logical
American Heritage Dictionary:
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log·i·cal
(lŏj'ĭ-kəl) 
adj.
logically log'i·cal·ly adv.
adj.
- Of, relating to, in accordance with, or of the nature of logic.
- Based on earlier or otherwise known statements, events, or conditions; reasonable: Rain was a logical expectation, given the time of year.
- Reasoning or capable of reasoning in a clear and consistent manner.
logically log'i·cal·ly adv.
SYNONYMS logical, analytic, ratiocinative, rational. These adjectives mean capable of or reflecting the capability for correct and valid reasoning: a logical mind; an analytic thinker; the ratiocinative process; a rational being.
ANTONYM illogical
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logical
Fowler's Modern English Usage:
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logically
especially when placed at the beginning of a sentence as an adverb qualifying the whole of it, often has little to do with the application of logic and simply prepares us for (or beguiles us into accepting) the writer's different point of view:
Logically, it is the Europeans who are out of step [with respect to time] and not us—Croydon Guardian, 2004.This statement does not deal with the relation between ideas but contests the assumptions on which the traditional ideas were originally based.
| loggia, lodestar, lodestone, locum | |
| lonelily, long, long-lived |
Computer Desktop Encyclopedia:
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logical
(1) A reasonable solution to a problem.
(2) A higher level view of an object; for example, the user's view versus the computer's view. See logical vs. physical.
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Roget's Thesaurus:
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logical
adjective
- Consistent with reason and intellect: consequent, intelligent, rational, reasonable. See reason/unreason.
- Able to reason validly: analytic, analytical, ratiocinative, rational. See reason/unreason.
Antonyms by Answers.com:
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logical
adj
Definition: probable, reasonable
Antonyms: illogical, improbable, irrational, unlikely, unreasonable
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[from the technical term logical device, wherein a physical device is referred to by an arbitrary ‘logical’ name] Having the role of. If a person (say, Les Earnest at SAIL) who had long held a certain post left and were replaced, the replacement would for a while be known as the logical Les Earnest. (This does not imply any judgment on the replacement.) Compare virtual.
At Stanford, ‘logical’ compass directions denote a coordinate system relative to El Camino Real, in which ‘logical north’ is always toward San Francisco and ‘logical south’ is always toward San Jose--in spite of the fact that El Camino Real runs physical north/south near San Francisco, physical east/west near San Jose, and along a curve everywhere in between. (The best rule of thumb here is that, by definition, El Camino Real always runs logical north-south.)
In giving directions, one might say: “To get to Rincon Tarasco restaurant, get onto El Camino Bignum going logical north.” Using the word ‘logical’ helps to prevent the recipient from worrying about that the fact that the sun is setting almost directly in front of him. The concept is reinforced by North American highways which are almost, but not quite, consistently labeled with logical rather than physical directions. A similar situation exists at MIT: Route 128 (famous for the electronics industry that grew up along it) wraps roughly 3 quarters around Boston at a radius of 10 miles, terminating near the coastline at each end. It would be most precise to describe the two directions along this highway as ‘clockwise’ and ‘counterclockwise’, but the road signs all say “north” and “south”, respectively. A hacker might describe these directions as logical north and logical south, to indicate that they are conventional directions not corresponding to the usual denotation for those words.
Word Tutor:
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logically
IN BRIEF: In a manner characterized by clear reasoning.
People that think logically are a nice contrast to the real world.
— Matt Biershbach
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Random House Word Menu:
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categories related to 'logical'
Wikipedia on Answers.com:
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Logical conjunction
"∧" redirects here. For exterior product, see Exterior algebra.
In logic and mathematics, a two-place logical operator and, also known as logical conjunction, results in true if both of its operands are true, otherwise the value of false.
The analogue of conjunction for a (possibly infinite) family of statements is universal quantification, which is part of predicate logic.
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Notation
And is usually expressed with the prefix operator K, or an infix operator. In mathematics and logic, the infix operator is usually ∧; in electronics 
; and in programming languages, & or and. Some programming languages have a related control structure, the short-circuit and, written &&, and then, etc.
Definition
Logical conjunction is an operation on two logical values, typically the values of two propositions, that produces a value of true if and only if both of its operands are true.
The conjunctive identity is 1, which is to say that AND-ing an expression with 1 will never change the value of the expression. In keeping with the concept of vacuous truth, when conjunction is defined as an operator or function of arbitrary arity, the empty conjunction (AND-ing over an empty set of operands) is often defined as having the result 1.
Truth table
The truth table of 
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| INPUT | OUTPUT | |
| A | B | A AND B |
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
Introduction and elimination rules
As a rule of inference, conjunction introduction is a classically valid, simple argument form. The argument form has two premises, A and B. Intuitively, it permits the inference of their conjunction.
- A,
- B.
- Therefore, A and B.
or in logical operator notation:
Here is an example of an argument that fits the form conjunction introduction:
- Bob likes apples.
- Bob likes oranges.
- Therefore, Bob likes apples and oranges.
Conjunction elimination is another classically valid, simple argument form. Intuitively, it permits the inference from any conjunction of either element of that conjunction.
- A and B.
- Therefore, A.
...or alternately,
- A and B.
- Therefore, B.
In logical operator notation:
...or alternately,
Properties
commutativity: yes
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associativity: yes
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distributivity: with various operations, especially with or
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with exclusive or:
with material nonimplication:
with itself:
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idempotency: yes
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monotonicity: yes
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truth-preserving: yes
When all inputs are true, the output is true.
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falsehood-preserving: yes
When all inputs are false, the output is false.
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Walsh spectrum: (1,-1,-1,1)
Nonlinearity: 1 (the function is bent)
If using binary values for true (1) and false (0), then logical conjunction works exactly like normal arithmetic multiplication.
Applications in computer engineering
In high-level computer programming and digital electronics, logical conjunction is commonly represented by an infix operator, usually as a keyword such as "AND", an algebraic multiplication, or the ampersand symbol "&". Many languages also provide short-circuit control structures corresponding to logical conjunction.
Logical conjunction is often used for bitwise operations, where 0 corresponds to false and 1 to true:
0 AND 0=0,0 AND 1=0,1 AND 0=0,1 AND 1=1.
The operation can also be applied to two binary words viewed as bitstrings of equal length, by taking the bitwise AND of each pair of bits at corresponding positions. For example:
11000110 AND 10100011=10000010.
This can be used to select part of a bitstring using a bit mask. For example, 10011101 AND 00001000 = 00001000 extracts the fifth bit of an 8-bit bitstring.
In computer networking, bit masks are used to derive the network address of a subnet within an existing network from a given IP address, by ANDing the IP address and the subnet mask.
Logical conjunction "AND" is also used in SQL operations to form database queries.
The Curry-Howard correspondence relates logical conjunction to product types.
Set-theoretic intersection
The intersection used in set theory is defined in terms of a logical conjunction: x ∈ A ∩ B if and only if (x ∈ A) ∧ (x ∈ B). Because of this, set-theoretic intersection shares several properties with logical conjunction, such as associativity, commutativity, and idempotence.
Natural language
The logical conjunction and in logic is related to, but not the same as, the grammatical conjunction and in natural languages.
English "and" has properties not captured by logical conjunction. For example, "and" sometimes implies order. For example, "They got married and had a child" in common discourse means that the marriage came before the child. The word "and" can also imply a partition of a thing into parts, as "The American flag is red, white, and blue." Here it is not meant that the flag is at once red, white, and blue, but rather that it has a part of each color.
See also
- And-inverter graph
- AND gate
- Binary and
- Bitwise AND
- Boolean algebra (logic)
- Boolean algebra topics
- Boolean conjunctive query
- Boolean domain
- Boolean function
- Boolean-valued function
- Conjunction introduction
- Conjunction elimination
- De Morgan's laws
- First-order logic
- Fréchet inequalities
- Grammatical conjunction
- Logical disjunction
- Logical negation
- Logical graph
- Logical value
- Operation
- Peano-Russell notation
- Propositional calculus
External links
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This entry is from Wikipedia, the leading user-contributed encyclopedia. It may not have been reviewed by professional editors (see full disclaimer)
Translations:
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Logical
Nederlands (Dutch)
logisch, rationeel, analytisch beredeneerd, vanzelfsprekend, systematisch uitgewerkt, samenhangend, weloverdacht
Français (French)
adj. - logique
Deutsch (German)
adj. - logisch
Ελληνική (Greek)
adj. - λογικός
Português (Portuguese)
adj. - lógico, razoável, natural
Русский (Russian)
логический, последовательный, разумный
Español (Spanish)
adj. - lógico, dialéctico, consecuente, natural
Svenska (Swedish)
adj. - logisk, följdriktig
中文（简体）(Chinese (Simplified))
合乎逻辑的, 合理的
中文（繁體）(Chinese (Traditional))
adj. - 合乎邏輯的, 合理的
한국어 (Korean)
adj. - 논리적인 , 논리적으로 생각하는, 조리에 닿는
日本語 (Japanese)
adj. - 論理的な, 当然の, 論理学の
العربيه (Arabic)
(صفه) منطقي, منطقي التفكير
עברית (Hebrew)
adj. - הגיוני, שכלי, לוגי, סביר, עקבי
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American Heritage Dictionary
The American Heritage® Dictionary of the English Language, Fourth Edition Copyright © 2007, 2000 by Houghton Mifflin Company. Updated in 2009. Published by Houghton Mifflin Company. All rights reserved.
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