-I-

(i)  for all X,Y subset E: (X in Q and Y in Q) <=> union(X,Y) in Q

(ii) a Only dogs bark and only dogs run <=> only dogs bark or run
     b Not all dogs bark and not all dogs run <=/=> not all dogs bark or run

Idiom
Fixed combination of elements with an idiosyncratic (not (completely) °compositional) meaning, such as kick the bucket, spill the beans. Idioms are generally inaccessible for syntactic and/or semantic variation: sentence (ii) cannot mean that some people died last week.

(i)    He kicked the bucket last week
(ii) * Some buckets were kicked last week

(iii)  advantagei was taken ti of Bill
(iv)   he kicked the proverbial bucket

Idiosyncrasy
MORPHOLOGY: a property of words or phrases which cannot be derived by the rules of a language. Words can be idiosyncratic in a variety of ways: (a) semantically (by having some unpredictable aspect to their meaning), (b) phonologically (by being an exception to a phonological rule), or (c) morphologically (by being an exception to a word formation rule). EXAMPLE: an idiosyncratic property of the English verb derive is that it does not have a nominal counterpart formed with the suffix -al (*derival).
LIT. Halle (1973), Spencer (1991).

Iff
SEMANTICS: the abbreviation of if and only if, which is used as °equivalence in mathematical statements and the logical °meta language. Also indicated by <->.
LIT. Gamut (1991).

Illocutionary act
°Speech act.

Illocutionary force
SEMANTICS: the status of an utterance as a question, promise, threat, etc. This term should not be confused with illocutionary act, which is a °speech act, expressing the intention of the speaker. EXAMPLE: the sentence Do you know what time it is? is uttered with the illocutionary force of a yes-no question, but uttering it is an illocutionary act of a request: it would be improper to answer with a simple 'yes'.
LIT. Austin (1962).

Immediate dominance
°Dominance.

Immediate precedence
°Precedence.

Imperative
Sentence type expressing an order, or request:

(i)  Tell me about it.

(ii) Vertel (jij) me eens hoe dat zit(?)
     'Tell (you) me now how it is'

Imperfective
°Aspect.

Implication
SEMANTICS: 1. (material implication) the combination in °propositional logic of two formulae with the connective -> (if ... then ...), also called conditional. The implication of phi and psi, phi -> psi, is only false if phi (which is called the antecedent) is true while psi (the consequent) is false:

(i)	phi		psi	phi -> psi
	 1		 1	    1
	 1		 0	    0
	 0		 1 	    1
	 0		 0	    1

(ii) (p V q) -> q

Implicit transposition
°Conversion.

Improper movement
SYNTAX: illicit movement from an °A-bar-position to an A-position, as in (i):

(i) * [IP Johni seems [CP t'i [IP ti knows it all]]]

Improperness
°Properness.

Inalienable possession
SEMANTICS: the possessive relation that a person has with his body parts or properties, as distinguished from the possessive relation with things that he can give away or loose. EXAMPLE: John has blue eyes is a case of inalienable possession, while John has a blue car is a case of alienable possession. The notion of inalienable possession is also used to explicate the ambiguity of e.g. John broke his leg: in the reading which is closest to John's leg broke, his designates inalienable possession.

Inchoative
MORPHOLOGY/SEMANTICS: term used for verbs whose meanings can be paraphrased as 'TO BEGIN TO...' (e.g. inflame and depopulate) or verbs which express the beginning of a state or process, like harden (become hard), die (become dead) or break. The term is also used in explicating the ambiguity of John will eat his lunch in an hour: the inchoative reading is the one in which it will take an hour before John is to eat his lunch.

Inclusion
°Dominance.

Incorporation
SYNTAX/MORPHOLOGY: a phenomenon by which a word, usually a verb, forms a kind of compound with, for instance, its direct object or adverbial modifier, while retaining its original syntactic function. Chukchee, a paleosiberian language spoken in North Eastern Siberia, provides a wealth of examples. The constructions in (i) and (ii) have the same meaning and use the same roots. However, in (ii) the root qora 'reindeer' has been incorporated into the verb:

(i)  t@	-pelark@n	qoran@		`I'm leaving the reindeer'
     I	-leave		reindeer
(ii) t@	-qora-pelark@n				ibid

Indefinite article
°Determiner.

Index
Diacritic to indicate °coreference, as in:

(i) Johni loves himselfi

Indexicality
°Deixis.

Indirect context
°Opaque context.

Indirect question
Question which is embedded in a sentence:

(i) I wonder [who she is]

Individual constant
SEMANTICS: a basic expression of °predicate logic which refers to one specific individual in the °universe of discourse. For individual constants lowercase characters from the beginning of the alphabet are used.
LIT. Gamut (1991).

Individual term
SEMANTICS: an expression in °predicate logic which can figure as an argument of a predicate and which denotes an individual in the °universe of discourse. Mostly used as a cover term for individual constants and individual variables. Both refer to entities or individuals in a universe of discourse. In predicate logic language, individual terms are represented with lowercase characters.
LIT. Gamut (1991).

Individual variable
SEMANTICS: a basic expression of °predicate logic which is used as a place-holder with a °predicate letter, instead of an °individual constant. In effect, it stands for an unspecified argument of the predicate. Individual variables can be bound by °quantifiers, and are indicated by characters of the end of the alphabet.
LIT. Gamut (1991).

Infinitivus pro Participio (IPP)
SYNTAX: idiosyncratic property of Dutch verb-clusters in perfect tense. Compare (i) and (ii):

(i)   *	Jan heeft gemoeten kiezen
	Jan has   must_PART choose
(ii)	Jan heeft moeten kiezen
	Jan has   must_INF choose
	'Jan has had to choose'

Infix
MORPHOLOGY: an °affix which is placed inside another morpheme. EXAMPLE: Tagalog, a language spoken at the Philippines, has a number of infixes. From the monomorphemic root sulat 'writing' the derived verb sumulat 'to write' is formed by infixing -um- after the initial consonant. The existence of infixes is not uncontroversial. Broselow & McCarthy (1983) and McCarthy (1986) argue that infixation is just a special kind of prefixation or suffixation.

INFL
SYNTAX: functional head containing (in English) °auxiliaries and/or tense and/or agreement features. Also written as I (I⁰). More recently, INFL has been reinterpreted as a conflation of two separate heads °AGR(eement) and °T(ense).
LIT. Chomsky (1981, 1991), Pollock (1989).

Inflection
MORPHOLOGY: one of the main types of morphological operations by which an affix is added to a word. An inflectional affix adds a particular grammatical function to a word without changing the category of that word, or even leading to a different word. We may say that inflected forms are just variants of one and the same word. EXAMPLE: count nouns in English can be pluralized by adding the inflectional ending -s (dog-dogs, noun-nouns). The plural forms dogs and nouns are variants of the base nouns dog and noun. Traditionally inflection is distinguished from °derivation (the second type of major morphological operation). Although it is not possible to draw a sharp border between both types of operation, there are at least two differences: (i) inflection is never category changing, while derivation typically is category changing, and (ii) inflection is usually peripheral to derivation. Some linguists (e.g. Aronoff (1976), Anderson (1982), Perlmutter (1988)) assume that inflection and derivation belong to different components of the grammar. This view is not uncontroversial though, since others (e.g. Halle (1973), Kiparsky (1982)) assume that inflection and derivation are reflexes of one and the same operation, namely affixation.
SYNTAX: inflectional affixes have recently been analyzed as the source or head of °functional projections like °IP,°AGRP, °DP, etc. EXAMPLE: if (i)a is the underlying syntactic structure of John walks, the ultimate stage of which is the result of either Affix hopping (cf. (i)b) or °Verb movement (cf. (i)c) (both syntactic operations) then inflection is not a morphologcal but a syntactic phenomenon.

(i)  a  [IP John [I' [I -s ] [VP [V walk ]]]]
     b  [IP John [I' ej [VP [V [V walk ] [I -s ]j ] ]]]
     c  [IP John [I' [I [V walk ]j [I -s ]] [VP ej ]]]

(ii) a  [IP John [I' [I e ] [VP [V walks ]]]]
     b  [IP John [I' [I [V walks ]j [I e ]] [VP ej ]]]

Inherent case
SYNTAX: °Case which is dependent on °theta-marking (as opposed to °structural case). Also 'oblique case'. Usually Genitive, Dative, and Partitive are considered inherent case. EXAMPLE: the assignment of genitive case by a noun is inherent, hence must coincide with theta-marking. This implies that a noun cannot be the case-assigning head in an °ECM construction, and no °Raising to Subject in an NP is possible. Hence the illformedness of (i) and (ii).

(i)   * John's belief [ Mary's/of Mary to be a spy ]
(ii)  * John's appearance [ t to be a spy ]

Inheritance
A process in which a category 'inherits' some feature of a lower category. MORPHOLOGY: the phenomenon that a category can inherit (part of) the °argument structure of the category from which it is derived. EXAMPLE: the noun driver is said to inherit the internal argument of the verb drive from which it is derived, cf. Rochelle drives trucks / Rochelle is a driver of trucks, where trucks is the internal argument.
LIT. Sproat (1985), Booij (1988), Spencer (1991).
SYNTAX: in the °Barriers theory of Chomsky (1986b) a maximal projection is said to inherit barrierhood in case the first maximal projection it dominates is a °Blocking Category.
LIT. Chomsky (1986b).

Insert alpha
SYNTAX: instance of the general transformational rule 'affect alpha'. Few rules that insert material in the course of a derivation are currently being defended. Some examples are of-insertion, and post-d-structure insertion of the subject of °tough-movement constructions.
LIT. Chomsky (1981).

Intension
SEMANTICS: a technical term for meaning, used in opposition to the notion °extension. The extension of an expression is the class of objects to which that expression refers, the intension is the abstract concept or property which determines the applicability of the expression and hence the extension. In °intensional logic and °Montague Grammar the intension of an expression is a function which gives the extension in every possible world.
LIT.: Gamut (1991).

Intensional adjectives
SEMANTICS: adjectives like former and possible, which, in constructions like former president and possible candidate, cannot be interpreted as sets of entities that are 'former' or 'possible', as would be the case with °extensional adjectives like red. The phrase the former president does not denote the individual that is both a president and 'former', but it denotes the individual that was president in a preceding term. In this way intensional adjectives manipulate the temporal or modal parameter that is relevant for the interpretation of the nouns they combine with.
LIT. Chierchia & McConnell-Ginet (1990).

Intensional context
°Opaque context.

Intensional logic
SEMANTICS: a cover term for those extensions of °propositional logic and °predicate logic in which truth and reference are construed relative to possible worlds, moments of time, or contexts. Modal logic and temporal logic are the two most important instances of intensional logic. Modal logic studies the logic of possibility and necessity, and temporal logic studies the logic of time by means of tense operators. In °Montague Grammar an intensional logic is used in which a formal distinction can be made between the °extension and °intension of an expression.
LIT.: Gamut (1991).

Interface
SYNTAX: level of syntactic representation which interacts with (maps onto) other cognitive systems. LF and PF are considered interfaces by 'virtual necessity'.

Internal argument
MORPHOLOGY/SYNTAX: the °argument of a verb that has to be realized inside the maximal projection of that verb. Each verb may have one or more internal arguments. The argument which is closest to the verb is sometimes called the direct internal argument, while the others are called the indirect internal arguments. EXAMPLE: the argument structure of the English transitive verb open contains an °external argument (Agent) and two internal arguments (Theme and Instrument) as can be inferred from the sentence Tom opened the door with his key, where the door is the direct internal argument, and with his key the indirect internal argument.
LIT. Williams (1981b), Levin & Rappaport (1986), Spencer (1991).

Internal domain (of A)
SYNTAX: (minimalist theory) the minimal °complement domain (of A).
LIT. Chomsky (1992).

Internal negation
SEMANTICS: the internal negation of a °generalized quantifier Q is the set of complements of the sets in Q with respect to E. Formally:

(i) Q Neg = { X subset E : (E - X) in Q }

Internal theta-role
SYNTAX: the °theta-role assigned to an °internal argument.
LIT. Chomsky (1981, 1986a), Williams (1980).

Internalization
MORPHOLOGY: a process by which the °external argument of the base becomes the °internal argument of the derived word. Internalization has two stages. First, the addition of a new external argument, and then °demotion of the old external argument to internal position. EXAMPLE: the English adjective modern has the external argument theme (the factory is modern). If the verbal suffix -ize is added, this theme argument becomes the internal argument due to the fact that -ize itself supplies the external argument agent (they modernized the factory).
LIT. Williams (1981b), Di Sciullo & Williams (1987), Spencer (1991).

Interpretation
°Semantic interpretation.

Interpretation function
SEMANTICS: the function mapping constants of °predicate logic to their denotation in the universe of discourse. °Individual constants are mapped to individuals and n-place predicate letters are mapped to sets of ordered n-tuples,
LIT. Gamut (1991).

Interpretive rules
SEMANTICS: rules that interpret syntactic structures in terms of a semantic representation or in terms of truth and reference. In a strictly °compositional semantics (e.g. °Montague Grammar), there will be a interpretive rule for every syntactic rule.

Interpretative semantics
A branch of generative grammar which, in the seventies, opposed °generative semantics by defending a model of grammar with an autonomous syntax and a distinct semantic component of interpretive rules.
LIT. Chomsky (1972), Jackendoff (1972), Newmeyer (1980).

Intersective adjective
°Extensional adjective.

IP
SYNTAX: Inflection Phrase. The °functional projection of INFL.
LIT. Chomsky (1986b).

IPP
°Infinitivus pro Participio.

IS A Condition
MORPHOLOGY: a condition proposed by Allen (1978) to express two salient facts about compounds: (a) the syntactic category of a compound is determined by its rightmost member, (b) the meaning of a compound is contained in the meaning of its rightmost member. EXAMPLE: the English compound houseboat is a noun as is boat, and a houseboat is a kind of boat. The Is A Condition is the predecessor of Williams' (1981a) °Righthand Head Rule.
LIT. Allen (1978).

Island
SYNTAX: domain which does not allow extraction. Most of the islands distinguished today were first described in Ross (1967). EXAMPLE: Well-known examples are wh-islands, Complex NP's and coordinate structures. The restrictions on extractability (Island conditions) are often designated as the °Wh-island Condition, the °Complex NP Constraint (CNPC), and the °Coordinate Structure Constraint (CSC), respectively. °Bounding theory.
LIT. Ross (1967).

Island Condition
°Island.

Isolating language
MORPHOLOGY: a traditional term used for languages in which there is very little (overt) morphology. Separate grammatical concepts or functions tend to be conveyed by separate words and not by morphological processes. Chinese and Vietnamese are isolating languages.

It-cleft
°Cleft.

I-within-i condition
SYNTAX: well-formedness condition in the °GB-framework:

(i) * [A ... B ...] where A and B bear the same index