Encyclopedia - History Of Logic: Encyclopedia Ii - History Of Logic - Traditional Logic
"Traditional Logic" generally means the textbook tradition that begins with Antoine Arnauld and Nicole's Logic, or the Art of Thinking, b...   » Read the article

Encyclopedia - History Of Logic: Encyclopedia Ii - History Of Logic - Logic In Greece
In Greece, two main competing logical traditions emerged. Stoic logic traced its roots back to Euclid of Megara, a pupil of Socrates, and...   » Read the article

Encyclopedia - History Of Logic: Encyclopedia Ii - History Of Logic - Medieval Logic
"Medieval Logic" (also known as "Scholastic Logic") generally means the form of Aristotelian logic developed in medieval Occident through...   » Read the article

Encyclopedia - Logic Synthesis: Encyclopedia Ii - Logic Synthesis - History Of Logic Synthesis
The roots of logic synthesis can be traced to the treatment of logic by George Boole (1815 to 1864), in what is now termed Boolean algebr...   » Read the article

Encyclopedia - Logic: Encyclopedia - Logic
Logic, from Classical Greek λόγος (logos), originally meaning the word, or what is spoken, (but coming to mean thought or reason) is...   » Read the article

Encyclopedia - Logic Pro: Encyclopedia Ii - Logic Pro - History Of The Logic Sequencer
Logic started life as the MIDI sequencer C-Lab Creator on the Atari ST platform in the 1980s (the ST was an early favorite among MIDI use...   » Read the article

Encyclopedia - Arithmetic Logic Unit: Encyclopedia - Arithmetic Logic Unit
The arithmetic logic unit/arithmetic-logic unit (ALU) of a computer's CPU is a part of the execution unit, a core component of all CPUs. ...   » Read the article

Encyclopedia - Abductive Reasoning: Encyclopedia - Abductive Reasoning
Abduction, or abductive reasoning, is the process of reasoning to the best explanations. In other words, it is the reasoning process that...   » Read the article

Encyclopedia - Mathematical Logic: Encyclopedia Ii - Mathematical Logic - History
Mathematical logic was the name given by Giuseppe Peano to what is also known as symbolic logic. In essentials, it is still the logic of ...   » Read the article

Encyclopedia - Randomness: Encyclopedia - Randomness
The word random is used to express apparent lack of purpose, cause, or order. The term randomness is often used synonymously with a numbe...   » Read the article

Encyclopedia - Bertrand Russell: Encyclopedia - Bertrand Russell
The Right Honourable Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS (18 May 1872 – 2 February 1970), was an influential Bri...   » Read the article

Encyclopedia - Logic Programming: Encyclopedia Ii - Logic Programming - History
Logic Programming is an idea that has been investigated in the context of artificial intelligence since at least the time of John McCarth...   » Read the article

Encyclopedia - Logic: Encyclopedia Ii - Logic - Nature Of Logic
Because of its fundamental role in philosophy, the nature of logic has been the object of intense dispute: it is not possible clearly to ...   » Read the article

Encyclopedia - Logic: Encyclopedia Ii - Logic - Controversies In Logic
Just as we have seen there is disagreement over what logic is about, so there is disagreement about what logical truths there are. Logic...   » Read the article

Encyclopedia - Logic: Encyclopedia Ii - Logic - Topics In Logic
Throughout history, there has been interest in distinguishing good from bad arguments, and so logic has been studied in some more or less...   » Read the article

Encyclopedia - Multi-valued Logic: Encyclopedia Ii - Multi-valued Logic - History
The first known logician who didn't fully accept the law of the excluded middle was Aristotle (De Interpretatione, ch. IX), though he did...   » Read the article

Encyclopedia - Programmable Logic Controller: Encyclopedia Ii - Programmable Logic Controller - History
The PLC was invented in response to the needs of the American automotive industry. Before the PLC, control, sequencing, and safety interl...   » Read the article

Encyclopedia - Cirrus Logic: Encyclopedia Ii - Cirrus Logic - Graphics History
In the early 1990s, Cirrus Logic was a leading supplier of low-cost PC graphics chips. Cirrus's Windows accelerators were among the faste...   » Read the article

Encyclopedia - Second-order Logic: Encyclopedia Ii - Second-order Logic - The History And Disputed Value Of Second-order Logic
When predicate logic was introduced to the mathematical community by Frege (and independently — and more influentially — by Peirce, w...   » Read the article

Encyclopedia - Logic: Encyclopedia Ii - Logic - Nature Of Logic
Because of its fundamental role in philosophy, the nature of logic has been the object of intense disputation; and it is not possible to ...   » Read the article

Encyclopedia - Logic Synthesis: Encyclopedia Ii - Logic Synthesis - Multi Level Logic Minimization
Typical practical implementations of a logic function utilize a multilevel network of logic elements. Starting from an RTL description of...   » Read the article

Encyclopedia - Logic Synthesis: Encyclopedia Ii - Logic Synthesis - Behavioral Synthesis
With the goal of increasing designer productivity, there has been a significant amount of research on synthesis of circuits specified at ...   » Read the article

Encyclopedia - Mathematical Logic: Encyclopedia Ii - Mathematical Logic - Topics In Mathematical Logic
The main areas of mathematical logic include model theory, proof theory and recursion theory (often now referred to as computability theo...   » Read the article

Encyclopedia - Mathematical Logic: Encyclopedia Ii - Mathematical Logic - Technical Reference
Mathematical logic - First-order languages and structures. Definition. A first-order language is a collection of distinct typographica...   » Read the article

Encyclopedia - Logic Programming: Encyclopedia Ii - Logic Programming - Limitations Of Prolog As Logic Programming
However, Prolog did not include the negation or disjunction of mathematical logic because both individually and together they cause a lot...   » Read the article

Encyclopedia - Second-order Logic: Encyclopedia Ii - Second-order Logic - Why Second-order Logic Is Not Reducible To First-order Logic
An optimist might attempt to reduce second-order logic to first-order logic in the following way. Expand the domain from the set of all r...   » Read the article

Encyclopedia - Second-order Logic: Encyclopedia Ii - Second-order Logic - Second-order Logic And Metalogical Results
It is a corollary of Gödel's incompleteness theorem that one cannot have any notion of provability of second-order formulas given the st...   » Read the article

Encyclopedia - Programmable Logic Controller: 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 control...   » Read the article

Encyclopedia - Programmable Logic Controller: 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 control...   » Read the article

Encyclopedia - Programmable Logic Controller: Encyclopedia Ii - Programmable Logic Controller - Programming
PLCs programs are generally written in a special application on a personal computer then downloaded over a custom cable or standard netwo...   » Read the article

Encyclopedia - Transistor-transistor 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 ...   » Read the article

Encyclopedia - Programmable Logic Controller: 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 ...   » Read the article

Encyclopedia - Programmable Logic Controller: Encyclopedia Ii - Programmable Logic Controller - User Interface
PLCs may need to interact with people for the purpose of configuration, alarm reporting or everyday control. A Human-Machine Interface (H...   » Read the article

Encyclopedia - Programmable Logic Controller: 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, l...   » Read the article

Encyclopedia - Programmable Logic Controller: 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, l...   » Read the article

Encyclopedia - Arithmetic Logic Unit: Encyclopedia Ii - Arithmetic Logic Unit - Inputs And Outputs
The ALU takes as input the data to be operated on (called operands) and a code from the control unit indicating which operation to perfor...   » Read the article

Encyclopedia - Transistor-transistor Logic: Encyclopedia Ii - Transistor-transistor Logic - Sub-types
Variations of the basic TTL logic family include: Low-power TTL, which traded switching speed for a slight reduction in power consumptio...   » Read the article

Encyclopedia - Arithmetic Logic Unit: Encyclopedia Ii - Arithmetic Logic Unit - Alu Operations
Most ALUs will perform the following operations: integer arithmetic operations (addition, subtraction, multiplication) bitwise logic ope...   » Read the article

Encyclopedia - Cirrus Logic: Encyclopedia Ii - Cirrus Logic - Graphics Chipsets
DESKTOP CL-GD5420 - ISA SVGA chipset, highly integrated (RAMDAC + PLL), 1Mbyte CL-GD5422 - Enhanced version of the 5420 (32-bit internal...   » Read the article

Encyclopedia - Abductive Reasoning: 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 ...   » Read the article

Encyclopedia - Epimenides Paradox: 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"...   » Read the article

Encyclopedia - 7400 Series: Encyclopedia Ii - 7400 Series - History
Although the 7400 series was the first defacto industry standard TTL logic family, there were earlier TTL logic families such as the Sylv...   » Read the article

Encyclopedia - Abductive Reasoning: Encyclopedia Ii - Abductive Reasoning - Applications
Abduction has been applied in artificial intelligence for various tasks. The most direct application of abduction is that of automaticall...   » Read the article

Encyclopedia - Proof Theory: Encyclopedia Ii - Proof Theory - Kinds Of Proof Calculus
The three most well known proof calculi are: The Hilbert-style calculi The natural deduction calculus The sequent calculus To say these...   » Read the article

Encyclopedia - Kripke Semantics: Encyclopedia Ii - Kripke Semantics - Semantics Of Intuitionistic Logic
Kripke semantics for the intuitionistic logic follows the same principles as the semantics of modal logic, but it uses a different defini...   » Read the article

Encyclopedia - Epimenides Paradox: Encyclopedia Ii - Epimenides Paradox - Logical Analysis
If we define "liar" to mean that every statement made by a liar is false (so that Epimenides' statement amounts to "Anything said by a Cr...   » Read the article

Encyclopedia - Abductive Reasoning: Encyclopedia Ii - Abductive Reasoning - Set-cover Abduction
A different formalization of abduction is based on inverting the function that calculates the visible effects of the hypotheses. Formally...   » Read the article

Encyclopedia - Parallel Postulate: Encyclopedia Ii - Parallel Postulate - Logically Equivalent Properties
Several properties of Euclidean geometry are logically equivalent to Euclid's parallel postulate, meaning that they can be proven in a sy...   » Read the article

Encyclopedia - Kripke Semantics: Encyclopedia Ii - Kripke Semantics - Model Constructions
As in the classical model theory, there are methods for constructing a new Kripke model from other models. The natural homomorphisms in K...   » Read the article

Encyclopedia - Kripke Semantics: Encyclopedia Ii - Kripke Semantics - History And Terminology
Kripke semantics does not originate with Kripke, but instead the idea of giving semantics in the style given above, that is based on valu...   » Read the article

Encyclopedia - Idms: Encyclopedia Ii - Idms - Overview
IDMS - Logical Data Model. The data model offered to users is the CODASYL network model. The main structuring concepts in this model ar...   » Read the article

Encyclopedia - Proof Theory: Encyclopedia Ii - Proof Theory - Tableau Systems
Main article: Tableau systems Tableau systems apply the central idea of analytic proof from structural proof theory to provide decision p...   » Read the article

Encyclopedia - Idms: Encyclopedia Ii - Idms - History
The roots of IDMS go back to Dr. Charles Bachman's IDS (Integrated Data Store), an early database engine developed at General Electric. I...   » Read the article

Encyclopedia - Proof Theory: Encyclopedia Ii - Proof Theory - History
Although the formalisation of logic was much advanced by the work of such figures as Gottlob Frege, Peano, Russell and Dedekind, conventi...   » Read the article

Encyclopedia - Proof Theory: Encyclopedia Ii - Proof Theory - Ordinal Analysis
Main article: Ordinal analysis Ordinal analysis is a powerful technique for providing combinatorial consistency proofs for theories forma...   » Read the article

Encyclopedia - Karnaugh Map: Encyclopedia Ii - Karnaugh Map - When Not To Use K-maps
For expressions having more than four variables, the Quine-McCluskey algorithm, also called the method of prime implicants, should be use...   » Read the article

Encyclopedia - Proof Theory: Encyclopedia Ii - Proof Theory - Formal And Informal Proof
However, the proofs used in everyday mathematical practice are almost never like the formal proofs in proof theory. They are rather like ...   » Read the article

Encyclopedia - Proof Theory: Encyclopedia Ii - Proof Theory - Consistency Proofs
Main article: Consistency proof As we have discussed, the spur for the mathematical investigation of proofs in formal theories was Hilber...   » Read the article

Encyclopedia - Proof Theory: Encyclopedia Ii - Proof Theory - Structural Proof Theory
Main article: Structural proof theory Structural proof theory is the subdiscipline of proof theory that studies proof calculi that suppor...   » Read the article

Encyclopedia - Ordinal Fraction: Encyclopedia Ii - Ordinal Fraction - Data Modelling
Logical concepts are modelled mathematically by sets or by conditions. Concatenation of two concepts is modelled by the intersection of t...   » Read the article

Encyclopedia - Church–turing Thesis: Encyclopedia Ii - Church–turing Thesis - Success Of The Thesis
Since that time, many other formalisms for describing effective computability have been proposed, including recursive functions, the lamb...   » Read the article

Encyclopedia - Karnaugh Map: Encyclopedia Ii - Karnaugh Map - Usage In Boolean Logic
Normally, extensive calculations are required to obtain the minimal expression of a Boolean function, but one can use a Karnaugh map inst...   » Read the article

Encyclopedia - Karnaugh Map: Encyclopedia Ii - Karnaugh Map - Race Hazards
Karnaugh maps are useful for detecting and eliminating race hazards. In the above example, a potential race condition exists when C and ...   » Read the article

Encyclopedia - Power Optimization Eda: Encyclopedia Ii - Power Optimization Eda - Introduction And History
The increasing speed and complexity of today’s designs implies a significant increase in the power consumption of very-large-scale inte...   » Read the article

Encyclopedia - Power Optimization Eda: Encyclopedia Ii - Power Optimization Eda - Power Analysis Of Cmos Circuits
The power consumption of digital CMOS circuits is generally considered in terms of three components: The dynamic power component, relate...   » Read the article

Encyclopedia - Peirce's Law: Encyclopedia Ii - Peirce's Law - Peirce's Law Explained For Non-mathematicians
Peirce's law can be very confusing, especially if you're new to logic, so let's make it a little more concrete with an example. Unfortuna...   » Read the article

Encyclopedia - Randomness: Encyclopedia Ii - Randomness - Misconceptions/logical Fallacies
Popular perceptions of randomness are frequently wrong, based on logical fallacies. Following is an attempt to identify the source of suc...   » Read the article

Encyclopedia - History Of Computer Science: Encyclopedia Ii - History Of Computer Science - Emergence Of A Discipline
History of computer science - The theoretical groundwork. The mathematical foundations of modern computer science began to be laid by K...   » Read the article

Encyclopedia - Causality: Encyclopedia Ii - Causality - Causality Contrasted With Logical Implication
Logical conditional statements are not statements of causality. Since logical conditional statements and causal statements are both prese...   » Read the article

Encyclopedia - Planner Programming Language: Encyclopedia Ii - Planner Programming Language - Control Structure Controversy
However, computer memories were very small by current standards because they were expensive, being made of iron ferrite cores at that tim...   » Read the article

Encyclopedia - History Of Computer Science: Encyclopedia Ii - History Of Computer Science - Early History
History of computer science - Early computing. The earliest computers were, in fact, people, clerks who performed calculations. Compute...   » Read the article

Encyclopedia - Karnaugh Map: Encyclopedia Ii - Karnaugh Map - Example
Consider the following function: f(A, B, C, D) = E(4, 8, 9, 10, 11, 12, 14, 15) The values inside E tell us which rows have output 1. T...   » Read the article

Encyclopedia - Moral Relativism: Encyclopedia Ii - Moral Relativism - Some Philosophical Considerations
So-called descriptive relativists (for example, Ralph Barton Perry), accept that there are fundamental disagreements about the right cour...   » Read the article

Encyclopedia - Bertrand Russell: Encyclopedia Ii - Bertrand Russell - Russell's Philosophical Work
Bertrand Russell - Analytic philosophy. Russell is generally recognised as one of the founders of analytic philosophy, indeed, even of ...   » Read the article

Encyclopedia - Bertrand Russell: Encyclopedia Ii - Bertrand Russell - Influence On Philosophy
It would be difficult to overstate Russell's influence on modern philosophy, especially in the English-speaking world. While others were ...   » Read the article

Encyclopedia - Integrated Circuit: Encyclopedia Ii - Integrated Circuit - Other Developments
In the 1980s programmable integrated circuits were developed. These devices contain circuits whose logical function and connectivity can ...   » Read the article

Encyclopedia - Bertrand Russell: Encyclopedia Ii - Bertrand Russell - Asides
Actor Michael Wisher based the voice of Davros in the 1975 Doctor Who story Genesis of the Daleks on Russell. ... See also:Bertrand Ru...   » Read the article

Encyclopedia - Fuzzy Control System: Encyclopedia Ii - Fuzzy Control System - History & Applications
Fuzzy logic was first proposed by Lotfi A. Zadeh of the University of California at Berkeley in a 1965 paper. He elaborated on his ideas ...   » Read the article

Encyclopedia - Planner Programming Language: Encyclopedia Ii - Planner Programming Language - Early History Of Planner
Planner was the first language to feature procedural plans that were called by pattern-directed invocation using goals and assertions. A ...   » Read the article

Encyclopedia - Ordinal Fraction: Encyclopedia Ii - Ordinal Fraction - Positional Notation
The binary (or dyadic) positional notation for the first half is 1, and the second half is 2. The improper digit 0 plays the role of a wi...   » Read the article

Encyclopedia - Eight Queens Puzzle: Encyclopedia Ii - Eight Queens Puzzle - The Eight Queens Puzzle As An Exercise In Algorithm Design
Finding all solutions to the eight queens puzzle is a good example of a simple but nontrivial problem. For this reason, it is often used ...   » Read the article

Encyclopedia - Logic Programming: Encyclopedia Ii - Logic Programming - Prolog
Prolog was an early programming language that was billed by its designers as being based on mathematical logic. The basis for the claim t...   » Read the article

Encyclopedia - Bertrand Russell: Encyclopedia Ii - Bertrand Russell - Biography
Bertrand Russell was born on 18 May 1872 at Trellech, Monmouthshire, Wales, into an aristocratic English family. His paternal grandfather...   » Read the article

Encyclopedia - Bertrand Russell: Encyclopedia Ii - Bertrand Russell - Russell's Activism
Political and social activism occupied much of Russell's time for most of his long life, which makes his prodigious and seminal writing o...   » Read the article

Encyclopedia - Bertrand Russell: Encyclopedia Ii - Bertrand Russell - Russell Summing Up His Life
Admitting to failure in helping the world to conquer war and in winning his perpetual intellectual battle for eternal truths, Russell wro...   » Read the article

Encyclopedia - Bertrand Russell: Encyclopedia Ii - Bertrand Russell - Comments About Russell
Bertrand Russell - As a man. "Bertrand Russell would not have wished to be called a saint of any description; but he was a great and g...   » Read the article

Encyclopedia - Lambda Calculus: Encyclopedia Ii - Lambda Calculus - Logic And Predicates
By convention, the following two definitions (known as Church booleans) are used for the boolean values TRUE and FALSE: TRUE := λ ...   » Read the article

Encyclopedia - Randomness: Encyclopedia Ii - Randomness - Study Of Randomness
Many scientific fields are concerned with randomness : Algorithmic probability Chaos theory Game theory Information theory Pattern ...   » Read the article

Encyclopedia - Randomness: Encyclopedia Ii - Randomness - Generating Randomness
The many applications of randomness have led to many different methods for generating random data. These methods may vary as to how unpre...   » Read the article

Encyclopedia - Eight Queens Puzzle: Encyclopedia Ii - Eight Queens Puzzle - History
The problem was originally proposed in 1848 by the chess player Max Bezzel, and over the years, many mathematicians, including Gauss have...   » Read the article

Encyclopedia - Eight Queens Puzzle: Encyclopedia Ii - Eight Queens Puzzle - Counting All Solutions
The eight queens puzzle has 92 distinct solutions. If solutions that differ only by symmetry operations (rotations and reflections) of th...   » Read the article

Encyclopedia - Randomness: Encyclopedia Ii - Randomness - Study Of Randomness
Many scientific fields are concerned with randomness : Algorithmic probability Chaos theory Cryptography Game theory Information th...   » Read the article

Encyclopedia - Integrated Circuit: Encyclopedia Ii - Integrated Circuit - Key Industrial And Academic Data
Integrated circuit - Notable ICs. The 555 common multivibrator subcircuit (common in electronic timing circuits) The 741 operational a...   » Read the article

Encyclopedia - Randomness: Encyclopedia Ii - Randomness - Randomness Versus Unpredictability
Randomness should not be confused with practical unpredictability, which is a related idea in ordinary usage. Some mathematical systems, ...   » Read the article

Encyclopedia - Randomness: Encyclopedia Ii - Randomness - Applications And Use Of Randomness
"Unpredictable" random numbers were first investigated in the context of gambling, and many randomizing devices such as dice, shuffling p...   » Read the article

Encyclopedia - Randomness: Encyclopedia Ii - Randomness - History
Humankind has been concerned with randomness since prehistoric times, mostly through divination (reading messages in random patterns) and...   » Read the article

Encyclopedia - Game Theory: Encyclopedia Ii - Game Theory - Uses Of Game Theory
Games in one form or another are widely used in many different academic disciplines. Game theory - Economics and business. Economists h...   » Read the article

Dictionary - Idms: Encyclopedia Ii - Idms - Integrated Data Dictionary
One of the sophisticated features of IDMS was its built-in Integrated Data Dictionary (IDD). The IDD was primarily developed to maintain ...   » Read the article

Encyclopedia - History Of Logic: Encyclopedia Ii - History Of Logic - Logic In Islamic Philosophy
For after Muhammed's death, Islamic law placed importance on formulating standards of argument, which gave rise to a novel approach to ar...   » Read the article

Encyclopedia - History Of Logic: Encyclopedia Ii - History Of Logic - The Advent Of Modern Logic
Historically, Descartes, may have been the first philosopher to have had the idea of using algebra, especially its techniques for solving...   » Read the article