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names-channels using which the data transmition is
done. The connection of entities of domain to con-
crete transmited data brings the sense of calculation
of some fixed objects in the domain. This objects
can be corresponding structure divisions, regulative
documents and other objects of domain that do not
depend on concrete execution. The usage of label as
the channel of data transition/receiving will be used
for process execution assessment. For doing this
with each label a lot of entities of domain that repre-
sent the using resources, defined in the strategy, will
be connected. The execution of reduction step, in-
cluded such label will be estimated as the usage of
this resource, all such costs are saved during the
process execution. This makes it possible to estimate
the process execution in the context of all resources,
defined in the frames of strategy. All calculated
costs could be estimated in accordance with certain
rules and criteria, defined in the frames of strategy.
For further concrete process description let us
define the term of context of execution Δ for term
|Γ
⊢. Under this context we will understand the
vocabulary the key of which is label ∈, and the
value – object of conceptual model, connected with
this label. The sense of this context is in the connec-
tion of abstract names of π-calculus with using ob-
jects without the violation of the structure that is
defined by calculus and semantics. The term of π-
calculus that is having the empty context or does not
include the values of each label, we will call the
structure process model
. The term the context of
which contain the values for all labels we will call
the conceptual process model
.
,Δ ∈
⇒Γ
⊢ &∀ ∈
∩→ ∈Δ
,Δ ∈
⇒Γ
⊢&∃∈
∩→
∈Δ
The difference between these two types is in the
non-redex terms of the structure model, which can
be reduced in the conceptual model by the functions
execution that are connected with labels from the
context of process execution that are coded in the
same way as predicates in pre and post conditions.
In addition to writing in the context of execution
for label will be defined the term if the name type. In
the classical typed π-calculus for each name the type
is assigned that is an atomic type or channel type
(Pierce and Sangiorgi, 1993), (Barendregt et. al,
1977). We will extend this term for supporting the
semantic mark-up – will call the full type of the
name the pair
,
, where the first element is the
ordinary type of calculus and the second element is
the type, defined by the semantic object, connected
with this label. For the names that do not have the
connection with the semantic object, the second type
equals «null» type of using means of semantic mod-
elling. These changes will paired with using extend-
ed type system (Barendregt, 1991) for functions
defined by λ-calculus terms.
By its nature the process modelling using the π-
calculus does not operate with the definitions of ac-
tions (steps of the process) however they can be used
in the form of requirements in the strategy and using
the request to lots of model can be formulated. In the
strategy, the action will be represented as an indi-
vidual object, which is characterized, by the type of
the entity received as the input, the type of the result
and, optionally, the resources that are used for this
action execution.
For supporting the requests that operate the term
of action we will use the following agreement. Ac-
tion in the term of π-calculus is the term that is con-
ceptual process model reducing to the process,
consisting from prefixes of data transition, parallel
composition and empty process. The execution of
actions starts from receiving the data of label or
from executing some function where at least one of
the arguments is the label. The example of action
will be the process
,
̅
,
,
〈
,
〉
,
where the following interpretation in frames of the
considered domain can be presented: the information
system
for new employee x creates the unique
code a and transmits the employee data with its code
for further legislation
̅
,
. This action will be
characterised by the type of recieving object (new
employee) and the type of returning object (empty
type as the process terminates by the local data
transmition). For additional data identification there
can be identified the action according to the context
of process execution after the action reduction. The
set of actions that the process contains from is de-
fined by the process reduction and the selection of
all appropriate for action definition sub processes.
Summarising the receiving extensions we will
get:
1) The semantic mark-up of the process allows to
use in the processes pre and post conditions,
regulating the process execution depending on
the executing objects;
2) The context definition in the conceptual pro-
cess model allows to estimate the «price/value»
of process execution;
3) For the model there can be received the set of
executing actions in the terms of canonical
model, the received set can be compared with
set in the strategy by the coincidence of general
characteristics;
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