Situated Agents in Linguistic Contexts

Roussanka Loukanova

Independent Research, Uppsala, Sweden

Keywords:

Situation Theory, Situations, Context, Agent, Reference, Parameters, Restricted Parameters.

Abstract:

The paper looks at motivations from interdisciplinary applications for some of the major situation-theoretical

objects. We present potential applications of situation theory to computational semantics by introducing situ-

ational modelling of linguistic contexts and agents such as speakers and listeners in context.

1 INTRODUCTION

Underspeciﬁcation, partiality, and context depen-

dency are signature features of natural languages

and, more generally, of information. These fea-

tures present major difﬁculties in related theoretical

developments and adequate applications, incl. de-

velopment of dedicated software systems, decision-

problem models and solutions involving models of

states, events, actions, context, and other situations.

The methodology is demonstrated by Situation Se-

mantics for processing human language, but it can

be applied to broader models of information in na-

ture and for computational semantics of both natural

and artiﬁcial languages. Various domain-dependent

versions of situation theory and situation semantics

are gaining appearance in contemporary technologies,

software systems, and intelligent ontology systems.

One of the most prominent applications of Situation

Theory and Situation Semantics is for development

of intelligent user-computer interfaces.

Situation theory is a type based information the-

ory. It takes some set-theoretic objects as its basic

objects and uses them in constructs of more complex

situation theoretic objects, including situated types.

For a detailed discussion of situation theoretic objects,

such as types and propositionssimilar to the ones used

in this paper, see (Barwise and Perry, 1983). For a

more formal introduction, see (Loukanova, 2011b).

Here we present a brief introduction to some of the

most prospective features of Situation Theory includ-

ing generalized, restricted parameters, which we then

use for mathematical modelling of linguistic contexts

and agents.

Primitive Individuals. A collection (typically, a set)

A

IND

is designated as the set of primitive individuals

of the situation theory:

A

IND

= {a, b, c, . . .} (1)

The objects in A

IND

are set-theoretic objects, but they

are considered as primitives, not as complex situation-

theoretic constructions. In various versions of situa-

tion theory, designated for speciﬁc applications, some

of the individuals in A

IND

may be parts of other in-

dividuals in A

IND

, and as such can be in respective

part-of relations.

Space-time Locations. Simpliﬁed versions of situa-

tion theory use a collection (typically, a set) A

LOC

of

space-time points and regions units:

A

LOC

= {l, l

0

, l

1

, . . .} (2)

The collection A

LOC

is endorsed with relations of time

precedence ≺, time overlapping ◦, space overlapping

◦, and inclusion ⊆

t

, ⊆

s

, ⊆, between locations. In

some versions of situation theory, the space-tile loca-

tions can be given by complex objects. E.g., a simple

option (equivalent to the above) is that space-time lo-

cations are pairs of two components, one for space

locations, and one for time points or periods.

Primitive Relations. Signiﬁcantly, situation theory

has a collection (typically, a set) A

REL

of abstract,

primitive objects that are relations:

A

REL

= {r

0

, r

1

, . . .} (3)

The elements of A

REL

are abstract representatives of

real or virtual relations. For example, if situation the-

ory is used to model real world situations, these are

abstract representatives of properties of objects and

494

Loukanova R..

Situated Agents in Linguistic Contexts.

DOI: 10.5220/0004363004940503

In Proceedings of the 5th International Conference on Agents and Artiﬁcial Intelligence (LAFLang-2013), pages 494-503

ISBN: 978-989-8565-38-9

Copyright

c

2013 SCITEPRESS (Science and Technology Publications, Lda.)

relations between objects. E.g., humans (as well as

other living species) are attuned to distinguish prop-

erties of and relations between objects, perceptually

in the reality, or cognitively, i.e., conceptually. We

normally can recognise the property of an object to

be a book, while the speciﬁcs of that property may be

context dependent, a hardback book, a paperback, or

e-book. The set A

REL

depends on the actual applica-

tion of Situation Theory

1

. For example,

A

REL

= { man, woman, dog, run, smile, like, . . . } (4)

By introducing more complex situation-theoretic

objects, it is possible to deﬁne the extension of any

given relation r, in any given situation s as the set of

tuples of objects being in the relation r in s. For ex-

ample, we can distinguish when a primitive relation

of reading holds between two objects: a reader and an

object that is read.

Primitive Types. A collection (typically, a relatively

small set) of objects, which are called primitive or ba-

sic types:

B

TYPE

= { IND, LOC, REL, POL, ARG, (5a)

INFON, SIT, PROP, PAR, TYPE, |=} (5b)

where IND is the type of individuals; LOC: of space-

time locations; REL of relations; TYPE: of basic and

complex types; PAR: of parameters; POL: of two po-

larity objects, e.g., presented by the natural numbers

0 and 1; ARG: of abstract argument roles (primitive

and complex); INFON: of situation-theoretical ob-

jects that are basic or complex information units, de-

ﬁned later; PROP: of abstract objects that are propo-

sitions; SIT: of situations; |= is a type called “sup-

ports”.

Deﬁnition 1 (Assignment of Primitive Argument

Roles). A set of argument roles is assigned to each

of the primitive relations and each of the primitive

types by a function Args with the domain and range

of which are such that Dom(Args) = A

REL

∪ B

TYPE

,

and Range(Args) ⊆ A

ARG

.

For example, we can associate relations, such as

smile, read, give, respectively denoted by the lexemes

smile, read, give, etc., with arguments roles:

2

Simi-

larly to relations, each type is associated with a set of

argument roles. If a type T has a single argument role,

we call it a unary type, or a property type. In partic-

ular, IND, LOC, POL, PAR, TYPE, are unary types,

1

The the set-theoretical meta-theory of Situation theory,

including representation of A

REL

, is not the subject of this

paper.

2

The argument role of the object that is read is desig-

nated by the “misspelled” notations read-ed or readed.

each with one argument role, that can be declared as

ﬁlled only by elements of sets corresponding to the

types.

Argument Roles and Appropriateness Con-

straints. The argument roles of both relations and

types can be associated with types as constraints for

their appropriate ﬁlling.

Deﬁnition 2 (Argument Roles with Appropriateness

Constraints). A set of argument roles is assigned

to each of the primitive relations and to each of

the primitive types by a function Args with its do-

main and range of values such that Dom(Args) =

(A

REL

∪ B

TYPE

), and Range(Args) ⊆ (A

ARG

× TYPE),

so that for any primitive relation and any type

γ ∈ A

REL

∪ B

TYPE

with n-arguments: Args(γ) =

{harg

i

1

, T

i

1

i, . . . , harg

i

n

, T

i

n

i}, where T

1

, . . . , T

n

are sets

of types (basic or complex), which are speciﬁc for

γ and are called basic appropriateness constraints of

the argument roles of γ.

Notation 1. Often, we shall use the notation (6):

Args(γ) = {T

i

1

: arg

i

1

, . . . , T

i

n

: arg

i

n

} (6)

The very basic appropriateness constraints can be

expressed by associating argument roles with primi-

tive types, T

i

1

, . . . , T

i

n

∈ B

TYPE

. For example:

Args(give) = {IND : giver, (7a)

IND : receiver, IND : given} (7b)

For any relation or type (which can be primitive

or complex), the objects that ﬁll its argument roles

are restricted to satisfy the constraints associated with

the roles.

Deﬁnition 3 (Argument Filling). For any given re-

lation γ ∈ R

REL

and for any given type γ ∈ T

type

as-

sociated with the set of argument roles Args(γ) =

{T

i

1

: arg

i

1

, . . . , T

i

n

: arg

i

n

}, an argument ﬁlling for γ is

any total function θ with Dom(γ) = {arg

i

1

, . . . , arg

i

n

},

which is set-theoretically deﬁned by a set of ordered

pairs θ = { harg

i

1

, ξ

1

i. . . , harg

i

n

, ξ

n

i}, so that its val-

ues, θ(arg

i

1

) = ξ

1

, . .., θ(arg

i

n

) = ξ

n

, satisfy the ap-

propriateness constraints of the argument roles of γ:

T

i

1

: ξ

1

, .. ., T

i

n

: ξ

n

.

Infons, State of Affairs (soas), Situations. Next, I

shall give a mutually recursive deﬁnition of several

sets of situational objects:

• the set I

INF

, the elements of which are called in-

fons, and are basic or complex information units;

• the set R

REL

of all primitive and complex relations

(complex relations are deﬁned later): A

REL

⊂

R

REL

;

SituatedAgentsinLinguisticContexts

495

• the set T

TYPE

of all primitive and complex types:

B

TYPE

⊂ T

TYPE

;

• the collection S

SIT

of situations.

The basic informational units are identiﬁed by a

unique relation, an assignment of its argument roles

and a corresponding negative or positive polarity.

Deﬁnition 4 (Infons). The set I

INF

of all infons:

1. Basic infon is every tuple hγ, θ, τ, ii, where γ ∈

R

REL

is a relation (primitive or complex), LOC : τ

is a space-time location, (i.e., τ ∈ A

LOC

), POL : i

is polarity (i.e., i ∈ {0, 1}), and θ is an argument

ﬁlling for γ, i.e.:

θ = {harg

i

1

, ξ

1

i, . . . , harg

i

n

, ξ

n

i} (8)

for some situation-theoretical objects ξ

1

, . . . , ξ

n

satisfying the appropriateness constraints of γ.

2. Let B I

INF

be the set of all basic infons. B I

INF

⊂

I

INF

.

3. For representation of conjunctive and disjunctive

information, complex infons are formed by opera-

tors for conjunction and disjunction: h∧, σ

1

, σ

2

i ∈

I

INF

and h∨, σ

1

, σ

2

i ∈ I

INF

.

Other complex infons are constructed from vari-

ous situation theoretic objects, which we can add

later.

Notation 2. Often, in this paper, we use the tradi-

tional linear notation of basic infons:

≪ γ, arg

i

1

: ξ

1

, . . . , arg

i

n

: ξ

n

, LOC : τ;i ≫ (9a)

≪ γ, ξ

1

, . . . , ξ

n

, τ;i ≫ (9b)

Note 1. The notation (9a) does not assume any innate

order over the argument roles of γ. On the other hand,

in case that γ has more than one argument roles, the

notation (9b), e.g. as in (10b), (10d), makes sense

only by having some agreement about an order over

the argument roles of γ.

Example 1.1.

≪ book, arg : b, Loc : l;1 ≫ (10a)

≪ book, b, l;1 ≫ (10b)

≪ read, reader : a, readed : b, l;1 ≫ (10c)

≪ read, a, b, l;1 ≫ (10d)

Deﬁnition 5 (States of affairs, events, situations). We

deﬁne the following complex situational objects:

1. State of affairs (soa) is any set of infons that have

the same location component.

2. An event (course of event, coa) is any set of in-

fons.

3. A situation is any set of infons.

Basic Parameters. For each of the basic types

IND, LOC, REL, POL, SIT, situation theory that has a

collection (a set) of basic (primitive) parameters:

P

IND

= { ˙a,

˙

b, ˙c, . . .}, (11a)

P

REL

= { ˙r

0

, ˙r

1

, . . .}, (11b)

P

LOC

= {

˙

l

0

,

˙

l

1

, . . .}, (11c)

P

POL

= {

˙

i

0

,

˙

i

1

, . . .}, (11d)

P

SIT

= { ˙s

0

, ˙s

1

, . . .}. (11e)

Basic parameters are also called indeterminates. here

we follow the original Situation Theory, by denoting

speciﬁc basic parameters by dots. Often, we shall use

“meta-variables” for basic parameters and the type

shall be either explicitly stated or understood, e.g.,

typically, x is any parameter of type IND.

Infons, states of affairs, and situations, in which

some of the argument roles, including the space-time

location and polarity components, are ﬁlled by pa-

rameters, are called, respectively, parametric infons,

parametric soas, and parametric situations.

Example 1.2.

≪ read, reader : ˙a, readed :

˙

b,

˙

l;1 ≫ (12a)

≪ read, reader : a, readed :

˙

b,

˙

l;1 ≫ (12b)

≪ read, a, b, l;

˙

i ≫ (12c)

2 SITUATED PROPOSITIONS,

CONSTRAINTS AND

PARAMETERS

In the considered version of situation theory, we use

a specialized primitive type PROP ∈ B

TYPE

, with two

argument roles: a type T ∈ T

TYPE

, and an appropriate

argument ﬁlling θ for T. I will use the type PROP

for constructing abstract objects (set-theoretic tuples)

to model the abstract notion of a proposition, which

states that some given objects are of some given type,

in the following way:

Deﬁnition 6 (Propositions). Proposition is any tuple

hPROP, T, θi, where T ∈ T

TYPE

is a type that is asso-

ciated with a set of argument roles

Args(T) = {T

i

1

: arg

i

1

, . . . , T

i

n

: arg

i

n

} (13)

and θ is an argument ﬁlling for T, i.e.:

θ = {harg

i

1

, ξ

1

i, . . . , harg

i

n

, ξ

n

i} (14)

for some objects ξ

1

, . . . , ξ

n

such that θ satisfy the ap-

propriateness constraints of T:

T

i

1

: ξ

1

, . . . , T

i

n

: ξ

n

. (15)

ICAART2013-InternationalConferenceonAgentsandArtificialIntelligence

496

Notation 3. We use the notation (T, θ) for

hPROP, T, θi.

When a proposition hPROP, T, θi is true, we say

that the objects ξ

1

, . . . , ξ

n

are of type T with respect to

the argument role ﬁlling θ, and we write T : θ, or, in

case it is clear which roles are ﬁlled by which objects,

T : ξ

1

, . . . , ξ

n

. I.e., propositions are the result of ﬁll-

ing up the argument roles of a type with appropriate

objects. We shall use a special kind of propositions

deﬁned by Deﬁnition 7, based on the primitive type

|=. The type |=, pronounced “support”, has two ar-

gument roles, one that can be ﬁlled by any object that

is of the type SIT of situations, and the other can be

ﬁlled by any object that is of the type INF of inforns.

I.e.:

Args(|=) = {harg

sit

, SITi, harg

infon

, INFi} (16a)

≡ { SIT : arg

sit

, INF : arg

infon

} (16b)

Deﬁnition 7 (Situated Propositions). Situated propo-

sition is a situation-theoretical object

hPROP, |=, s, σi (17)

where s ∈ P

SIT

and σ ∈ I

INF

.

Notation 4. We use the notation (s |= σ) and say “the

proposition that σ holds in the situation s” or “the

proposition that the situation s supports the infon σ”.

Example 2.1.

(s |=≪ book, arg : b, Loc : l;1 ≫ ∧ (18a)

≪ read, reader : x, readed : b, Loc : l;1 ≫) (18b)

Situation theory uses an abstraction operator,

which recalls the λ-abstraction in functional λ-calculi,

but, in situation theory, abstraction operator is differ-

ent and does not deﬁne functions. In situation theory,

the abstraction operator results in complex types, with

abstract argument roles.

Deﬁnition 8 (Complex Types and Appropriateness

Constraints). Let Θ be a given proposition and

{ξ

1

, . . . , ξ

n

} be a set of parameters that occur in Θ.

Let, for each i ∈ {1, . . . , n} , T

i

be the union of all the

appropriateness constraints of all the argument roles

that occur in Θ and ξ

i

ﬁlls up.

Then the object λ{ξ

1

, . . . , ξ

n

}Θ ∈ T

TYPE

, i.e.,

λ{ξ

1

, . . . , ξ

n

}Θ is a complex type, with abstract argu-

ment roles denoted by [ξ

1

], . . . , [ξ

n

] and corresponding

appropriateness constraints associated in the follow-

ing way:

Args(λ{ξ

1

, . . . , ξ

n

}Θ) (19a)

= {T

1

: [ξ

1

], . . . , T

n

: [ξ

n

]} (19b)

The type λ{ξ

1

, . . . , ξ

n

}Θ, where Θ is a proposi-

tion, is alternatively denoted by

[ξ

1

, . . . , ξ

n

| Θ(ξ)] (20a)

[T

1

: ξ

1

, . . . , T

n

: ξ

n

| Θ(ξ)]. (20b)

Sometimes, we shall use a mixture of λ and bracketed

notation, for discriminating between the types of the

abstracted away parameters.

Example 2.2. The situation-theoretical object (21) is

the type of situations and locations where the speciﬁc

individual a walks; (22) is the type of individuals that

walk in a speciﬁc situation s and a speciﬁc location

l; (23a)–(23c) is the type of individuals that read a

speciﬁc book b, in a speciﬁc situation s and a speciﬁc

location l; (24a)–(24c) is the type of situations, lo-

cations and individuals, where the individual reads a

speciﬁc book b:

λ˙s,

˙

l ( ˙s |=≪ walk, walker : a, Loc :

˙

l;1 ≫) (21)

λx(s |=≪ walk, walker : x, Loc : l;1 ≫) (22)

λx(s |= (23a)

≪ read, reader : x, readed : b, Loc : l;1 ≫ ∧ (23b)

≪ book, arg : b, Loc : l;1 ≫) (23c)

λ˙s,

˙

l, x( ˙s |= (24a)

≪ read, reader : x, readed : b, Loc :

˙

l;1 ≫ ∧ (24b)

≪ book, arg : b, Loc :

˙

l;1 ≫) (24c)

Notation 5. For given object α and a set of appropri-

ateness constraints T, we write T : α iff α satisﬁes all

the constraints in T.

Property 1. Let Θ be a given proposition and

{ξ

1

, . . . , ξ

n

} be a set of parameters that occur in Θ.

Let, for each i ∈ { 1, . . . , n}, T

i

be the union of all the

appropriateness constraints of all the argument roles

that occur in Θ and ξ

i

ﬁlls up. Given that α

1

, . . . , α

n

are objects that satisfy appropriateness constraints

T

1

: α

1

, . . . , T

n

: α

n

, we have:

1. by Deﬁnition 8, λ{ξ

1

, . . . , ξ

n

}Θ ∈ T

TYPE

is a com-

plex type with argument roles (19a)–(19b).

2. Let θ be the total function that is set-theoretically

deﬁned by the set of ordered pairs θ =

{h[ξ

1

], α

1

i. . . , h[ξ

n

], α

n

i},

(a) by Deﬁnition 3, θ is an argument ﬁlling for the

type λ{ξ

1

, . . . , ξ

n

}Θ.

(b) by Deﬁnition 6: (λ{ξ

1

, . . . , ξ

n

}Θ : θ) is a

proposition, i.e., the proposition that the objects

from the argument the ﬁlling θ are of the com-

plex type λ{ξ

1

, . . . , ξ

n

}Θ, i.e.:

hPROP, λ{ξ

1

, . . . , ξ

n

}Θ, θi (25a)

≡ (λ{ξ

1

, . . . , ξ

n

}Θ : θ) (25b)

SituatedAgentsinLinguisticContexts

497

Abstractions over individuals in propositions re-

sult in complex types of individuals. In general, for

any given proposition Θ and a parameter ξ for an indi-

vidual, i.e., IND : ξ, which occurs in Θ, the situation-

theoretical object λ{ξ

1

}Θ ∈ T

TYPE

is a complex type,

that is the type of the individuals for which the propo-

sition Θ(ξ

1

) is true.

3 RESTRICTED PARAMETERS

AND PARAMETER

ASSIGNMENTS

Any basic parameter x of type τ (i.e., τ : x) can be

properly assigned only to a situation theoretic ob-

ject of type τ. Complex restricted parameters can be

properly assigned only to objects that satisfy the con-

straints associated with the restricted parameters. As-

sociating basic parameters with types has constrain-

ing effect. Thus, parameter assignments of both basic

and restricted parameters are constrained.

Deﬁnition 9 (Consistent Types). For any ﬁnite set T

of types:

1. T is consistent iff there is at least one situation

theoretic object that is of each of the types in T.

2. A type τ is compatible with T iff the set { τ} ∪ T

is consistent.

Deﬁnition 10 (Parameters). Basic (11a)–(11e) and

restricted parameters are parameters.

Restricted Parameters.

1. Let T be a ﬁnite (and consistent) set of types. If

x is a fresh parameter of type τ, i.e., τ : x, and τ is

compatible with the set T of types, then x

{τ}∪T

is

a parameter of type {τ}∪ T. We say that x

{τ}∪T

is

a parameter restricted by {τ} ∪ T.

2. Let ξ be a parameter and Θ(ξ) a proposition. Let

T be the set of all types associated with all the ar-

gument roles in Θ(ξ) that are ﬁlled by ξ

3

. (I.e.,

λξΘ(ξ) is a type and T is the set of the appropri-

ateness constraints of its argument role.) If the set

T of types is consistent, and x is a fresh parame-

ter of type τ, i.e., τ : x, such that τ is compatible

with T, then x

λξΘ(ξ)

is also a parameter of type τ.

We say that x

λξΘ(ξ)

is a parameter restricted by

λξΘ(ξ).

With the alternative denotation of the complex

type [ξ | Θ(ξ)], the restricted parameter x

λξΘ(ξ)

is

denoted by x

[ξ|Θ(ξ)]

.

3

Note that ξ may ﬁll more than one argument role in

Θ(ξ).

For any situation theoretic object γ(x

r

), in which

the restricted parameter x

r

is a constituent, we can

“connect” some or all of the parameters in it to ob-

jects by a parameter assignment function.

A parameter assignment c is deﬁned on x

T

, where

T is a set of consistent types, only if the proposition

(c(x

T

) : τ) is true for each type τ ∈ T.

A parameter assignment c is deﬁned on x

[ξ|Θ(ξ)]

only if the proposition (c(x

[ξ|Θ(ξ)]

) : [ξ | Θ(ξ)]) is true;

i.e., only if there is a parameter assignment c

′

for

Θ(ξ), such that c

′

(ξ) = c(x

[ξ|Θ(ξ)]

) and the proposi-

tion c

′

(Θ(ξ)) is true.

4 BIOLOGICAL BASIS OF

SITUATION THEORY

Restricted parameters represent generic patterns,

“blueprints”, that can be instantiated, i.e., realised,

by speciﬁc objects that satisfy the corresponding re-

strictions and are of respective types. In nature, bio-

logical entities carry blueprints that are restricted ac-

cording to shared features, e.g., of species. Parame-

ter assignments represent speciﬁc realisations of the

generic components in speciﬁc instances.

We take a stand that human cognitive abilities and

faculties, that are universal for humans, are expressed

by innate brain capacities for some fundamental oper-

ations:

• perception and recognition of entities, smells,

sounds, etc., that are located in three-dimensional

space, in time, and situated in environments

• perception and recognition of properties and rela-

tions, primitive and complex, “possessed” by en-

tities, in space, time, and situated in environments

• human brain faculties associate properties and re-

lations with abstract and speciﬁc objects, by argu-

ment roles and argument role assignments

• recognition of abstract patterns, i.e., of types and

parametric objects

• pattern construction via primitive abstract types

and abstraction over parametric objects

• pattern construction via restrictions over parame-

ters

• pattern matching i.e., an entity O is of type τ, τ : x.

Restricted parameters reﬂect innate human faculty

for developmentand attainment of concepts of objects

that have some properties and are in relations to other

kinds of objects, not necessarily referring to speciﬁc

objects in the reality. A youngster or an adult person

can get an idea what an object with certain properties

ICAART2013-InternationalConferenceonAgentsandArtificialIntelligence

498

could be, without having seen any such objects, in re-

ality or in other ways depicted. Such concepts are not

necessarily expressed by or associated with language.

5 LINGUISTIC CONTEXTS AND

AGENTS

Human language is used in contexts, that can be spo-

ken, written, pictural, virtual, in reasoning, “in the

mind”, or combining any of these ways of usage.

Language can be used by speakers that know its ab-

stract linguistic meanings and how the abstract lin-

guistic meanings can be “connected”, i.e., assigned

to speciﬁc interpretations. Abstract linguistic mean-

ings, taken out of any context of use, carry semantical

information, which is partial, parametric and some-

times ambiguous. I.e., normally, abstract linguistic

meanings, out of context, have structure with para-

metric constituents and abstractions over parameters.

When used in speciﬁc contexts, the abstract linguis-

tic meanings are assigned to speciﬁc interpretations,

by the speakers and listeners. The interpretations in

context can still be parametric and partial. Ambigui-

ties are typically resolved by speakers’ and listeners’s

who interprete depending on their perspectives.

Partiality of information about the objects desig-

nated by language parts is by introducing primitive

and complex, i.e., restricted, parameters. The restric-

tion r over a parameter x

r

represents a constraint r : a

that is necessary for an object a to be associated with

the parameter x

r

in a larger piece of information γ(x

r

).

The assignment of an object a to x

r

in γ(x

r

) results in

the instantiation γ(a). The constraint r itself is not

per-se a part of γ(a), but is an additional, necessary-

constraint information, satisﬁed by a, i.e., a is of type

r, r : a. A speaker-agent uses the restriction r to des-

ignate the object a, by assigning it to x

r

. The listener-

agent identiﬁes the object a ﬁlling the arguments in

γ(a), by the constraint r : a.

5.1 Linguistic Utterance Components

In this paper, we follow a tradition of using the tech-

nical notion of an utterance, as a situation type rep-

resenting minimal components of context, which are

crucial for association of linguistic meanings with

potentials for speciﬁc interpretations in speciﬁc con-

texts, i.e., in “utterances” of expressions, by speakers

addressing listeners. Depending on the areas of ap-

plications of situation theory, linguistic contexts can

be extended. The context (discourse) components in-

clude, as a minimum, the following kinds of informa-

tion:

1. Pure linguistic information: The expression ut-

tered are presented by a syntax-semantics inter-

face structure, which determines its abstract lin-

guistic meaning. The authors of this paper support

the view that the syntax-semantics interface In hu-

man language is innate faculty of brain physiol-

ogy. Computational approaches to language pro-

cessing would be more intelligent and adequate by

taking such a perspective.

2. Broad-linguistic information by utterance compo-

nents: the “speaker” agent that delivers the ex-

pression, for example by an utterance; the lis-

tener agent(s) that are addressed interpreters; the

time and the space location of the utterance; the

speaker’s references that assign particular objects

to language components; the knowledge and the

intentions of the speaker and the listener that

contribute to interpretations of abstract linguistic

meanings, assigning objects to parameters, and

disambiguation. This information can be pre-

sented by abstract utterance types, as parametric

situation theoretic constructs.

3. Extra-linguistic utterance information: language

speciﬁc word order and word inﬂection para-

digms, end-of-sentence punctuation, speech acts,

intra-sentential punctuation, intonation, gesture

and other means for expressing speaker’s perspec-

tives, stress, presenting “new” vs. “old” informa-

tion.

5.2 Some Biological Phenomena of

Syntax-semantics Interface

The extra-linguistic information presented by word

order and word inﬂection paradigms present a dis-

tinctive biological foundation of communications be-

tween humans via human language. The human brain

physiology supports multi-dimensional functionality

and multi-dimensional mental faculty. I.e., humans

comprehend and act in situations, which are parts

of the surrounding world, in three-dimensional space

and time continuity, discrete and continuous. On the

other side, speech production is linearised by limita-

tions of the physiology of vocal tracts. These limita-

tions are present in linear wording of predominantly

existing writing systems, for transposing speech on

carrying materials. Writing materials typically have

been two-dimensional (e.g., strings, plates, paper,

screens) and allow two-dimensional representation of

syntactic structure.

Tree-structure representations of syntactic struc-

tures of the linear wording of language expressions

were introduced and acknowledged by theoretical

SituatedAgentsinLinguisticContexts

499

and computational linguistics. Such tree-structure

analyses represent syntax-semantics interfaces, where

semantic counterparts, i.e., language utterances de-

scribe situations and informational units that consist

of multi-dimensional objects. In particular, primitive

and complex relations and properties in situation the-

ory have arguments that are not by necessarily or-

dered: they are sets. This is a distinctive feature of

situation-theoretical objects that reﬂects information

in nature and is biologically motivated. Argument as-

signments are associated with relations by indexing

functions.

The features of linear encoding and tree-structure

analyses of multi-dimensional structures are trans-

posed into artiﬁcial languages, such as formal lan-

guages in computational theories and programming

languages.

5.3 Situated Linguistic Agents

Denotations of human language expressions in spe-

ciﬁc contexts may depend on reference acts. A lin-

guistic reference act is an event consisting of at least

the following components: a language expression, an

object (real or abstract) referred to, which is called

the referent of the expression, and an utterance situa-

tion (or a broader discourse). The utterance situation

consists of subcomponents such as the speaker, the

speaker’s reference function, the space-time location

of the utterance, and the listener. The speaker’s act

of reference can be modeled by a function deﬁned on

language units with values the objects referred to. The

reference function itself isdependent on the utterance.

By using situation theoretical objects with restricted

parameters, the utterance components can be modeled

by situation-theoretical objects as follows, see also

(Loukanova, 2001; Loukanova, 2002b; Loukanova,

2002a).

The proposition expressing who is the speaker x,

who is the listener y, what is the space-time location,

and which is the expression α uttered in an utterance

situation u, i.e., a minimum of context information is

expressed by the situated proposition (26):

pu(u, l, x, y, α) ≡ (u |=≪ tells, x, y, α, l;1 ≫) (26)

Then, (27) is an abstract type of an utterance situation.

ru(l, x, y, α) ≡ [u | pu(u, l, x, y, α)] (27)

The type (28) is the type of a speaker agent in an

utterance situation u.

rsp(u, l, y, α) ≡ [x | pu(u, l, x, y, α)] (28)

The type of an individual to be a listener agent in an

utterance situation u is (29):

rlst(u, l, x, α) ≡ [y | pu(u, l, x, y, α)] (29)

The type of an object to be the utterance (or dis-

course) space-time location is given by (30):

rdl(u, x, y, α) ≡ [l | pu(u, l, x, y, α)] (30)

The type (31) is a type for the referent agent i.e.,

of the objects to be referred to by an expression α in

an utterance situation.

r

α

(u, l, x, y, s

res

) = [z | q(u, l, x, y, z, α)] (31)

where q(u, l, x, y, z, α) is a proposition such as (32a) or

(33a).

q(u, l, x, y, z, α) ≡ (32a)

(u

ru(l,x,y,α)

|= (32b)

≪ refers-to, x

rsp(u,l,y,α)

, z, α, l

rdl(u,x,y,α)

;1 ≫) (32c)

The proposition (32a), i.e., (32b)–(32c) asserts that

the speaker x

rsp

refers to z by using the expression α,

in the location l

rdl(u,x,y,α)

. More elaborate representa-

tion of the names can be expressed by the following

version of the proposition q(u, l, x, z, α):

q

′

(u, l, x, y, z, α, s

res

) ≡ (33a)

(u

ru(l,x,y,α)

|= (33b)

≪ refers-to, x

rsp(u,l,y,α)

, z, α, l

rdl(u,x,y,α)

;1 ≫ (33c)

∧ ≪ believes, x

rsp(u,l,y,α)

, (33d)

(s

res

|=≪ named, α, z;1 ≫), (33e)

l

rdl(u,x,y,α)

;1 ≫) (33f)

The proposition (33a), i.e., (33b)–(33f), asserts that

the speaker x

rsp

refers to z by using the name α and

believing that z is named α. In what follows, all the

abode restrictions shall be written without explicitly

specifying the parameter arguments.

6 NAMING EXPRESSIONS AND

SENTENTIAL MEANINGS

In this section, we turn to examples of referential ex-

pressions, such as proper names and deﬁnite descrip-

tions, for exposition of how Situation Theory can han-

dle such semantic phenomena. Semantics of naming

expressions gives essential contributions to semantics

of larger, encompassing language constructions, e.g.,

such as sentences and upward to larger texts. How-

ever, it is important how those contributions are han-

dled computationally, where is their proper placement

in the semantic representations, all of which should

also take into account the context and agent depen-

dency of their semantics.

ICAART2013-InternationalConferenceonAgentsandArtificialIntelligence

500

A distinctive semantic contribution of naming ex-

pressions provides means for potential reference to

objects, by the language users, i.e., “speaker” and

“listener” agents in context, e.g., by using sentences,

and so forth, up to text discourse. Typically, by ut-

terances of afﬁrmative sentences, speakers describe

some situations (not necessarily the same as the ut-

terances) as holding facts (i.e., infons). The objects,

which are the referents of name sub-expressions, par-

ticipate as ﬁllers of arguments roles of semantic re-

lations, in the facts that are stated to hold in the de-

scribed situations, by utterance situations. Then, it

is important not to misplace the additional semantic

contribution, however important, of the naming sub-

expressions as direct components of the facts (i.e. of

the infons) that are directly in the propositional con-

tent stated by a sentence utterance, and not directly in

the facts of the utterance itself.

E.g., by an utterance u of a sentence like “Maria

is reading the book”, a speaker may describe a situa-

tion s

1

as holding that a speciﬁc individual, referred

to by the name “Maria”, is involved in some activ-

ity, i.e., reading a speciﬁc book, referred to by the

deﬁnite description “the book”. The described situ-

ation s

1

may be part of or the same as u, i.e., s

1

⊆ u.

But it is also possible that s

1

is fully disjoint from u,

while both are related via the speaker’s references in

the utterance context. The speaker uses the name and

the deﬁnite description to identify the participants of

the reading fact. By the inﬂection of the verb lex-

eme “read”, the reading fact is located with respect to

the space-time location of the utterance. But these in-

formational pieces are additional, however important,

information that is linked to both the facts of the utter-

ance and the facts of the described situation, and they

should not be indiscriminately conjoined.

In general, for a given naming expression α,

in its abstract referential semantics, its denotation

4

den(α) = x

r

α

is givenby a restricted parameter,where

r

α

is like (31), as abstract linguistic meaning that is

dependent on potential contexts. Depending on the

expression α and applications, r

α

may have more or

alternative constraints in it, e.g., by (33b)–(33f). Im-

portantly, the object x

r

α

is parametric and its instan-

tiations are subject to the r

α

constraint expressed by

the semantics of the name α, as e.g., in (34a)–(35a)

and (36a)–(36d).

Potentially, an utterance and speaker’s references,

given as parametric components, can provide a spe-

ciﬁc object referred to by the expression α, as in-

stantiation of the restricted parameter x

r

α

. The re-

4

We present the denotation function without diverging to

more theoretical technicalities, which are subjects to other

ongoing and future work.

stricted parameter x

r

α

can get linked to speciﬁc ref-

erent depending on the speciﬁc utterance context and

the speaker agent. That speciﬁc referent, subjected

to satisfaction of the constraint r

α

, can ﬁll up relation

arguments in facts described by a larger expression,

in which the name α occurs, e.g., as in (37a)–(37b).

However important, and expressed by the semantics

of component name α, the restriction r

α

, while a

direct component of the restricted parameter itself,

provides “extra” semantic information, as necessar-

ily linked to the direct semantic content of the larger

expression.

Example 6.1.

r

MARIA

≡ [z | (u

ru(l,x,y,MARIA)

|= (34a)

≪ refers-to, x

rsp

, z

n

, MARIA, l

rdl

;1 ≫)] (34b)

where the restricted parameter z is recursively re-

stricted by the type n in (35a)–(35b), which expresses

that the object z is named MARIA by x

rsp

in a resource

situation s

0

:

n = [z | (s

0

|= (35a)

≪ named, MARIA, x

rsp

, z;1 ≫) (35b)

Example 6.2. The linguistic meaning of a noun

phrase (NP) that is a deﬁnite description, e.g., “the

book”, can be expressed by z

d

, where d is the type

(36a)–(36d), and s

2

and l

2

are parameters for a re-

source situation and its resource location for evalua-

tion of the NP THE BOOK. Typically, the resource sit-

uation s

2

and some of its component locations l

2

are

provided by the references of the speaker agent, and

while they might be the same as the utterance situa-

tion and some of its immediate component locations,

respectively, they might as well be “external” via con-

straints over parameters.

d = [z | (s

2

|=≪ book, z, l

2

;1 ≫ (36a)

∧ ≪ unique, z, (36b)

[z | (s

2

|=≪ book, z, l

2

;1 ≫)], (36c)

l

2

;1 ≫)] (36d)

The abstract, linguistic meaning of a sentence like

“Maria is reading the book” can be designated by the

following situated propositional type:

Example 6.3.

λs

1

, s

2

, l

1

, l

2

(s

1

|= (37a)

≪ read, z

r

MARIA

, z

d

, l

[l|l◦l

rdl

]

1

;1 ≫) (37b)

where r

MARIA

and d are, respectively, the constraints

(34a)–(35a) and (36a)–(36d).

SituatedAgentsinLinguisticContexts

501

7 CONCLUSIONS AND FUTURE

WORK

Conclusions: Advances in Theory for Applications

to New Technologies. This paper is part of broader

work on development of computational syntax-

semantics interface for human language. Mathemati-

cal models of the concepts of linguistic context and

agents in context concern fundamentals of syntax-

semantics interfaces in natural languages in general.

Our speciﬁc goal is theoretical development of com-

putational type-theory of information for human lan-

guage processing based on syntax-semantics inter-

face. We target theory of information that is supported

by the role of languages in nature, from the perspec-

tive of applications and software engineering in new

technologies.

The ﬁrst part of the paper is presenting ongoing

research in theoretical development of situation the-

ory for modelling complex information. One of the

primary applications of situation theory is to com-

putational semantics of human languages, for mod-

elling semantic domains and information designated

by human language, including linguistic contexts and

agents. Human language is notoriously ambiguous

and context dependent. While some authors may

point that as disadvantageous, these phenomenal fea-

tures present the core part of language productiv-

ity and efﬁciency, partly because it allows different

agents, in different contexts, to express varying infor-

mation, with familiar expressions. Something more,

language expressions, even when considered unam-

biguous, when out of context, carry partial and para-

metric information, which is not necessarily and fully

instantiated in speciﬁc contexts when used by spe-

ciﬁc agents. In many cases, agents such as lan-

guage users, speakers, listeners, and readers, appre-

ciate parametric, partial and under-speciﬁed informa-

tion expressed by language even in speciﬁc contexts.

This presents needs of a theory that models partial,

parametric and underspeciﬁed information, that also

models the context-dependency of language and in-

formation. This means that such a theory of informa-

tion has the capacities to model interrelated context

components and language agents in context. Situa-

tion theory has been under development for meeting

such needs.

Future Work. Recent years have been charac-

terised with new technological advancements across

sciences and industries, by involving hardware and

software engineering. Well established, classical the-

ories and methodologies may be fully sufﬁcient as the

foundations of some of these new technologies. The

most challenging technological advances occur con-

currently with new developments of their scientiﬁc

foundations, including new methodologies, and new

approaches to mathematical models of the domains,

for which the technologies are used and applied.

From this perspective, a new interdisciplinary area

is emerging, which conjoins theoretical developments

in sub-ares that are often considered and developed

separately, but are getting co-involved in the context

of new technologies. In particular, the primary sub-

areas that are forming foundations of new technol-

ogy advances involve (1) mathematics of the concepts

of computations, e.g., mathematics of algorithms and

programs (2) classic and new approaches to computa-

tional models of various domains of applications (3)

hardware and software engineering (4) computational

approaches in life sciences.

A representative of this new interdisciplinary area

has been emerging as Domain Science and Engineer-

ing (DSaE), see (Bjørner, 2012). On its side, our pa-

per represents ongoing research on development of

Situation Theory, as a computational theory of in-

formation, which contributes to domain science , by

modelling domains and domain dependent entities,

parts, materials, relations, situations, states, events,

etc. Situation theory is information type-theory of

domains. We view DSaE approach as a computa-

tional realisation, in its domain science, of versions

of Situation Theory, depending on areas of applica-

tions, speciﬁcally for applications in computer soft-

ware engineering. In its current stage, DSaE encom-

passes series of versions of Situation Theory that are

software implementable. A new line of research is

on modelling the concepts of states, events, actions,

processes, relations (predicates) in Situation Theory

depending on applications.

Extensive research have been demonstrating that

model-theoretic approaches to computational seman-

tics of human language are highly productive, for an

overview see (Loukanova, 2010). In brief, such ap-

proaches involve translation of human language into

a formal language, which provides computational se-

mantics of the human language. This is desirable for

various reasons, in case formal languages are math-

ematically grounded and equipped with relevant se-

mantics. On the other hand, ﬁnding a sufﬁciently ad-

equate formal language that covers the semantic phe-

nomena of human language, and is also computation-

ally expressive, has been widely open area. It is also

important that the formal language supports syntax-

semantics interfaces for human language and cov-

ers ambiguity and context-dependency (Loukanova,

2010). In this direction, closely related line of re-

search is development of new approach to the fun-

ICAART2013-InternationalConferenceonAgentsandArtificialIntelligence

502

damentals of computation and algorithms. In partic-

ular, new theories of recursion for untyped versions

of full recursion (Moschovakis, 1994), and for typed

cyclic recursion (Moschovakis, 2006), model the con-

cepts of algorithms, in a novel way that covers funda-

mental features of mathematics of computation pro-

cesses. In particular, the formal language and theory

of acyclic recursion L

λ

ar

(Moschovakis,2006) presents

a novel approach to modelling the logical concepts

of meaning and synonymy, by targeting adequateness

of computational semantics of human language. Ini-

tial work on the theoretical aspects of computational

syntax-semantics interface has covered major syntac-

tical constructions of human language (Loukanova,

2011a) by using L

λ

ar

in Generalized Constraint-Based

Lexicalized Grammar (CBLG). Work in that direction

is ongoing. Further work is necessary in the following

directions:

• mathematical modelling of the domains of seman-

tic structures of L

λ

ar

. E.g., in this direction, we tar-

get versions of Situation Semantics.

• developments of type-theory of recursion, in sev-

eral directions for adequacy depending on appli-

cations (Loukanova, 2012). Further work is nec-

essary towards (1) type-theory of full recursion

(2) type-theory of recursion with extended type

systems, for example with dependent types

Another closely related work involves using ver-

sions of Situation Theory and type-theory of algo-

rithms (i.e., of recursion) in large-scale grammati-

cal frameworks for human language. In particular, a

highly expressive new grammatical framework (GF)

(Ranta, 2004; Ranta, 2011), has been under devel-

opments for multi-lingual translations, by targeting

universal, typed-directed syntax that covers seman-

tic fundamentals of human-language. We maintain

the view that GF, as a new branch of CBLG, is open

and highly prospective for further work on syntax-

semantics interfaces, e.g., in the lines of the new ideas

and approaches presented in this paper.

The new foundational developments, such as Sit-

uation Theory and Typed theory of Recursion, target

more adequate, reliable and intelligent foundations of

technological applications. In the same time, they are

part of the ever advancing, scientiﬁc understanding of

the fundamentals of information and computation.

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