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Loglan, the logical language


The name Loglan, in this context, refers to the logical language that James Cooke Brown first started to develop in the 1950s. Loglan forms an example of a logical language because the developers based the language on predicate logic which forms a way of defining logical relationships. However, for practical purposes, you could view the language as an example of a fill the blanks language as each of the main type of words used in Loglan effectively form an incomplete sentence where you fill in the blanks to complete the meaning. For example, the Loglan word meaning to see, vizka, has three blanks and forms the sentence x sees y against background z as in mi vizka tu meaning I see you (you don't have to use all the blanks in loglan).

Loglan could form a future auxiliary language as it has a number of advantages over natural languages and languages such as Esperanto.

  • Loglan has a set of consistent rules - no exceptions
  • Consistent spelling (the base words come in either CVCCV or CCVCV form (where C stands for "consonant" and V for "vowel")).
  • Simpler rule set. Loglan has about 200 rules, far less than a natural language.
  • A defined way to grow so any additions follow a set of rules as the language grows and develops. So, once you know Loglan, your knowledge doesn't get out dated as the language changes.
  • Simpler grammar. No nouns, adverbs, imperfect forms, etc. to learn.

Table of Contents

Chapter 1 - Overview of Loglan

You construct a sentence in Loglan from three groups of words:


You use predicates to form the main subject of a sentence. If fact, you can view a predicate words as an incomplete sentence. Just fill in the blanks to say what you want to say. Each predicate word has from one to five blanks to fill in.

Predicates come in three main forms.

  • Base words
  • Compound words
  • Loan words

Base Words

These form the main set of words used in Loglan. They have a constant spelling; either CVCCV form or CCVCV form. They all end in a vowel and they all have only one meaning each.


NB. The letters x, y and z represent the blanks.

CVCCV form

  • vizka - x sees y against background z
  • hasfa - x is the house of y
  • tarci - x is a star of galaxy y
  • fundi - x likes y more than z
  • takna - x talks to y about z

CCVCV form

  • cnida - x needs y for z
  • clika - x is similar to x in feature z
  • tcaro - x is a motorised vehicle
  • jmite - x meets y
  • zvoto - x is outside of y

Compound Words

The base words in Loglan number about 1 500. To say more you can use two or more base words to make a metaphor. If you think others can use the metaphor you can combine the words to make a new word. Each base word has a combining form which you can use to construct more complex words.


  • fagctu - ash. Constructed from fagro (fire) and ctuda (excrement); fagro ctuda. The word fagro has the combining form fag and ctuda the combining form of ctu so the metaphor fagro ctuda becomes the word fagctu.
  • bamfoa - sphere. Constructed from balma (ball) and forma (form / shape); balma forma. The word balma has the combining form bam and forma the combining form of foa so the metaphor balma forma becomes the word bamfoa.
  • trigru - forest / wood. Constructed from tricu (tree) and grupa (group); tricu grupa. The word tricu has the combining form tri and grupa the combining form of gru so the metaphor tricu grupa becomes the word trigru.

Loan Words

When using Loglan you try to use Loglan word to construct a metaphor for a new idea of concept. However, you might not have the opportunity to do that at all time such as when an idea or concept has a close relationship to one group of people. In such cases, Loglan allows borrowing but with certain rules.


  • proteini - x is a protein of type y
  • cerkopithekui - x is a cercopithecus (a primate) of that genus


These form a set of words that you use to fill in the blanks of the predicates. They form the objects or agents that you talk about. Arguments come in three forms:

We use a little word to tell the difference between a name and a normal predicate word used as an argument; either le or la. The little word le means the one I call and the little word la means the one that actually is. The word 'le' then forms a prefix for a description and the little word la forms a prefix for a name.


Names in Loglan come in two types:

  • Proper Names
  • Predicate Names

All proper names end in a consonant and can have any number of letters. We can use predicates as names if we use the little word la first. As predicates together form a metaphor we use the little word gu to show where the name ends and the main predicate of the sentence starts.


Proper names:

  • Frans - France
  • Sol - Sun
  • Romas - Rome

Predicate Names

  • la farfu - father / dad
  • la ratcu - Rat

Predicates as arguments

You can use predicates words as arguments to the main predicate of a sentence to form the object or agent of a predicate. To do so, you need to add the little word le to show that the you mean the one I call and then use the little word gu to show when the argument predicate comes to an end and the main sentence predicate begins.


  • le nirli gu tcatro - the girl is driving (a vehicle)
  • le farfu gu kamla - the father comes
  • le hasfa gu redro - the house is red
  • le prano mrenu gu goztsefui - the running man is late

Little words as arguments

Loglan has a number of little words that you can use for common occurring actors or objects.


  • tu - you
  • ti - this
  • toi - that ( the last mentioned remark)
  • da - he / she / it

Little words

Little words form a type of control word for sentences. You can use them to form brackets, add time and place or add additional information to a sentence. You can also use some little words for common words you might use such as me, it or numbers.


  • mi - me / I / myself
  • gu - a separator between predicates / a right boundary marker
  • to - the number two
  • rau - ... because of reason ...
  • e - and

Chapter 2 - Putting Things Together - Forming Sentences

You build a proper sentence in Loglan around a predicate word. You then fill what blanks you need and then add any additional information using little words.

Simple sentences

(vizka = x sees y against background z)

  • mi vizka tu - I see you (main predicate = vizka)
  • tu vizka mi - You see me (main predicate = vizka)
  • mi ridle ba le bukcu - I read something from a book (main predicate = ridle with arguments = ba and le bukcu)

More complex sentences

  • mi nu vizka tu - I am seen by you (you see me) (main predicate = vizka and using the place converter nu to swap arguments)
  • mi vizka tu, ui - I see you (which I am happy about) (main predicate = vizka and using the emotional indicator ui)

(soisni = x is sleepier than y) (cioru = many / too much) (muspli = x exercises muscles y)

  • la maris soisni rau lepo da cioru muspli - Mary feels sleepy because she has exercised too much (main predicate = soisni with rau to give a physical cause)

(tcatro = x drives vehicle y from z to a via b) (livhao = x is the home of y) (turka = x work on y for purpose z) (sitfa = x is the place of b in reference frame z)

  • le mrenu gu tcatro le tcaro le livhao le turka sitfa pa - the man drove the car from home to the work place (main predicate = tcatro and using the little word pa to put the event in the past)
  • le mrenu gu tcatro le tcaro le livhao le turka sitfa fa - the man will drive the car from home to the work place (main predicate = tcatro and using the little word fa to put the event in the future)

Chapter 3 - The Power of Little Words

Much of the expressive power of Loglan lies in the little words. A basic sentence in Loglan just defines a relationship between actors and objects but says nothing about the whys, whens or wheres. For example, mi vizka tu defines a relationship between me and you of the type seeing; "I see you" but says nothing about where or when or why. We can use the little words to add those additional informations.

Little words come in different types:

Logical Operators and Connections - joining things together

Time and Space -the wheres and whens

Modifiers - the whys

Numbers and Letters

He, she and it

Logical Operators and Connections

Loglan has five basic logical operators for joining things together and one way to separate sentences. Loglan also has an operator for please indicate which :

  • a - the or operator
  • e - the and operator
  • o - the if and only if operator
  • u - the whether or not operator
  • no - the inverse operator
  • i - the start of a sentence
  • ze - mixing things together
  • ha - How connected

Loglan then extends these basic operator for connecting words or sentences in different ways

The OR Operator


In Loglan, we define the Or operator as true if one item it links together has a value of true. The little word a connects predicates together.


  • mi tcatro a maifle - I am a driver or a pilot (or both)
  • le tetri gu solflo a kleda - the weather is sunny or cold (or both)
  • le bakso gu redro a dirlu a groda - the box is red or lost or large (or any combination)

ca, ka, anoi and ica

The little word a forms the foundations for a set of "OR" words.

  • ca - forms an OR operation with predicates as arguments
  • ka - forms an OR operation as a but as a forethought connection. It works with the little word ki
  • anoi - represents an if relationship and results from NOT OR
  • ica - connects two sentences together with an OR operation



  • le mrenu ca fumna gu godzi - the man or woman goes
  • le katmu gu fundi le cutri ca ficlu - the cat likes water or fish


  • le ka mrenu ki fumna gu godzi - the man or woman goes
  • le katmu gu fundi le ka cutri ki ficlu - the cat likes water or fish


  • mi fundi le bukcu anoi le sinma - I like the book if I like the film


  • mi fundi le bukcu ica le sinma - I like the book or I like the film

The AND Operator

The AND operator links together a group of items so that for the whole group to have the value true all the items have to have the value true. If one or more items have the value false then the whole group has the value false.


The little word e links together predicates.


  • la djan gu herkeu e larmao - John is a hairdresser and an artist
  • da tcaro e plebekti - that is a car and a toy

ce, ke and enoi

The other AND operators in Loglan follow on from e.

The little word ce joins together arguments and so does ke but we use ke in a forethought way and it works together with ki. We can use the little word enoi to mean ... but not ....



  • da lemi hasfa ce livhao - this is my house and home
  • le tetri gu cetlo ce briflo - the weather is wet and windy
  • tu ponsu le grobou ce botsu - you own the ship and the boat


  • da lemi ke hasfa ki livhao - this is my house and home
  • mi clika lemi ke matma ki farfu - I am like my mother and father


  • mi madzo le hasfa enoi le livhao - I make a house but not a home

The IF and only IF operator


The little word o means if and only if. We can use it to link predicates together.


  • mi godzi o dzoru - I go if and only if I walk
  • mi clivi o brute - I am alive if and only if I breath

co, ko, onoi and ico

We can extend the basic little word o for connecting arguments ans sentences.

  • co - links arguments together
  • ko - the forethought equivalent and works with ki
  • onoi - the exclusive OR (XOR) operator that means a XOR b but not both
  • ico - links sentences



  • mi hapci co crano pernu - I am a happy (if and only if smiling) person
  • da nakso le bakso co kuvbao - Someone fix the box if and only chest


  • mi ko hapci ki crano gu pernu - I am a happy (if and only if smiling) person


  • le crina onoi le solflo gu tetri - the weather is either raining or sunny but not both
  • mi kamla le fusto onoi le livhao - I come to the office or the home but not both


  • mi klama le fusto ico klama le livhao - I come to the office or I come to the home but not both

The Whether or Not Operator


The little word u means x whether or not y and links together predicates.


  • mi godzi u brecea - I go, whether or not I am ready
  • da bakso u redro - it is a box, whether or not it is red
  • ti bukcu u ponsu ti - it is a book, whether or not I own it

cu, ku and icu

We can use the little word cu to link together arguments and so does ku. However, ku works as a forethought operator and works with ki. The little word icu links sentences.



  • mi godzi le hasfa cu vemsia - I go to the house, whether or not I go to the shop
  • le katmu cu kangu gu fundi le ficlu - The cat, whether or not the dog, likes the fish


  • mi godzi le ku hasfa ki vemsia - I go to the house, whether or not I go to the shop
  • tu fleti la Romas cu Pari's - you fly to Rome, whether or not you fly to Paris


  • tu vrelaa icu mi vrecoa - you are tall, whether or not I am short

The Inverse Operator


We use the little word no to invert or negate a relationship. I can mean slightly different things depending exactly where it appears in a sentence.


  • no, mi vizka tu - It is not the case that I see you (no relationship between you and me)
  • mi no vizka tu - I don't see you (but there is a relationship between you and me but its not seeing. I could hear you instead, for example)
  • mi vizka no tu - I don't see you (I see something but its not you)

Start a Sentence


The little word i indicates the start of a sentence. We can also combine i with other operators to produce sentence combining forms such as ica (i + ca).


  • mi vizka tu. i tu vizka mi - I see you. You see me.
  • mi fleti la Romas. i tu stolo le livhao - I fly to Rome. You stay at home.

Mixing Things Together


Sometimes a composition forms something. For example, a black and white cat composed of both black fir and white fir. In loglan, if we say a black and white cat (le nigro ce blabi katmu) we mean the cat is both black and white at the same time, which not only forms and example of an impossibility but also we do not mean that. Loglan, however, does provide a word to mix things together.


  • le nigro ze blabi katmu - black and white cat
  • le redro ze vegri hasfa - The red and green house

How Connected


For an OR operation to have a truth value of true only one item in the list need a truth value of true. So, the question "would you like sugar or milk in your coffee" has the answer "yes" if I would like sugar or if I would like milk or if I would like milk and sugar. It only has the answer "no" if I want neither milk nor sugar. Technically correct the answer "yes", but not very useful. If I answer "yes" do I want milk, sugar or both? To over come this, Loglan provides the little word ha to mean which if any.


  • ei, tu danza le sakta ha le malna kii letu skafi - Would you like sugar or milk with your coffee?

Time and Space

A simple sentience in Loglan only defines a relationship between the arguments but says nothing about where on when the relationship holds true. Unlike some natural languages, you can chose to add time and space to a sentence in Loglan or chose to leave it out.

The Loglan sentence, mi viska tu means I see you or I was seen by you or I will see you. English forces us to add in the time; was it past, present or future? But in Loglan mi viska tu can hold true if I see you now or I have seen you or even if I will see you at some point in the future. Loglan does not force you to refer to time or space.

Loglan treats time and space the same. That means you place a relationship in time the same way that you place it in space; you add one of three words for time and one of three words for space. Whatever you can do with time words you can do with space words.

For time we have the following three words:

  • pa
  • na
  • fa

For space we have the following three words:

  • vi
  • va
  • vu

pa, na, and fa

If we want to add time into a sentence Loglan provides us with three little words to do that; pa, na and fa. You can add theses little words anywhere in the sentence.

The little word pa refers to the past and means before.

  • mi vizka tu pa - I saw you
  • mi pa vizka tu - I saw you
  • pa mi vizka tu - I saw you

The little word na refers to now and means at the instance of.

  • mi na vizka tu - I see you now

The last of the three, fa, refers to the future and means after.

  • mi vizka tu fa - I will see you

vi, va and vu

The little words vi, va and vu indicate place and work like the words for time; they go anywhere in the sentence.

The little word vi means here or close to this place

  • mi viska tu vi - I see you here
  • mi vi viska tu - I see you here
  • vi mi viska tu - I see you here

The little word va means over there or nearby.

  • mi vizka tu va - I saw you nearby

The last little, vu word refers to a place far away; over there or yonder.

  • mi vizka tu vu - I saw you far away over there

zi, za, and zu

You can add more details to the time and space words using the zi, za, and zu little words.

  • zi - near or very short duration
  • za - soon or a short duration
  • zu - long time or long duration


  • fazi - very short time in the future
  • vuzu - a very long distance away
  • naza - in a little while

The context determines how long is long and how short is short. The existence of humans on Earth is a short time in geological ages but and hour might mean a long time to wait for a bus.

Other Places and Other Times

The use of vi, va, vu and pa, na, fa defines time and place relative to the speaker. We can use the little word la to define a place or time relative to something else if we combine it with the place and time words.

  • mi vizka tu lena kinkra - I saw you at the time of the convention
  • mi lena kinkra gu vizka tu - I, at the time of the convention, saw you
  • mi vizka tu lefa kinkra - I will see you at the time of the convention
  • mi vizka tu levi kinkra - I saw you at the place of the convention
  • mi vizka tu leva kinkra - I saw you near the place of the convention


The basic Loglan sentence just defines a relationship but Loglan allows you to add more information if you wish. These extra words we group together as:

  • Sentence modifiers
  • Argument modifiers
  • Free modifiers

Sentence Modifiers

Sentence modifiers include the time and space words and the logical contention words. They also include modal and causal relative operators. You can place a modal anywhere in a sentence but if they appear anywhere other than on the end of a sentence you might need a gu to say when the modeal ends and the remaining part of the sentence continues.

Modal Operators

Modal operators add information on who or in what way something relates to something else. They all come in CVV form.

  • kii - With as in mi godzi kii tu (I walk with you)
  • tie - using tool as in Da pa tie leda najda gu kutla de (someone, with a knife, cut something. Note the use of gu to end the modal)
  • hea - with help as in mi kamla le hijra hea tu (I came here with your help)

Causal Operators

Causal operators work just the same way as modal operators. Causal operators give the reason why a relationship holds.

  • kou - because of physical reason as in mi cetlo kou le crina (I am wet because of the rain)
  • moi - because of motive as in mi kamla le hijra moi lepo mi danza lepo mi vizka tu (I came because I wanted to see you)
  • rau - because of reason as in mi fundi tu rau lepo tu minspu (I like you because you are clever)
  • soa - because of premise as in letu kukreo gu denro soa lepo ra dortau gu denro (your rifle is dangerous because all weapons are dangerous)

Argument Modifiers

Argument modifiers adds additional information to an argument such as making claims or identifying the argument.

  • ji - adds more information to identify the argument as in lemi hasfa ji le redro hasfa, gu snire (my house - the red house - is close)
  • ja - makes a claim and adds more information about the argument as in lemi hasfa ja le redro hasfa, gu snire (my house, which is a red house, is close)

Free Modifiers

Theses modifiers add more information about the writer / speaker or about the sentence as a whole. They can go anywhere in a sentence without effecting the sentence (except after le, la and the others in that group). Loglan contains a number of different types of free modifiers, which includes.

  • Attitude
  • Discursive
  • Parenthesis


These all have a VV form and form groups depending on the first letter. The 'a' series deals with intention, 'e' with requests, 'i' with conviction, 'o' with obligation and 'u' with motive. The second letter deals with degree with 'a' as positive, 'i' mid way and 'u' as negative. Some examples:

  • ua - satisfaction
  • ui - happy
  • uo - anger
  • uu - sorrow
  • oa - must / feel obliged to do so
  • ou - Doesn't matter
  • ia - agree
  • ii - maybe
  • iu - don't know
  • ei - is it so
  • eo - please
  • eu - assume
  • ai - intend
  • au - don't care


Loglan has a set of numbers composed of 10 little words which represent a single digit each:

  • 0 - ni
  • 1 - ne
  • 2 - to
  • 3 - te
  • 4 - fo
  • 5 - fe
  • 6 - so
  • 7 - se
  • 8 - vo
  • 9 - ve

All odd numbers end in e and all even numbers end in o. You can form larger numbers though combining words in the same way we combine digits.


  • 10 - neni
  • 123 - netote


You can add fi on to the end of a number to describe a sequence such as first, second, third.


  • Nefi - first
  • tofi - second
  • tefi - third


Loglan has away to refer to each letter. You might want to do this when using letters as variables. You just need to add an ending to the letter depending on weather you use a Latin of Greek letter, vowel or consonant. NB Loglan does not use the letter c or w for Greek letters as Greek has no corresponding sounds (c = sh and w = eu in Loglan).

  • -ei for lower case Latin consonant letters
  • -si for lower case Latin vowel letters
  • -ai for upper case Latin consonant letters
  • -ma for upper case Latin vowel letters
  • -eo for lower case Greek consonant letters
  • gao- for upper case Greek consonant letters
  • -fi for lower case vowel letters
  • gao,- for upper case Greek vowel letters


  • A - Ama
  • a - asi
  • B - Bai
  • b - bei
  • Alpha - gao,afi
  • alpha - afi
  • Beta - gaobeo
  • beta - beo

He, She and It

Gender in Loglan

In many natural languages when referring to a person you also have to refer to the person's gender. For example, in English, if you refer to a man you use "he" and for a woman you use "she". The words "he" and "she" automatically tells you the person's gender. Loglan, however, does not specify gender like in English. Instead, Loglan maintains gender neutrality.

First Letter

Loglan has a number of ways to refer to a person. One way involves using the first letter of the person's name.


  • John helps people. He works as a doctor. - la djan helba lo pernu. i la D kicmu
  • Mary has arrived. She's in the red car over there. - la Maris godzi le hijra. i la M nenri le redro tcaro va ti

He, She, it

Loglan has no specifi words for "he", "she" or "it". Instead it has variables da, de, di, do, and du, which takes the place of the person or item in the order they appear in a conversation or sentence. So, you can use da to refer to the first person or item mentioned and de for the second person or item as you would use "he", "she" or ""it".


  • John helps people. He works as a doctor. - la djan helba lo pernu. i da kicmu
  • Mary has arrived. She's in the red car over there. - la Maris godzi le hijra. i de nenri le redro tcaro va ti

Chapter 4 Using Loglan

A cartoon written in loglan.


  • Hello - loi
  • Good bye - loa
  • How are you? - tu he
  • How do you feel? - ei tu djela
  • What is your name? - hu namci tu
  • My name is <name> - la <name> namci lemi


  • What is the time? - hu jolkeo
  • The time is <time> - le <time> jolkeo
  • When? What interval of time? - nia hu
  • When? At what point in time? - na hu


  • What did you say? Who? Which? - ie
  • Why? What for? - moi hu
  • What is it? - he
  • How? By what means? Using what? - tie hu
  • What is this? - ti ie
  • What is that? - ta ie
  • Is it true that ...? ei, ...
  • Whatever - rabu, rabe, rabo, raba
  • How did that happen? What caused that to happen? - kou hu
  • How many? - ho
  • How's it going? - tu ie nu vetci
  • Why? For who? - dii hu
  • Why? For what motivation? - moi hu
  • Why? For what reason - rau hu?
  • Why? To please whom? - lui hu
  • Why? According to what premise? - soa hu

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The "Title Page" means, for a printed book, the title page itself, plus such following pages as are needed to hold, legibly, the material this License requires to appear in the title page. For works in formats which do not have any title page as such, "Title Page" means the text near the most prominent appearance of the work's title, preceding the beginning of the body of the text.

The "publisher" means any person or entity that distributes copies of the Document to the public.

A section "Entitled XYZ" means a named subunit of the Document whose title either is precisely XYZ or contains XYZ in parentheses following text that translates XYZ in another language. (Here XYZ stands for a specific section name mentioned below, such as "Acknowledgements", "Dedications", "Endorsements", or "History".) To "Preserve the Title" of such a section when you modify the Document means that it remains a section "Entitled XYZ" according to this definition.

The Document may include Warranty Disclaimers next to the notice which states that this License applies to the Document. These Warranty Disclaimers are considered to be included by reference in this License, but only as regards disclaiming warranties: any other implication that these Warranty Disclaimers may have is void and has no effect on the meaning of this License.


You may copy and distribute the Document in any medium, either commercially or noncommercially, provided that this License, the copyright notices, and the license notice saying this License applies to the Document are reproduced in all copies, and that you add no other conditions whatsoever to those of this License. You may not use technical measures to obstruct or control the reading or further copying of the copies you make or distribute. However, you may accept compensation in exchange for copies. If you distribute a large enough number of copies you must also follow the conditions in section 3.

You may also lend copies, under the same conditions stated above, and you may publicly display copies.


If you publish printed copies (or copies in media that commonly have printed covers) of the Document, numbering more than 100, and the Document's license notice requires Cover Texts, you must enclose the copies in covers that carry, clearly and legibly, all these Cover Texts: Front-Cover Texts on the front cover, and Back-Cover Texts on the back cover. Both covers must also clearly and legibly identify you as the publisher of these copies. The front cover must present the full title with all words of the title equally prominent and visible. You may add other material on the covers in addition. Copying with changes limited to the covers, as long as they preserve the title of the Document and satisfy these conditions, can be treated as verbatim copying in other respects.

If the required texts for either cover are too voluminous to fit legibly, you should put the first ones listed (as many as fit reasonably) on the actual cover, and continue the rest onto adjacent pages.

If you publish or distribute Opaque copies of the Document numbering more than 100, you must either include a machine-readable Transparent copy along with each Opaque copy, or state in or with each Opaque copy a computer-network location from which the general network-using public has access to download using public-standard network protocols a complete Transparent copy of the Document, free of added material. If you use the latter option, you must take reasonably prudent steps, when you begin distribution of Opaque copies in quantity, to ensure that this Transparent copy will remain thus accessible at the stated location until at least one year after the last time you distribute an Opaque copy (directly or through your agents or retailers) of that edition to the public.

It is requested, but not required, that you contact the authors of the Document well before redistributing any large number of copies, to give them a chance to provide you with an updated version of the Document.


You may copy and distribute a Modified Version of the Document under the conditions of sections 2 and 3 above, provided that you release the Modified Version under precisely this License, with the Modified Version filling the role of the Document, thus licensing distribution and modification of the Modified Version to whoever possesses a copy of it. In addition, you must do these things in the Modified Version:

  1. Use in the Title Page (and on the covers, if any) a title distinct from that of the Document, and from those of previous versions (which should, if there were any, be listed in the History section of the Document). You may use the same title as a previous version if the original publisher of that version gives permission.
  2. List on the Title Page, as authors, one or more persons or entities responsible for authorship of the modifications in the Modified Version, together with at least five of the principal authors of the Document (all of its principal authors, if it has fewer than five), unless they release you from this requirement.
  3. State on the Title page the name of the publisher of the Modified Version, as the publisher.
  4. Preserve all the copyright notices of the Document.
  5. Add an appropriate copyright notice for your modifications adjacent to the other copyright notices.
  6. Include, immediately after the copyright notices, a license notice giving the public permission to use the Modified Version under the terms of this License, in the form shown in the Addendum below.
  7. Preserve in that license notice the full lists of Invariant Sections and required Cover Texts given in the Document's license notice.
  8. Include an unaltered copy of this License.
  9. Preserve the section Entitled "History", Preserve its Title, and add to it an item stating at least the title, year, new authors, and publisher of the Modified Version as given on the Title Page. If there is no section Entitled "History" in the Document, create one stating the title, year, authors, and publisher of the Document as given on its Title Page, then add an item describing the Modified Version as stated in the previous sentence.
  10. Preserve the network location, if any, given in the Document for public access to a Transparent copy of the Document, and likewise the network locations given in the Document for previous versions it was based on. These may be placed in the "History" section. You may omit a network location for a work that was published at least four years before the Document itself, or if the original publisher of the version it refers to gives permission.
  11. For any section Entitled "Acknowledgements" or "Dedications", Preserve the Title of the section, and preserve in the section all the substance and tone of each of the contributor acknowledgements and/or dedications given therein.
  12. Preserve all the Invariant Sections of the Document, unaltered in their text and in their titles. Section numbers or the equivalent are not considered part of the section titles.
  13. Delete any section Entitled "Endorsements". Such a section may not be included in the Modified version.
  14. Do not retitle any existing section to be Entitled "Endorsements" or to conflict in title with any Invariant Section.
  15. Preserve any Warranty Disclaimers.

If the Modified Version includes new front-matter sections or appendices that qualify as Secondary Sections and contain no material copied from the Document, you may at your option designate some or all of these sections as invariant. To do this, add their titles to the list of Invariant Sections in the Modified Version's license notice. These titles must be distinct from any other section titles.

You may add a section Entitled "Endorsements", provided it contains nothing but endorsements of your Modified Version by various parties—for example, statements of peer review or that the text has been approved by an organization as the authoritative definition of a standard.

You may add a passage of up to five words as a Front-Cover Text, and a passage of up to 25 words as a Back-Cover Text, to the end of the list of Cover Texts in the Modified Version. Only one passage of Front-Cover Text and one of Back-Cover Text may be added by (or through arrangements made by) any one entity. If the Document already includes a cover text for the same cover, previously added by you or by arrangement made by the same entity you are acting on behalf of, you may not add another; but you may replace the old one, on explicit permission from the previous publisher that added the old one.

The author(s) and publisher(s) of the Document do not by this License give permission to use their names for publicity for or to assert or imply endorsement of any Modified Version.


You may combine the Document with other documents released under this License, under the terms defined in section 4 above for modified versions, provided that you include in the combination all of the Invariant Sections of all of the original documents, unmodified, and list them all as Invariant Sections of your combined work in its license notice, and that you preserve all their Warranty Disclaimers.

The combined work need only contain one copy of this License, and multiple identical Invariant Sections may be replaced with a single copy. If there are multiple Invariant Sections with the same name but different contents, make the title of each such section unique by adding at the end of it, in parentheses, the name of the original author or publisher of that section if known, or else a unique number. Make the same adjustment to the section titles in the list of Invariant Sections in the license notice of the combined work.

In the combination, you must combine any sections Entitled "History" in the various original documents, forming one section Entitled "History"; likewise combine any sections Entitled "Acknowledgements", and any sections Entitled "Dedications". You must delete all sections Entitled "Endorsements".


You may make a collection consisting of the Document and other documents released under this License, and replace the individual copies of this License in the various documents with a single copy that is included in the collection, provided that you follow the rules of this License for verbatim copying of each of the documents in all other respects.

You may extract a single document from such a collection, and distribute it individually under this License, provided you insert a copy of this License into the extracted document, and follow this License in all other respects regarding verbatim copying of that document.


A compilation of the Document or its derivatives with other separate and independent documents or works, in or on a volume of a storage or distribution medium, is called an "aggregate" if the copyright resulting from the compilation is not used to limit the legal rights of the compilation's users beyond what the individual works permit. When the Document is included in an aggregate, this License does not apply to the other works in the aggregate which are not themselves derivative works of the Document.

If the Cover Text requirement of section 3 is applicable to these copies of the Document, then if the Document is less than one half of the entire aggregate, the Document's Cover Texts may be placed on covers that bracket the Document within the aggregate, or the electronic equivalent of covers if the Document is in electronic form. Otherwise they must appear on printed covers that bracket the whole aggregate.


Translation is considered a kind of modification, so you may distribute translations of the Document under the terms of section 4. Replacing Invariant Sections with translations requires special permission from their copyright holders, but you may include translations of some or all Invariant Sections in addition to the original versions of these Invariant Sections. You may include a translation of this License, and all the license notices in the Document, and any Warranty Disclaimers, provided that you also include the original English version of this License and the original versions of those notices and disclaimers. In case of a disagreement between the translation and the original version of this License or a notice or disclaimer, the original version will prevail.

If a section in the Document is Entitled "Acknowledgements", "Dedications", or "History", the requirement (section 4) to Preserve its Title (section 1) will typically require changing the actual title.


You may not copy, modify, sublicense, or distribute the Document except as expressly provided under this License. Any attempt otherwise to copy, modify, sublicense, or distribute it is void, and will automatically terminate your rights under this License.

However, if you cease all violation of this License, then your license from a particular copyright holder is reinstated (a) provisionally, unless and until the copyright holder explicitly and finally terminates your license, and (b) permanently, if the copyright holder fails to notify you of the violation by some reasonable means prior to 60 days after the cessation.

Moreover, your license from a particular copyright holder is reinstated permanently if the copyright holder notifies you of the violation by some reasonable means, this is the first time you have received notice of violation of this License (for any work) from that copyright holder, and you cure the violation prior to 30 days after your receipt of the notice.

Termination of your rights under this section does not terminate the licenses of parties who have received copies or rights from you under this License. If your rights have been terminated and not permanently reinstated, receipt of a copy of some or all of the same material does not give you any rights to use it.


The Free Software Foundation may publish new, revised versions of the GNU Free Documentation License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns. See http://www.gnu.org/copyleft/.

Each version of the License is given a distinguishing version number. If the Document specifies that a particular numbered version of this License "or any later version" applies to it, you have the option of following the terms and conditions either of that specified version or of any later version that has been published (not as a draft) by the Free Software Foundation. If the Document does not specify a version number of this License, you may choose any version ever published (not as a draft) by the Free Software Foundation. If the Document specifies that a proxy can decide which future versions of this License can be used, that proxy's public statement of acceptance of a version permanently authorizes you to choose that version for the Document.


"Massive Multiauthor Collaboration Site" (or "MMC Site") means any World Wide Web server that publishes copyrightable works and also provides prominent facilities for anybody to edit those works. A public wiki that anybody can edit is an example of such a server. A "Massive Multiauthor Collaboration" (or "MMC") contained in the site means any set of copyrightable works thus published on the MMC site.

"CC-BY-SA" means the Creative Commons Attribution-Share Alike 3.0 license published by Creative Commons Corporation, a not-for-profit corporation with a principal place of business in San Francisco, California, as well as future copyleft versions of that license published by that same organization.

"Incorporate" means to publish or republish a Document, in whole or in part, as part of another Document.

An MMC is "eligible for relicensing" if it is licensed under this License, and if all works that were first published under this License somewhere other than this MMC, and subsequently incorporated in whole or in part into the MMC, (1) had no cover texts or invariant sections, and (2) were thus incorporated prior to November 1, 2008.

The operator of an MMC Site may republish an MMC contained in the site under CC-BY-SA on the same site at any time before August 1, 2009, provided the MMC is eligible for relicensing.

How to use this License for your documents

To use this License in a document you have written, include a copy of the License in the document and put the following copyright and license notices just after the title page:

Copyright (c) YEAR YOUR NAME.
Permission is granted to copy, distribute and/or modify this document
under the terms of the GNU Free Documentation License, Version 1.3
or any later version published by the Free Software Foundation;
with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.
A copy of the license is included in the section entitled "GNU
Free Documentation License".

If you have Invariant Sections, Front-Cover Texts and Back-Cover Texts, replace the "with...Texts." line with this:

with the Invariant Sections being LIST THEIR TITLES, with the
Front-Cover Texts being LIST, and with the Back-Cover Texts being LIST.

If you have Invariant Sections without Cover Texts, or some other combination of the three, merge those two alternatives to suit the situation.

If your document contains nontrivial examples of program code, we recommend releasing these examples in parallel under your choice of free software license, such as the GNU General Public License, to permit their use in free software.