theory (often now referred to as computability theory). Axiomatic set theory is sometimes considered too. There are many overlaps with computer science, since many early pioneers in computer science, such as Alan Turing, were mathematicians and logicians.
The study of programming language semantics derives from model ...
See also:Mathematical logic, Mathematical logic - History, Mathematical logic - Topics in mathematical logic, Mathematical logic - Some fundamental results, Mathematical logic - Technical reference, Mathematical logic - First-order languages and structures, Mathematical logic - Terms formulas and sentences, Mathematical logic - Assignment functions, Mathematical logic - Logical satisfaction, Mathematical logic - Logical implication and truth, Mathematical logic - Variable substitution, Mathematical logic - Substitutability Read more here: » Mathematical logic: Encyclopedia II - Mathematical logic - Topics in mathematical logic |
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| | | | | History of logic: Encyclopedia II - Mathematical logic - Technical reference
Mathematical logic - First-order languages and structures.
Definition. A first-order language is a collection of distinct typographical symbols classified as follows:
The equality symbol ; the connectives , ; the universal quantifier and the parentheses , .
A countable set of variable symbols .
A set of constant symbols .
A set of function symbol ...
See also:Mathematical logic, Mathematical logic - History, Mathematical logic - Topics in mathematical logic, Mathematical logic - Some fundamental results, Mathematical logic - Technical reference, Mathematical logic - First-order languages and structures, Mathematical logic - Terms formulas and sentences, Mathematical logic - Assignment functions, Mathematical logic - Logical satisfaction, Mathematical logic - Logical implication and truth, Mathematical logic - Variable substitution, Mathematical logic - Substitutability Read more here: » Mathematical logic: Encyclopedia II - Mathematical logic - Technical reference |
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| | | | | | | | History of logic: Encyclopedia II - Programmable logic controller - PID loops PLCs may include logic for single-variable generic industrial feedback loop, a "proportional, integral, derivative" loop, or "PID controller."
A PID loop is the standard solution to many industrial process control processes that require proportional, integral("improve errors") or derivative ("faster response") control techniques. A PID loop could be used to control the temperature of a manufacturing process, for example.
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See also:Programmable logic controller, Programmable logic controller - Digital vs. Analog Signals, Programmable logic controller - Example: Digital vs Analog, Programmable logic controller - How PLC's package I/O capabilities: Modular Rack P2P, Programmable logic controller - Programming, Programmable logic controller - PID loops, Programmable logic controller - User interface, Programmable logic controller - History Read more here: » Programmable logic controller: Encyclopedia II - Programmable logic controller - PID loops |
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| | | | | History of logic: Encyclopedia II - Programmable logic controller - PID loops PLCs may include logic for single-variable generic industrial feedback loop, a "proportional, integral, derivative" loop, or "PID controller."
A PID loop is the standard solution to many industrial process control processes that require proportional, integral("improve errors") or derivative (" faster response")" control techniques .. A PID loop could be used to control the pH level of water in a swimming pool.
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See also:Programmable logic controller, Programmable logic controller - Digital vs. Analog Signals, Programmable logic controller - Example: Digital vs Analog, Programmable logic controller - How PLC's package I/O capabilities: Modular Rack P2P, Programmable logic controller - Programming, Programmable logic controller - PID loops, Programmable logic controller - User interface, Programmable logic controller - History Read more here: » Programmable logic controller: Encyclopedia II - Programmable logic controller - PID loops |
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| | | | | | History of logic: Encyclopedia II - Transistor-transistor logic - Theory TTL integrated circuits are examples of small-scale to medium-scale integration. Each "chip" contains the equivalent of a few dozen to a few hundred transistors, contrasting with early very-large-scale integration (VLSI) devices that had the equivalent of up to 10,000 transistors, and modern microprocessors that are equivalent to tens of millions of transistors.
The fundamental switching action of a TTL gate is based on a multiple-emitter input transistor. This replaces the multiple input diodes of the earlier DTL logic, with improved ...
See also:Transistor-transistor logic, Transistor-transistor logic - History, Transistor-transistor logic - Functions, Transistor-transistor logic - Theory, Transistor-transistor logic - Comparison with other logic families, Transistor-transistor logic - Sub-types, Transistor-transistor logic - Applications Read more here: » Transistor-transistor logic: Encyclopedia II - Transistor-transistor logic - Theory |
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| | | | | History of logic: Encyclopedia II - Programmable logic controller - How PLC's package I/O capabilities: Modular Rack P2P Modular PLCs have a limited number of connections built in for inputs and outputs. Typically, expansions are available if the base model does not have enough I/O.
Rack-style PLCs have processor modules with separate [optional] I/O modules, which may occupy many racks. These often have thousands of discrete and analog inputs and outputs. Often a special high speed serial I/O link is used so that racks can be remotely mounted from the processor, reducing the wiring costs for large plants.
PLCs used in larger I/O systems may have ...
See also:Programmable logic controller, Programmable logic controller - Digital vs. Analog Signals, Programmable logic controller - Example: Digital vs Analog, Programmable logic controller - How PLC's package I/O capabilities: Modular Rack P2P, Programmable logic controller - Programming, Programmable logic controller - PID loops, Programmable logic controller - User interface, Programmable logic controller - History Read more here: » Programmable logic controller: Encyclopedia II - Programmable logic controller - How PLC's package I/O capabilities: Modular Rack P2P |
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| | | | | | History of logic: Encyclopedia II - Programmable logic controller - Digital vs. Analog Signals Digital or Discrete signals behave as switches, yielding simply an On or Off signal (1 or 0, True or False, respectively). Pushbuttons, limit switches, and photo-eyes are examples of devices providing a discrete signal. Discrete signals are judged using either voltage or current, where a specific range is denominated as On and another as Off. A PLC might use 24VDC I/O, with values above 22VDC representing On and values below 2VDC representing Off. Initially, PLCs had only discrete I/O. Current inputs are less sensitive to electr ...
See also:Programmable logic controller, Programmable logic controller - Digital vs. Analog Signals, Programmable logic controller - Example: Digital vs Analog, Programmable logic controller - How PLC's package I/O capabilities: Modular Rack P2P, Programmable logic controller - Programming, Programmable logic controller - PID loops, Programmable logic controller - User interface, Programmable logic controller - History Read more here: » Programmable logic controller: Encyclopedia II - Programmable logic controller - Digital vs. Analog Signals |
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| | | | | History of logic: Encyclopedia II - Programmable logic controller - Digital vs. Analog Signals Digital or Discrete signals behave as switches, yielding simply an On or Off signal (1 or 0, True or False, respectively). Pushbuttons, limit switches, and photo-eyes are examples of devices providing a discrete signal. Discrete signals are judged using either voltage or current, where a specific range is denominated as On and another as Off. A PLC might use 24VDC I/O, with values above 22VDC representing On and values below 2VDC representing Off. Initially, PLCs had only discrete I/O. Current inputs are less sensitive to electrical noise (i ...
See also:Programmable logic controller, Programmable logic controller - Digital vs. Analog Signals, Programmable logic controller - Example: Digital vs Analog, Programmable logic controller - How PLC's package I/O capabilities: Modular Rack P2P, Programmable logic controller - Programming, Programmable logic controller - PID loops, Programmable logic controller - User interface, Programmable logic controller - History Read more here: » Programmable logic controller: Encyclopedia II - Programmable logic controller - Digital vs. Analog Signals |
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| | | | | | | History of logic: Encyclopedia II - Arithmetic logic unit - ALU operations Most ALUs will perform the following operations:
integer arithmetic operations (addition, subtraction, multiplication)
bitwise logic operations (and, not, or, xor)
bit-shifting operations (shifting or rotating a word by a specified number of bits to the left or right, with or without sign extension)
Many standard ALUs do not handle integer division or any floating point operations since they can be emulated through indirect means; however, several algorithms do exist for implementing division in h ...
See also:Arithmetic logic unit, Arithmetic logic unit - History, Arithmetic logic unit - ALU operations, Arithmetic logic unit - Inputs and outputs, Arithmetic logic unit - Notes Read more here: » Arithmetic logic unit: Encyclopedia II - Arithmetic logic unit - ALU operations |
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| | | | | | History of logic: Encyclopedia II - Abductive reasoning - History of the concept The philosopher Charles Peirce introduced abduction into modern logic. In his works before 1900, he mostly uses the term to mean the use of a known rule to explain an observation, e.g., “if it rains the grass is wet” is a known rule used to explain that the grass is wet.
He later used the term to mean creating new rules to explain new observations, emphasising that abduction is the only logical process that actually creates anything new. Namely, he described the process of science as a combination of abduction, deduction and implicati ...
See also:Abductive reasoning, Abductive reasoning - Logic-based Abduction, Abductive reasoning - Set-Cover Abduction, Abductive reasoning - History of the concept, Abductive reasoning - Applications Read more here: » Abductive reasoning: Encyclopedia II - Abductive reasoning - History of the concept |
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| | | | | History of logic: Encyclopedia II - Epimenides paradox - History The Epimenides paradox, as a problem in logic, appears to have a relatively recent origin, although the statement "Cretans, always liars" has quite a history itself.
Epimenides was a philosopher and religious prophet who, against the general sentiment of Crete, proposed that Zeus was immortal. As he wrote in his poem Cretica,
They fashioned a tomb for thee, O holy and high one-
The Cretans, always liars, evil beasts, idle bellies!
But thou art not dead: thou livest and abidest forever,
For in th ...
See also:Epimenides paradox, Epimenides paradox - Logical analysis, Epimenides paradox - History, Epimenides paradox - Sources Read more here: » Epimenides paradox: Encyclopedia II - Epimenides paradox - History |
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