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
;
SituatedAgentsinLinguisticContexts
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)
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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 lling 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)
SituatedAgentsinLinguisticContexts
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
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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
SituatedAgentsinLinguisticContexts
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.
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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|ll
rdl
]
1
;1 ) (37b)
where r
MARIA
and d are, respectively, the constraints
(34a)–(35a) and (36a)–(36d).
SituatedAgentsinLinguisticContexts
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-
ICAART2013-InternationalConferenceonAgentsandArtificialIntelligence
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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