Haspelmath (2023): Defining the word

Haspelmath defines a word as a free morph, a clitic, or a root or compound possibly augmented by nonrequired affixes and augmented by required affixes if there are any. A clitic is a bound morph that is neither a root nor an affix, and a required affix is one that must be present in a free form unless another affix replaces it. This file checks the definitions, Morphology.Comparative.IsWordIn and its parts, against the paper's examples, and compares the definition with Bloomfield's minimum free form, which it is meant to correct.

Main results

• to_clitic_zu_prefix: English infinitival to is a clitic and German zu- a prefix.
• genitive_clitic_suffix: English genitive 's is a clitic and German -s a suffix.
• alber_required, geb_required: Italian alber needs the suffix -o or -i and German geb the suffix -en or -t, so the bare roots are not words.
• tree_word: English tree has no required affix, so it is a word, though not a free form.
• bloomfield_too_narrow, bloomfield_too_broad: tree and the clitic to are words but not minimum free forms, and a tree is a minimum free form but not a word.
• wordsAt_affix_words: the words at .affix of the English and Italian forms are words, while a=tree, one word at .clitic, is not.

Implementation notes

Each example is an inventory of the paper's free forms, each a list of morphs with textbook attachment labels, with the classes of its roots. The definition of an affix refers to the roots of Definition 6, which needs a free form with the root as its only contentful morph; on the free forms the paper cites for Definition 2 these are exactly the contentful morphs (roots_contentful), and the other inventories take the contentful morphs as roots. The English article's distribution comes from the 2021 paper's a house, a big house. Compounds are not formalized.

References

• [Blo33]
• [Has21a]
• [Has23]

Roots

def Haspelmath2023.my : Morphology.Morph

The English possessive my.

Equations

• Haspelmath2023.my = Morphology.Morph.procl "my"

def Haspelmath2023.husband : Morphology.Morph

The English object root husband.

Equations

• Haspelmath2023.husband = Morphology.Morph.root "husband"

def Haspelmath2023.a : Morphology.Morph

The English article a.

Equations

• Haspelmath2023.a = Morphology.Morph.procl "a"

def Haspelmath2023.cafe : Morphology.Morph

The English object root café.

Equations

• Haspelmath2023.cafe = Morphology.Morph.root "café"

def Haspelmath2023.he : Morphology.Morph

The English pronoun he.

Equations

• Haspelmath2023.he = Morphology.Morph.procl "he"

def Haspelmath2023.is : Morphology.Morph

The English auxiliary is.

Equations

• Haspelmath2023.is = Morphology.Morph.free "is"

def Haspelmath2023.work : Morphology.Morph

The English action root work.

Equations

• Haspelmath2023.work = Morphology.Morph.root "work"

def Haspelmath2023.ing : Morphology.Morph

The English progressive suffix -ing.

Equations

• Haspelmath2023.ing = Morphology.Morph.suff "ing"

def Haspelmath2023.nice : Morphology.Morph

The English property root nice.

Equations

• Haspelmath2023.nice = Morphology.Morph.root "nice"

def Haspelmath2023.now : Morphology.Morph

The English adverb now.

Equations

• Haspelmath2023.now = Morphology.Morph.free "now"

def Haspelmath2023.ouch : Morphology.Morph

The English interjection ouch.

Equations

• Haspelmath2023.ouch = Morphology.Morph.free "ouch"

def Haspelmath2023.freeForms : List (List Morphology.Morph)

The English free forms cited for Definitions 1 and 2 are nice, work, now, ouch, my husband, a café and he is working.

Equations

• One or more equations did not get rendered due to their size.

def Haspelmath2023.freeFormsClass (m : Morphology.Morph) : Option Morphology.Comparative.RootClass

The classes of the English roots.

Equations

• One or more equations did not get rendered due to their size.

theorem Haspelmath2023.roots_contentful (m : Morphology.Morph) : m ∈ freeForms.flatten → (Morphology.Comparative.IsRootIn freeForms freeFormsClass m ↔ Morphology.Comparative.IsContentful freeFormsClass m)

On these free forms the roots of Definition 6 are the contentful morphs.

Clitics and affixes

def Haspelmath2023.to : Morphology.Morph

The English infinitival to.

Equations

• Haspelmath2023.to = Morphology.Morph.procl "to"

def Haspelmath2023.destroy : Morphology.Morph

The English action root destroy.

Equations

• Haspelmath2023.destroy = Morphology.Morph.root "destroy"

def Haspelmath2023.thorough : Morphology.Morph

The English property root thorough.

Equations

• Haspelmath2023.thorough = Morphology.Morph.root "thorough"

def Haspelmath2023.ly : Morphology.Morph

The English adverbial suffix -ly.

Equations

• Haspelmath2023.ly = Morphology.Morph.suff "ly"

def Haspelmath2023.infinitives : List (List Morphology.Morph)

The English infinitives to destroy and to thoroughly destroy.

Equations

• Haspelmath2023.infinitives = [[Haspelmath2023.to, Haspelmath2023.destroy], [Haspelmath2023.to, Haspelmath2023.thorough, Haspelmath2023.ly, Haspelmath2023.destroy]]

def Haspelmath2023.infinitivesClass (m : Morphology.Morph) : Option Morphology.Comparative.RootClass

The classes of the English roots.

Equations

• One or more equations did not get rendered due to their size.

def Haspelmath2023.aus : Morphology.Morph

The German particle aus 'out'.

Equations

• Haspelmath2023.aus = Morphology.Morph.pref "aus"

def Haspelmath2023.zu : Morphology.Morph

The German infinitival zu-.

Equations

• Haspelmath2023.zu = Morphology.Morph.pref "zu"

def Haspelmath2023.geh : Morphology.Morph

The German action root geh 'go'.

Equations

• Haspelmath2023.geh = Morphology.Morph.root "geh"

def Haspelmath2023.en : Morphology.Morph

The German infinitive suffix -en.

Equations

• Haspelmath2023.en = Morphology.Morph.suff "en"

def Haspelmath2023.ausZuGehen : List (List Morphology.Morph)

The German infinitive aus-zu-gehen 'to go out'.

Equations

• Haspelmath2023.ausZuGehen = [[Haspelmath2023.aus, Haspelmath2023.zu, Haspelmath2023.geh, Haspelmath2023.en]]

def Haspelmath2023.ausZuGehenClass (m : Morphology.Morph) : Option Morphology.Comparative.RootClass

The class of the German root.

Equations

• Haspelmath2023.ausZuGehenClass m = if m = Haspelmath2023.geh then some Morphology.Comparative.RootClass.action else none

theorem Haspelmath2023.to_clitic_zu_prefix : Morphology.Comparative.IsCliticIn infinitives infinitivesClass (Morphology.Comparative.IsContentful infinitivesClass) «to» ∧ Morphology.Comparative.IsAffixIn ausZuGehen ausZuGehenClass (Morphology.Comparative.IsContentful ausZuGehenClass) zu

English to precedes an adverb as well as a verb, so it is a clitic, while German zu- always occurs on a verb root and is a prefix.

def Haspelmath2023.kim : Morphology.Morph

The English and German object root Kim.

Equations

• Haspelmath2023.kim = Morphology.Morph.root "Kim"

def Haspelmath2023.s_gen : Morphology.Morph

The English genitive 's.

Equations

• Haspelmath2023.s_gen = Morphology.Morph.encl "s"

def Haspelmath2023.umbrella : Morphology.Morph

The English object root umbrella.

Equations

• Haspelmath2023.umbrella = Morphology.Morph.root "umbrella"

def Haspelmath2023.the : Morphology.Morph

The English article the.

Equations

• Haspelmath2023.the = Morphology.Morph.procl "the"

def Haspelmath2023.dog : Morphology.Morph

The English object root dog.

Equations

• Haspelmath2023.dog = Morphology.Morph.root "dog"

def Haspelmath2023.bone : Morphology.Morph

The English object root bone.

Equations

• Haspelmath2023.bone = Morphology.Morph.root "bone"

def Haspelmath2023.boy : Morphology.Morph

The English object root boy.

Equations

• Haspelmath2023.boy = Morphology.Morph.root "boy"

def Haspelmath2023.i : Morphology.Morph

The English pronoun I.

Equations

• Haspelmath2023.i = Morphology.Morph.procl "I"

def Haspelmath2023.love : Morphology.Morph

The English action root love.

Equations

• Haspelmath2023.love = Morphology.Morph.root "love"

def Haspelmath2023.genitives : List (List Morphology.Morph)

The English genitives Kim's umbrella, the dog's bone and the boy I love's umbrella.

Equations

• One or more equations did not get rendered due to their size.

def Haspelmath2023.genitivesClass (m : Morphology.Morph) : Option Morphology.Comparative.RootClass

The classes of the English roots.

Equations

• One or more equations did not get rendered due to their size.

def Haspelmath2023.s_genDe : Morphology.Morph

The German genitive -s.

Equations

• Haspelmath2023.s_genDe = Morphology.Morph.suff "s"

def Haspelmath2023.ring : Morphology.Morph

The German object root Ring 'ring'.

Equations

• Haspelmath2023.ring = Morphology.Morph.root "Ring"

def Haspelmath2023.genitivesDe : List (List Morphology.Morph)

The German genitive Kim-s Ring 'Kim's ring'.

Equations

• Haspelmath2023.genitivesDe = [[Haspelmath2023.kim, Haspelmath2023.s_genDe, Haspelmath2023.ring]]

def Haspelmath2023.genitivesDeClass (m : Morphology.Morph) : Option Morphology.Comparative.RootClass

The classes of the German roots.

Equations

• Haspelmath2023.genitivesDeClass m = if m = Haspelmath2023.kim ∨ m = Haspelmath2023.ring then some Morphology.Comparative.RootClass.object else none

theorem Haspelmath2023.genitive_clitic_suffix : Morphology.Comparative.IsCliticIn genitives genitivesClass (Morphology.Comparative.IsContentful genitivesClass) s_gen ∧ Morphology.Comparative.IsAffixIn genitivesDe genitivesDeClass (Morphology.Comparative.IsContentful genitivesDeClass) s_genDe

English 's also follows a verb, so it is a clitic, while German -s always follows a noun and is a suffix.

Required affixes

def Haspelmath2023.alber : Morphology.Morph

The Italian object root alber 'tree'.

Equations

• Haspelmath2023.alber = Morphology.Morph.root "alber"

def Haspelmath2023.o : Morphology.Morph

The Italian singular suffix -o.

Equations

• Haspelmath2023.o = Morphology.Morph.suff "o"

def Haspelmath2023.i_pl : Morphology.Morph

The Italian plural suffix -i.

Equations

• Haspelmath2023.i_pl = Morphology.Morph.suff "i"

def Haspelmath2023.italian : List (List Morphology.Morph)

The Italian free forms alber-o 'tree' and alber-i 'trees'.

Equations

• Haspelmath2023.italian = [[Haspelmath2023.alber, Haspelmath2023.o], [Haspelmath2023.alber, Haspelmath2023.i_pl]]

def Haspelmath2023.italianClass (m : Morphology.Morph) : Option Morphology.Comparative.RootClass

The class of the Italian root.

Equations

• Haspelmath2023.italianClass m = if m = Haspelmath2023.alber then some Morphology.Comparative.RootClass.object else none

theorem Haspelmath2023.alber_required : Morphology.Comparative.IsRequiredAffixIn italian italianClass (Morphology.Comparative.IsContentful italianClass) o alber ∧ ¬Morphology.Comparative.IsWordIn italian italianClass (Morphology.Comparative.IsContentful italianClass) [alber] ∧ Morphology.Comparative.IsWordIn italian italianClass (Morphology.Comparative.IsContentful italianClass) [alber, o]

alber needs -o unless -i replaces it, so -o is a required affix, alber is not a word and alber-o is.

def Haspelmath2023.geb : Morphology.Morph

The German action root geb 'give'.

Equations

• Haspelmath2023.geb = Morphology.Morph.root "geb"

def Haspelmath2023.t : Morphology.Morph

The German imperative plural suffix -t.

Equations

• Haspelmath2023.t = Morphology.Morph.suff "t"

def Haspelmath2023.german : List (List Morphology.Morph)

The German free forms geb-en '(to) give' and geb-t 'give (pl.)'.

Equations

• Haspelmath2023.german = [[Haspelmath2023.geb, Haspelmath2023.en], [Haspelmath2023.geb, Haspelmath2023.t]]

def Haspelmath2023.germanClass (m : Morphology.Morph) : Option Morphology.Comparative.RootClass

The class of the German root.

Equations

• Haspelmath2023.germanClass m = if m = Haspelmath2023.geb then some Morphology.Comparative.RootClass.action else none

theorem Haspelmath2023.geb_required : Morphology.Comparative.IsRequiredAffixIn german germanClass (Morphology.Comparative.IsContentful germanClass) en geb ∧ ¬Morphology.Comparative.IsWordIn german germanClass (Morphology.Comparative.IsContentful germanClass) [geb]

geb takes -en or the alternative required suffix -t, so the bare root is not a word.

def Haspelmath2023.tree : Morphology.Morph

The English object root tree.

Equations

• Haspelmath2023.tree = Morphology.Morph.root "tree"

def Haspelmath2023.s_pl : Morphology.Morph

The English plural suffix -s.

Equations

• Haspelmath2023.s_pl = Morphology.Morph.suff "s"

def Haspelmath2023.house : Morphology.Morph

The English object root house.

Equations

• Haspelmath2023.house = Morphology.Morph.root "house"

def Haspelmath2023.big : Morphology.Morph

The English property root big.

Equations

• Haspelmath2023.big = Morphology.Morph.root "big"

def Haspelmath2023.trees : List (List Morphology.Morph)

The English free forms a tree and trees, with a house and a big house for the article.

Equations

• One or more equations did not get rendered due to their size.

def Haspelmath2023.treesClass (m : Morphology.Morph) : Option Morphology.Comparative.RootClass

The classes of the English roots.

Equations

• One or more equations did not get rendered due to their size.

theorem Haspelmath2023.tree_word : ¬Morphology.Comparative.IsRequiredAffixIn trees treesClass (Morphology.Comparative.IsContentful treesClass) s_pl tree ∧ Morphology.Comparative.IsWordIn trees treesClass (Morphology.Comparative.IsContentful treesClass) [tree] ∧ [tree] ∉ trees

-s can be absent from a free form, as in a tree, without another affix replacing it, so it is not required, and tree is a word although it is not a free form.

Bloomfield's minimum free form (§3.1)

theorem Haspelmath2023.bloomfield_too_narrow : (Morphology.Comparative.IsWordIn trees treesClass (Morphology.Comparative.IsContentful treesClass) [tree] ∧ ¬Morphology.IsMinimalFreeForm trees [tree]) ∧ Morphology.Comparative.IsWordIn infinitives infinitivesClass (Morphology.Comparative.IsContentful infinitivesClass) [«to»] ∧ ¬Morphology.IsMinimalFreeForm infinitives [«to»]

Bloomfield's definition is too narrow: tree and the clitic to are words but not free forms, so not minimum free forms.

theorem Haspelmath2023.bloomfield_too_broad : Morphology.IsMinimalFreeForm trees [a, tree] ∧ ¬Morphology.Comparative.IsWordIn trees treesClass (Morphology.Comparative.IsContentful treesClass) [a, tree]

Bloomfield's definition is too broad: a tree cannot be broken up into free forms, so it is a minimum free form, but it is a clitic and a root, not a word.

Words at an attachment

theorem Haspelmath2023.wordsAt_affix_words : (∀ f ∈ trees, ∀ w ∈ Morphology.Morph.wordsAt Morphology.Morph.Attachment.affix f, Morphology.Comparative.IsWordIn trees treesClass (Morphology.Comparative.IsContentful treesClass) w) ∧ (∀ f ∈ italian, ∀ w ∈ Morphology.Morph.wordsAt Morphology.Morph.Attachment.affix f, Morphology.Comparative.IsWordIn italian italianClass (Morphology.Comparative.IsContentful italianClass) w) ∧ Morphology.Morph.wordsAt Morphology.Morph.Attachment.clitic [a, tree] = [[a, tree]] ∧ ¬Morphology.Comparative.IsWordIn trees treesClass (Morphology.Comparative.IsContentful treesClass) [a, tree]

The words at .affix of the English forms with tree and of the Italian forms are words, while a=tree, one word at .clitic, is not.