in a formal manner: The store was formally opened on Tuesday.
as regards form; in form: It may be formally correct, but it is substantively wrong.

1350–1400; Middle English. See formal1, -ly

formally, formerly. Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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World English Dictionary
formal1 (ˈfɔːməl)
1.  of, according to, or following established or prescribed forms, conventions, etc: a formal document
2.  characterized by observation of conventional forms of ceremony, behaviour, dress, etc: a formal dinner
3.  methodical, precise, or stiff
4.  suitable for occasions organized according to conventional ceremony: formal dress
5.  denoting or characterized by idiom, vocabulary, etc, used by educated speakers and writers of a language
6.  acquired by study in academic institutions: a formal education
7.  regular or symmetrical in form: a formal garden
8.  of or relating to the appearance, form, etc, of something as distinguished from its substance
9.  logically deductive: formal proof
10.  philosophy
 a.  of or relating to form as opposed to matter or content
 b.  pertaining to the essence or nature of something: formal cause
 c.  (in the writings of Descartes) pertaining to the correspondence between an image or idea and its object
 d.  being in the formal mode
11.  denoting a second-person pronoun in some languages used when the addressee is a stranger, social superior, etc: in French the pronoun ``vous'' is formal, while ``tu'' is informal
[C14: from Latin formālis]

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

c.1400, in good form, from formal + -ly (2). Meaning in prescribed or customary form is from 1560s.
Online Etymology Dictionary, © 2010 Douglas Harper
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Example sentences
Now the south will have to focus on the intricate process of formally
  disentangling itself from the north.
Show that you're a hipster through your accessories or your shoes, but dress
Though formally homeless, few of those who lack settled abodes sleep on the
  streets, nor do many live in dingy hotels or hostels.
Unless formally hedged, plants require little pruning.
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