according to or agreeing with the principles of logic: a logical inference.
reasoning in accordance with the principles of logic, as a person or the mind: logical thinking.
reasonable; to be expected: War was the logical consequence of such threats.
of or pertaining to logic.

1490–1500; < Medieval Latin logicālis. See logic, -al1

logicality [loj-i-kal-i-tee] , logicalness, noun
logically, adverb
hyperlogical, adjective
hyperlogically, adverb
hyperlogicalness, noun
hyperlogicality, noun
nonlogical, adjective
nonlogically, adverb
nonlogicalness, noun
nonlogicality, noun
overlogical, adjective
overlogically, adverb
overlogicalness, noun
overlogicality, noun
prelogical, adjective
prelogically, adverb
quasi-logical, adjective
quasi-logically, adverb
superlogical, adjective
superlogically, adverb
superlogicality, noun
unlogical, adjective
unlogically, adverb

1, 3. valid.

1–3. unreasonable.
Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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World English Dictionary
logical (ˈlɒdʒɪkəl)
1.  relating to, used in, or characteristic of logic
2.  using, according to, or deduced from the principles of logic: a logical conclusion
3.  capable of or characterized by clear or valid reasoning
4.  reasonable or necessary because of facts, events, etc: the logical candidate
5.  computing of, performed by, used in, or relating to the logic circuits in a computer

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009
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Word Origin & History

early 16c., "pertaining to logic," from logic + -al. Attested from 1580s as "conformable to laws of reasoning;" 1860 as "following as a reasonable consequence." Related: Logically.
Online Etymology Dictionary, © 2010 Douglas Harper
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Example sentences
Humans are the animal that can reason creatively and abstractly, or perform the
  inverse, imagine logically and rationally.
He includes a section on the historical context of the mystery to see if it is
  possible to explain the story logically.
We lend a meaning to an expression knowing that logically it does not belong to
They would hardly greet the good that did not logically fall,-as if it excluded
  their own merit, or shook their understandings.
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