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implTN-TS : Sen(ΣTN) → Sen(ΣTS)
be implementation relations. Let the transactions of a medium be defined by
ΣT = ( ΣTK ΣTI ΣTN, ΣTS, implTK-TI, implTI-TN, implTI-TS )
Let ΣR be a signature of roles and αTR : ΣT → ΣR,
Let ΣP be a signature of protocols and αTP : ΣT → ΣP
Let ΣP be a signature of channels and αTC : ΣT → ΣC
Let ΣM be a signature of processes and αTM : ΣT → ΣM
Where αTX be a functor defined by
αTX(ΣT) = ( αTX(ΣTK) αTX(ΣTI), αTX(ΣTN), αTX(ΣTS), αTX(implTK-TI),
αTX(implTI-TN), αTX(implTI-TS)).
Let be the communication language. Then, we define for the medium communication
language with its transitions
A -mk-> A’ implies O -mk-> O for all mk
∈ Sen(ΣTK) (Ax1)
A -mi-> A’ implies O -mi-> O for all mi
∈ Sen(ΣTI) (Ax2)
A -mn-> A’ implies O -mn-> J(αTR(mn),O) for all mn
∈ Sen(ΣTN) (Ax3)
A -ms-> A’ implies J(αTR(ms),O) -ms-> O for all ms
∈ Sen(ΣTN) (Ax4)
Then, a media reference structure is given by
MRMS = ( ΣD, iDTK,.iDTI, iDTN, iDTS.
ΣTK ΣTI ΣTN, ΣTS, implTK-TI, implTI-TN, implTI-TS,
αTR, αTP, αTC, αTM
{Ax1, Ax2, Ax3,Ax4})
Lechner, U. and Schmid, B.F. (2000) Communities and Media - Towards a
Reconstruction of Communities on Media. In: Sprague, E., (Ed.) Hawaiian
Int. Conf. on System Sciences (HICSS 2000), IEEE Press]
Media Structure:
Let L = (Sign, Sen, Mod, |=, |-) be a general logic. Let ΣR, ΣP, ΣD, ΣC, ΣCS,
ΣOS, ΣMS, ΣCN, in Sign.
A media structure M is defined as
M = CR : L : ThR : MR : JR : nR : Roles
CP : L : ThP : MP : JP : nP : Protocols
CD : L : ThD : MD : JD : nD : D
CC : L : ThC : MC : JC : nC : Channels
CCS : L : ThCS : MCS : JCS : ChannelSystem
COS : L : ThOS : MOS : OrganizationSystem
CMS : L : ThMS : ModelSystem
CSS : L : SyntaxSystem
CLS : LogicSystem
( MRRole(CR), MRProtocol(CP), MRDomain(CD), MRChannels(CC),
MRChannelSystem(CCS), MROrganizationSystem(COS), MRModel-
System(CMS),
MRSyntaxSystem(CSS), MRLogicSystem(CLS) )
where
CR , CP, CD, CC, CCS, COS, CMS, CSS, CLS ∈ Sen(ΣCN)
Roles ⊆ Sen(ΣR),
Protocols ⊆ Sen(ΣP),
D ⊆ Sen(ΣD),
Channels ⊆ Sen(ΣC), nR, nC, nR, nP ⊆ Sen(ΣC), ChannelSystem
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