·English Semantics - Glossary Part III (Chapters 9-11)

Accidents

(Aristotle) Possible but not defining features of a thing (in contrast to the essence of that thing).

Essential

(Aristotle) The kind of features that are needed to describe a thing and that define the category.

True

(Correspondence theory) A successful match between a utterance and a situation. (Semantic interpretation of predicate logic symbols - Set theory) Represented by *(T)* and also symbolized by the numeral *1*, it is a match between a whole sentence and the situation it describes. [p]v = 1

False

(Correspondence theory) An unsuccessful match between a utterance and a situation. (Semantic interpretation of predicate logic symbols - Set theory) Represented by *(F)* and also symbolized by the numeral *0*, it is a mismatch between a whole sentence and the situation it describes. [p]v = 0

Truth conditions

(Correspondence theory) The conditions in the world that would make a sentence true.

Event schema

(Hovav&Levin) A verb's grammatically relevant features.

Root meaning

(Hovav&Levin) The idiosyncratic component of a verb's meaning. Each one belongs also to an ontological classification, for example state, result state, manner, instrument, and so on.

Conceptual semantics

(Jackendoff) A decompositional theory of meaning whose central principle is that describing meaning involves describing mental representations, in Jackendoff this is called the *Mentalist Postulate*: Meaning in natural language is an information structure that is mentally encoded by human beings. In this approach semantic components break down into smaller, simpler, semantic components.

Groups

(Jackendoff) A semantic class of nouns. [+b, +i] collective nouns (a government, a committee...)

Individuals

(Jackendoff) A semantic class of nouns. [+b, -i] count nouns (a banana, a car...)

Aggregates

(Jackendoff) A semantic class of nouns. [-b, +i] plural nouns (bananas, cars...)

Substances

(Jackendoff) A semantic class of nouns. [-b, -i] mass nouns (water, oxygen...)

Conceptual structure

(Jackendoff) It has a syntax of its own: semantic categories are built up from simpler elements by rules of combination.

THINGS

(Jackendoff) Semantic classes of nominals or nouns. *Features:* *[±BOUNDED]*: to distinguish between count nouns [+BOUNDED]/[+b] and mass nouns [-BOUNDED]/[-b]. The idea is that count nouns are basically units (if we divide up a banana we don't get further instances of the basic unit; on the other hand we can divide a gallon of water into eight pints of water. *[±INTERNAL STRUCTURE]*: to distinguish between plural count nouns [+INTERNAL STRUCTURE]/[+i] and mass nouns [-INTERNAL STRUCTURE]/[-i]. *Semantic classes of nouns:* *individuals*: [+b, -i] count nouns (a banana, a car...) *groups*: [+b, +i] collective nouns (a government, a committee...) *substances*: [-b, -i] mass nouns (water, oxygen...) *aggregates*: [-b, +i] plural nouns (bananas, cars...)

Semantic categories

(Jackendoff) They are: Event, State, Material Thing (or Object), Path, Place and Property. At the level of conceptual structure a sentence is built up of them.

Containment schema

(Johnson) A kind of image schema which derives from our experience of the human body itself as a container; from experience of being physically located ourselves within bounded locations like rooms, beds, and so on; and also of putting objects into containers.

Image schema

(Johnson) A primitive level of conceptual category underlying metaphor and which provide a link between bodily experience and higher cognitive domains such as language. Some examples are: *containment schema*, *path schema* and *force schema*.

Gestalt structures

(Johnson) A term to refer to schema as parts which "hang together" in a way that is motivated by experience. "An organized, unified whole within our experience and understanding that manifests a repeatable pattern or structure. Some people use the term "gestalt" to mean a mere form or shape with no internal structure. In contrast to such a view, my entire project rests on showing that experiential gestalts have internal structure that connects up aspects of our experience and leads to inferences in our conceptual structure." - Johnson

Idealized cognitive models (ICMs)

(Lakoff) (*Cognitive semantics*) (ICMs) Categories that are related to bodies of real-world knowledge, which themselves are conceptual structures. They represent belief systems and theories about the world that underpin linguistic communication. They are culturally based linked domains of knowledge.

Radial categories

(Lakoff) (*Cognitive semantics*) A term suggesting that lexical items form a type of complex category. These categories have a prototypical sense and the structure of the category is represented by links to other related senses. The links are conventionalized and therefore learned rather than inferred in context. In this view lexemes are stored as complex categories that show typicality effects. These categories are culturally specified.

Cognitive semantics

(Lakoff) A theory on semantics that states that there is no separation of linguistic knowledge from general thinking or cognition. Contrary to the influential views of the philosopher Jerry Fodor or of Noam Chomsky, the scholars in this group see linguistic behaviour as another part of the general cognitive abilities which allow learning, reasoning, and so on. The studies in this theory have tended to blur, if not ignore, the commonly made distinctions between linguistic knowledge and encyclopedic, real-world knowledge; and between literal and figurative language. A kind of semantics that take the view that we have no access to a reality independent of human categorization and that therefore the structure of reality as reflected in language is a product of the human mind. Consequently they reject the *correspondence theory of truth*. For these writers, linguistic truth and falsity must be relative to the way an observer construes a situation, based on his or her conceptual framework. The real focus of investigation should, in this view, be these conceptual frameworks and how language use reflects them.

Middle constructions

(Levin) One of the types of involving alternations of argument structure in which verbs like 'cut' and 'break' can be grouped, but not 'touch' or'hit' (so verb classes can be set up within this approach). Example: These shirts wash well. This car drives very smoothly. The bread cuts easily. Crystal vases break easily. ˟Cats touch easily. ˟Door frames hit easily.

Body part ascension constructions

(Levin) One of the types of involving alternations of argument structure in which verbs like 'touch', 'hit' and 'cut' can be grouped, but not 'break' (so verb classes can be set up within this approach). Example: Mary slapped Fred's face. Mary slapped Fred in the face. Igor tapped Lavinia's shoulder. Igor tapped Lavinia on the shoulder. Margaret cut [Bill's arm / Bill on the arm]. Janet broke [Bill's finger / ˟Bill on the finger]. Terry touched [Bill's shoulder / Bill on the shoulder]. Carla hit [Bill's back / Bill on the back].

Markerese

(Lewis) A pejorative way of referring to a metalanguage (a language of primitive elements).

Intersection

(Semantic interpretation of predicate logic symbols - Set theory) ...of sets. Represented by *A ∩ B*, which is the set consisting of the elements which are members of both A and B, e.g. {Venus, Mars, Jupiter, Saturn} ∩ {Mars, Jupiter, Uranus, Pluto} = {Mars, Jupiter}

Sentence

(Semantic interpretation of predicate logic symbols - Set theory) Also called whole sentence. It is the match (true) or lack of match (false) with the situation it describes.

Ordered pair

(Semantic interpretation of predicate logic symbols - Set theory) Represented by *<a, b>*, where the ordering is significant, e.g. <Mercury, Venus> ≠ <Venus, Mercury>

Ordered n-tuple

(Semantic interpretation of predicate logic symbols - Set theory) Represented by *<a1, a2, a3 ... an>*, e.g. the 4-tuple <Mercury, Venus, Earth, Mars>

Subset

(Semantic interpretation of predicate logic symbols - Set theory) Represented by *A ͟c B*, where every member of A is a member of B, e.g. {Venus, Jupiter} ͟c {x: x is a planet in the solar system}

Set membership

(Semantic interpretation of predicate logic symbols - Set theory) Represented by *x Є A*, e.g. Mercury Є {x: x is a planet in the solar system}

Set

(Semantic interpretation of predicate logic symbols - Set theory) Represented by *{...}* and which can be identified by listing members, e.g. {Mercury, Mars, Earth...} or by describing an attribute of the members, e.g. {x: x is a planet in the solar system}.

Cardinality of A

(Semantic interpretation of predicate logic symbols - Set theory) Represented by *ǀAǀ*, which is the number of member in A. ǀAǀ = five (A has five members). ǀAǀ > ǀBǀ (A has more members than B) ǀAǀ - ǀBǀ (The set of members of A that are not also members of B)

Predicate constants

(Semantic interpretation of predicate logic symbols - Set theory) They identify the sets of individuals for which the predicate holds.

Constant terms

(Semantic interpretation of predicate logic symbols - Set theory) Individuals or sets of individuals in the situation. Example: v = The 1974 world heavyweight title fight between Muhammad Ali and George Foreman in Zaire. a = Ali, f = Foreman, r = referee

Classical theory

(Taylor) A theory whose implications are: a. Word meanings can be defined in terms of sets of features. b. The features are individually necessary and jointly sufficient. c. Categories have clear boundaries. d. All members of a category have equal status. e. The features are binary. This theory is *rejected by cognitive semantics* that identifies it with formal approaches to language; that is because: 1) It proves impossible to establish the set of defining features that is shared by all members of a lexical category. 2) The theory is psychologically implausible given the evidence of prototypicality effects, where for example, speakers' behaviour seems to show that they view some members of a category as better examples than others.

Connectives in propositional logic

*Connective*....*Syntax*....*English* ......¬................¬*p*..........It isn't the case that *p* ......^................*p*^*q*........*p* and *q* ......˅................*p*˅*q*.........*p* and/or *q* ......˅e..............*p*˅e*q*.......*p* or *q* but not both ......->..............*p*->*q*........if *p*, then *q* ......≡..............*p*≡*q*........*p* if and only if *q*

Rules

... of containment schema (Johnson)

Correspondence theory

... of truth. A theory employed by formal semanticists to characterize the relation between representational and denotational meaning. Speakers are held to be aware of what situation an utterance describes and to be able to tell whether the utterance and the situation match up or *correspond*. A successful match is called *true*, and an unsuccessful match is called *false*. Another way of describing this is to say that the listener who understands the sentence is able to determine the *truth conditions* of the uttered sentence, that is, know what conditions in the world would make the sentence true.

Relational

... view of quantifying determiners. It treats the determiner as a two-place predicate taking sets as arguments.

Functional

... view of quantifying determiners. The determiner is viewed as a function that maps a common noun denotation onto a noun phrase, which is the generalized quantifier. The generalized quantifier then takes a VP denotation as an argument to build propositions.

Opaque

...contexts. This term figuratively describes the fact that the truth or falsity of the subordinate clause seems to be independent of the truth or falsity of the whole sentences. Example: Jones believes *that Punakha is in Bhutan*. Jones believes *that Paris is in Japan*.

Logical operators

...for modal logics. 1. Symbolized by ◊, expressing "it is possible that" (it is true in some possible worlds). 2. Symbolized by □, expressing "it is necessary that" (it is true in all possible worlds). They can be put in front of any formula of the predicate logic.

Conative constructions

...involving 'at'. (Levin) One of the types of involving alternations of argument structure in which verbs like 'hit' and 'cut' can be grouped, but not 'touch' or'break' (so verb classes can be set up within this approach). Example: He chopped the meat. He chopped at the meat. They shot the bandits. They shot at the bandits. Margaret cut at the bread. ˟Janet broke at the vase. ˟Terry touched at the cat. Carla hit at the door.

Prototype model

...of categories (Rosch). A theory which has been the most powerful influence on cognitive semantics about categories. The claims of this theory can be summarized as: a. Categories have fuzzy boundaries. b. There are central and peripheral members of a category. c. Categories have marginal examples whose membership is doubtful. d. Category members do not all share the same discrete features. e. Attributes are not all binary features but may be from a range of mental representations including images, schemas, exemplars, etc.

Implications

...of containment schema (Johnson) Natural inferences about containment, "entailments".

Categorization

A central view in *cognitive semantics* is that semantic structure, along with cognitive domains, reflects the *mental categories* which people have formed from their experience of growing up and acting in the world. This view has several consequences: the first is a rejection of classical theories of categories, the second is the acceptance of embodiment theories, and the third is to dissolve the distinction between linguistic and encyclopedic knowledge in the use of lexical categories.

Model

A formal structure representing linguistically relevant aspects of a situation. This term refers also to the *domain* (a model of a situation which identifies the linguistically relevant entities, properties and relations) and *naming function* (a procedure, or set of procedures, which match the logical symbols for nouns, verbs, etc. with the items in the model that they denote) together.

Binary features

A format which is used for semantic components similar to that used in phonology and syntax. This allows a characterization of antonyms by a difference of the value plus or minus a feature, and so offers a more economical format. woman - [+FEMALE] [+ADULT] [+HUMAN] bachelor - [-FEMALE] [+ADULT] [+HUMAN] [-MARRIED] spinster - [+FEMALE] [+ADULT] [+HUMAN] [-MARRIED] wife - [+FEMALE] [+ADULT] [+HUMAN] [+MARRIED]

Synchronic linguistics

A kind of linguistics where considerations of historical change might be ignored, as if in describing a language we could factor out or "freeze" time.

Objectivist semantics

A kind of semantics rejected by cognitive semantics that has the basic metaphysical belief that categories exist in objective reality, together with properties and relations, independently of consciousness. Associated with this is the view that the symbols of language are meaningful because they are associated with these objective categories. This gives rise to a particular approach to semantics which Lakoff characterizes under three "doctrines".

Locative alternation verbs

A kind of verbs for which the speaker can choose between alternate mappings, or *linkings*, between grammatical and theta-roles. Example: He *loaded* newspapers onto the van. He *loaded* the van with newspapers. She *sprayed* pesticide onto the roses. She *sprayed* the roses with pesticide. (In the second versions there is an interpretation of completeness, while this is not true of the first versions). (Rappaport&Levin / Pinker) *1)* Verbs of movement with the semantic structure "X causes Y to move into/onto Z": a. Simple motion verbs: 'put, push...' b. Motion verbs which specify the motion (especially manner): 'pour, drip, slash...' These typically have an argument structure where the THEME argument occurs as object and the GOAL argument occurs in an 'into/onto'-prepositional phrase. *2)* Verbs of change of state with the semantic structure "X causes Z to change state by means of moving Y into/onto it": 'fill, coat, cover...'. These typically have an argument structure where the PATIENT occurs as the object and what we might call the INSTRUMENT occurs in a 'with'-prepositional phrase. *3)* Verbs of movement which share the semantic structure "X causes Y to move into/onto Z" with verbs such as 'brush' and thus can have the same argument structure, but which also describe a kind of motion which causes an effect on the entity Z: 'spray, paint, brush...' This class allows the speaker a choice: either to emphasize the movement or to focus on the change of Z's state. Vera sprayed paint onto the wall. Vera sprayed the wall with paint. *4)* Verbs describing removal: a. Verbs of removal with the semantic structure "X causes Y to go away from Z": 'remove, take..." These verbs have the THEME as direct object and the SOURCE in a 'from'-prepositional phrase, and no other pattern. b. Verbs which share the shame semantic structure "X causes Y to go away from Z" but include specification of the means of removal, either: -the manner of removal: 'wipe, rub, scrub...' -the instrument of removal: 'brush, hose, mop...' These verbs occur with the same pattern as a. but can also occur with the SOURCE as direct object and no overt THEME. c. Verbs which have the semantic structure "X causes Z to change by removing Y": change of state verbs which focus on the resultant state: 'clear, empty, drain...' These verbs allow an alternation between two patterns: the first is the argument structure shared with the other two classes, where the THEME is direct object and the SOURCE is in a 'from'-prepositional phrase, and the second is where the SOURCE occurs as direct object and the THEME in an 'of'-prepositional phrase.

Incompatibility

A lexical relation between words, also called less generally antonymy. Lexical items P, Q, R... are incompatible if they share a set of features but differ from each other by one or more contrasting features. Example: bachelor - [MALE] [ADULT] [HUMAN] [UNMARRIED] spinster - [FEMALE] [ADULT] [HUMAN] [UNMARRIED] wife - [FEMALE] [ADULT] [HUMAN] [MARRIED]

Hyponymy

A lexical relation between words. A lexical item P can be defined as a hyponym of Q if all the features of Q are combined in the feature of P. Example: woman - [FEMALE] [ADULT] [HUMAN] spinster - [FEMALE] [ADULT] [HUMAN] [UNMARRIED]

Domain

A model of a situation which identifies the linguistically relevant entities, properties and relations. (See Model-theoretical semantics)

Grammaticalization

A process where lexical categories may over time develop into functional categories and independent words become inflections.

Generalized quantifier theory

A proposal which derives from an application of set theory in mathematical logic. It is a translation of a noun phrase as a set of sets. Example: [Most] students are hardworking. *Most (A, B) = 1 iff ǀA ∩ Bǀ > ǀA -Bǀ*.......(Most A are B is true if the cardinality of the set of things that are both A and B is greater than the cardinality of the set of things which are A but not B) *All (A, B) = 1 iff A ͟c B*.......(All A are B is true if and if only set A is a subset of set B) *Some (A, B) = 1 iff A ∩ B ≠ ∅*.......(Some A are B is true if and only if the set of things which are members of both A and B is not empty) *No (A, B) = 1 iff A ∩ B ≠ ∅*.......(No A are B is true if and only the set of things which are members of both A and B is empty) *Fewer than seven (A, B) = 1 iff ǀA ∩ Bǀ < 7*.......(Fewer than seven As are B is true if and only if the cardinality of the set of things which are members of both A and B is less than seven)

Open proposition

A proposition which is incomplete because is a generalization: until the value of x is set for some individual(s) the expression cannot be true or false. ∀x (S(x) -> W(x, p)) (For every thing x, if x is a student then x wrote a paper.)

Evidentiality

A semantic system that allows speakers to communicate their attitudes toward the source of information conveyed in their propositions. In some languages this is an obligatory feature represented by morphological marking, often on the verb. Typically such systems distinguish between types of direct knowledge, from witnessing something, and other, indirect forms, including inference and being told.

Modality

A semantic system, or systems, that allow speakers to express varying degrees of commitment to a proposition. It is typically divided into *deontic*, relating to judgments of social obligation, permission, and prohibition, and *epistemic*, relating to judgments of fact.

INSTRUMENT

A thematic role which is also called the "state changer" by Pinker; while Rappaport and Levin call it the "displaced theme". This role may be paraphrased as: "entities which by being moved cause a change of state in something to/from which they are moved."

Deontic modality

A type of modality that allows the expression of obligation and permission, often in terms of morality and law.

Epistemic modality

A type of modality that concerns the resources available to the speaker to express judgement of fact versus possibility. Allan's scale of implicatures such that each is stronger than the next about the fact of *p*: a. I know that *p*. b. I am absolutely certain that *p*. c. I am almost certain that *p*. d. I believe that *p*. e. I am pretty certain that *p*. f. I think that *p*. g. I think/believe that *p* is probable. h. I think/believe that perhaps *p*. i. Possibly *p*. j. I suppose it is possible that *p*. k. It is not impossible that *p*. l. It is not necessarily impossible that *p*. m. It is unlikely that *p*. n. It is very unlikely that *p*. o. It is almost impossible that *p*. p. It is impossible that *p*. q. It is not the case that *p*. r. It is absolutely certain that not-*p*.

Predicate logic

A universal metalanguage that builds on the investigation of sentence connectives in propositional logic and goes on to investigate the internal structure of sentences, for example, the truth-conditional effect of certain words like the English quantifiers 'all, some, one', and so on.

Naming function

Also called *denotation assignment function*. It is a procedure, or set of procedures, which match the logical symbols for nouns, verbs, etc. with the items in the model that they denote. (See Model-theoretical semantics)

Diachronic linguistics

Also called *historical*. A kind of linguistics where considerations of historical change are not ignored.

Denotation assignment function

Also called *naming function*. It is a procedure, or set of procedures, which match the logical symbols for nouns, verbs, etc. with the items in the model that they denote. (See Model-theoretical semantics)

Semantic components

Also called Semantic primitives. The smallest components of meaning which are combined differently (or *lexicalized*) to form different words. Example: woman - [FEMALE] [ADULT] [HUMAN] bachelor - [MALE] [ADULT] [HUMAN] [UNMARRIED] spinster - [FEMALE] [ADULT] [HUMAN] [UNMARRIED] wife - [FEMALE] [ADULT] [HUMAN] [MARRIED] Some linguists claim that we need them to describe grammatical processes correctly, that is, it is grammatically necessary to recognize that certain units of meaning are shared by different lexical items. We could reflect this in two complementary ways: one is by setting up verb classes; the other is to factor out the shared element of meaning and view it as this kind of components. cut - CAUSE, CHANGE, CONTACT, MOTION break - CAUSE, CHANGE touch - CONTACT hit - CONTACT, MOTION

Modal logics

An approach that employs a two-fold division of epistemic modality into *fact* versus *possibility*. This distinction can be made discussing *possible words*. There are two logical operators indicating "it is possible that" and "it is necessary that".

Functional approach

An approach to language with which cognitive linguists identify themselves. It implies a quite different view of language than that of the formal approach: that externally, principles of language use embody more general cognitive principles; and that internally, explanation must cross boundaries between levels of analysis. In this view the difference between language and other mental processes is possibly one of degree but is not one of kind. Thus it makes sense to look for principles shared across a range of cognitive domains. Similarly, it is argued that no adequate account of grammatical rules is possible without taking the meaning of elements into account.

Formal approach

An approach to language, such as *generative grammar* (Chomsky) that are often associated with a certain view of language and cognition: that knowledge of linguistic structures and rules forms an autonomous module (or faculty), independent of other mental processes of attention, memory, and reasoning. This external view of an independent linguistic module is often combined with a view of internal modularity: that different levels of linguistic analysis, such as phonology, syntax and semantics, form independent modules. In this view, the difference between modules is one of kind: thus externally, it is good practice to investigate linguistic principles without reference to other mental faculties; and internally, to investigate, say, syntactic principles without reference to semantic content. This characterization of this kind of approach concentrates on epistemological implications. It also implies the desirability and possibility of stating the autonomous principles in ways that are formally elegant, conceptually simple, and mathematically well-formed.

Denotational approach

An approach to meaning which is the search for how the symbols of language relate to reality. This is used by formal semanticists.

Representational

An approach to meaning. For semanticists like Jackendoff semantic analysis involves discovering the conceptual structure which underlies language. For such linguists the search for meaning is the search for mental representations.

Isomorphism

It is a homomorphism (or more generally a morphism) that admits an inverse. Two mathematical objects are isomorphic if an isomorphism exists between them.

Wide scope

It is said of one quantifier when it contains the other. For example, in this sentence the universal quantifier comes leftmost and therefore contains the existential quantifier in its scope. Everyone loves someone. ∀xƎy (L(x, y)).......(For every person x, there is some person y that they love).

Variable

Lower-case letter from the end of the alphabet (w,x,y,z) to leave the identity of the subject unspecified. Examples: x is asleep: A(x) y smokes: S(y)

Quantification

One important feature of natural languages that formal semanticists have to deal with in their translation into logical form. In English, some words used for this purpose are 'one, some, a few, many, a lot, most, all'.

Scope ambiguity

One of the ambiguities found in natural languages. *A)* This one can occur when there is *more than one quantifier* in a sentence. Example: *Everyone loves someone.* *Interpretation 1:* Meaning - Everyone has someone that they love. Formula - *∀xƎy (L(x, y))*.......(For every person x, there is some person y that they love). *Interpretation 2:* Meaning - There is some person who is loved by everyone. Formula - *Ǝy∀x (L(x, y))*.......(For some person y, there is every person x that loves y). *B)* It can also occur when a sentence contains a *combination of quantifier and negation*. Example: *Everybody didn't visit Limerick.* *Interpretation 1 (surface scope or isomorphic interpretation):* Meaning - Nobody visited Limerick. Formula - *∀x ¬(V(x, l))*.......(For every person x, it's not the case that x visited Limerick). *Interpretation 2 (inverse scope or non-isomorphic interpretation):* Meaning - Not everybody visited Limerick. Formula - *¬∀x (V(x, l))*.......(It's not the case that every person x visited Limerick).

Katz's Semantic Theory

One of the earliest approaches to semantics within generative grammar. Two *central ideas* of this theory are: 1. Semantic rules have to be *recursive* for the same reason as syntactic rules: that the number of possible sentences in a language is very large, possibly finite. 2. The relationship between a sentence and its meaning is not arbitrary and unitary (i.e. syntactic structure and lexical content interact so that 'John killed Fred' and 'Fred killed John' do not have the same meaning despite containing the same lexical element). In other words, meaning is *compositional*. The way words are combined into phrases and phrases into sentences determines the meaning of the sentences. This theory reflects this by having rules which take input from both the syntactic component of the grammar, and from the dictionary. For these linguists the *aims* of the semantic component, paralleling the aims of syntax, are: 1. To give specifications of the meanings of lexical items. 2. To give rules showing how the meanings of lexical items build up into the meanings of phrases and so on up to sentences. 3. To do this in a universally applicable metalanguage. The first two aims are met by having two components: firstly, a dictionary which pairs lexical items with a semantic representation; and secondly, a set of *projection rules*, which show how the meanings of sentences are built up from the meanings of lexical items. The third aim is partially met by the use of semantic components.

Model-theoretical semantics

One term of Montague's work and similar approaches. It has led to a number of related but distinct approaches, like *situation semantics* and *discourse representation theory*. In such an approach semantic analysis consists of three stages: firstly, a translation from a natural language like English into a logical language whose syntax and semantics are explicitly defined. Secondly, the establishment of a mathematical model of the situations that the language describes. Thirdly, a set of procedures for checking the mapping between the expressions in the logical language and the modeled situations. For this third step, we need to add three further elements: 1. A *semantic interpretation* for the symbols of the predicate logic. 2. A *domain*: a model of a situation which identifies the linguistically relevant entities, properties and relations. 3. A *denotation assignment function*: a procedure, or set of procedures, which match the logical symbols for nouns, verbs, etc. with the items in the model that they denote. This function is also sometimes called a *naming function*.

Intension

Referring to sense. It is, of an expression, a function from possible worlds to its extensions. In other words the function will give us the denotation of a particular linguistic expression in possible circumstances.

Existential quantifier

Symbolized as Ǝ, to represent the English quantifier "some". Example: [A / Some / At least one] student wrote a paper. Ǝx (S(x) ^ P(s, e)).......(There is (at least) one thing x such that x is a student and x wrote a paper.) (At least) One student kissed Kylie. Ǝx (S(x) ^ K(x, k)) Kylie kissed (at least) one student. Ǝx (S(x) ^ K(k, x))

Universal quantifier

Symbolized as ∀, to represent both English quantifiers "all" and "every". Example: [All students / Every student] wrote a paper. ∀x (S(x) -> W(x, p)).......(For every thing x, if x is a student then x wrote a paper.) Every student knows the professor. ∀x (S(x)->K(x, p)) The professor knows every student. ∀x (S(x)->K(p, x))

Problems with Components of Meaning

The *first problem* concerns the identification of semantic primitives. These primitives have been attacked: -from a philosophical perspective: these semantic components are simply a variation of and equivalent to, the necessary and sufficient conditions approach. It proves impossible to agree on precise definitions of word meaning. The resulting practical problems for the decompositional semanticist include knowing how to validate any proposed set of primitives, and when to stop identifying them, that is knowing what are the right features and how many is enough. -and from a psychological perspective: there is no experimental evidence for semantic primitives. Some studies seem to show that in processing language we appear to treat words as atoms of meaning, and therefore do not divide them into subcomponents in order to understand them. The *second problem* has been on the use of metalanguages. The criticism has been that these devices are ad hoc and unsystematic: at best another arbitrary language; at worst, a kind of garbled version of the English, French, and so on. of the writer.

Embodiment schemas

The effect that characteristics of the human body may have on language.

Social embodiment

The effects of the social purposes to which language is put and the social contexts in which it is used.

Neural embodiment

The influence of how the brain is structured.

Experiential embodiment

The influence of the experiences an individual has had.

Componential analysis

The kind of analysis that states that words are not the smallest semantic unit but are built up of smaller components of meaning which are combined differently (or *lexicalized*) to form different words.

Individual constant

The letter given to a subject which is a lower-case letter, and usually chosen from 'a' to 't'. Examples: Mulligan: m.......Mulligan smokes. S(m) Bill: b.......Bill is asleep. A(b)

Predicate letter

The letter given to the predicate when translated to logic. It is a capital letter. Examples: is asleep: A.......Bill is asleep. A(b) smokes: S.......Mulligan smokes. S(m)

Intensionality

The property of sentences which reveal an interpretative or cognitive behaviour (intensional). This term is applied whenever linguistic behaviour reveals a relation between an agent and a thought. The areas where this term seems most clearly exhibited in natural languages are: *modality, tense, aspect and verbs of propositional attitude*.

Propositional attitudes

The speaker attitudes to the proposition expressed. The choice of verb reflects a difference in propositional attitude between certainty and degrees of lack of certainty.

Restricted quantification

They helps solve the problem of isomorphism. Example: Here the information from the rest of the noun phrase is placed into the quantifying expression as a restriction on the quantifier. All students are hardworking. Restricted format - (∀x: S(x)) H(x) Standard format - (∀x)(S(x)->H(x)) One student if hardworking. Restricted format - (Ǝx: S(x)) H(x) Standard format - (Ǝx)(S(x) ^ H(x))

Redundancy rules

They predict the automatic relationships between components so that the statement of semantic components is also more economical if they are included. Example: HUMAN -> ANIMATE ADULT -> ANIMATE ANIMATE -> CONCRETE MARRIED -> ADULT If we state these rules once for the whole dictionary, we can avoid repeating the component on the right of a rule in each of the entries containing the component on the left.

No

This English determiner can be represented by a combination of the existential quantifier and negation. Example: No student wrote a paper. ¬Ǝx (S(x) ^ W(x, p)).......(It is not the case that there is a thing x such that x is a student and x wrote a paper. There is no x such that x is a student and x wrote a paper). It can also be represented by using material implication. Example: No student wrote a paper. ∀x (S(x) -> ¬P(x, e)).......(For every thing x, if x is a student then it is not the case that x wrote a paper).

Formal semantics

This term is usually used for a family of denotational theories which use logic in semantic analysis (it can also be labelled *logical semantics*). Other names which focus on particular aspects or versions of this general approach include *truth conditional semantics*, *model-theoretic semantics*, and *Montague Grammar*. This approach elaborates further the use of truth, truth conditions, and logic. For the semanticists following this approach, a primary function of language is that it allows us to talk about the world around us.

Scope

This term refers to what the predicate expression is said to be of the quantifier in a proposition.

Bind

This term refers to what the quantifying expression is said to do to the variable in the predicate expression in a proposition.

Other quantifiers

·Some quantifiers can stand alone: everything - every thing - (∀x: T(x)) everybody - every person (∀x: P(x)) everywhere - every location (∀x: L(x)) ·Other seem to incorporate an existential quantifier: something - some thing - (Ǝx: T(x)) someone - some person - (Ǝx: P(x)) somewhere - some location - (Ǝx: L(x))