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Logic for Media | The Computational Media Metaphor Ulrike Lechner

Beat F. Schmid

Media and Communications Management Institute University St. Gallen, Muller Friedberg Str. 8, CH-9000 St.Gallen Email: [email protected]

Media and Communications Management Institute University St. Gallen Muller Friedberg Str. 8, CH-9000 St.Gallen Email: [email protected]

Abstract: New media as they are established by information and communications technology demand for reconsidering the notion of a medium as a carrier of information and with it the concepts for representation, organization, processing and dissemination of information. We explore a general model for media, the Computational Media Metaphor and utilize Rewriting Logic and Labelled Deductive Systems to model media. We obtain a general description of media according to which the medium can be built as well as a generic media architecture. Our example is the NetAcademy, a computational medium for the scienti c community. Keywords: Medium, Multi Agent System, Labelled Deductive System, Rewriting Logic

I. Introduction Information technology has been changing the notion of a medium as a mere carrier of information, with computers as rst arti cial media capable of processing the information they carry and the Internet as a carrier providing ubiquity. The term \new media" refers typically to the technology, e.g., fancy multimedia as well as ubiquity of information. However, technology has the potential to renew the notion of medium more thoroughly. We are particularly interested in new ways to represent, to process information, to organize information and dissemination of information. Thus, we explore how information is turned into a medium. We explore a general model for media, the computational media metaphor [1]. Media are envisioned as spheres for communities of agents and we model those communities als multi-agent systems, considering ve aspects of those media. (1) logic to represent information, (2) agents to process information, (3) channels to transport information, (4) an organization with roles and protocols to describe the behavior of a collection of agents, and (5) possible worlds to relate the representation in the medium to the \real world" outside

the medium. The computational media metaphor is a means to understand communities and their communication platforms and describe them in terms of the enabling technology and science, namely computer science. We employ Rewriting Logic [2] and Labelled Deductive Systems [3] for modeling media. From the general model for media we infer a framework, a generic architecture and a design method. Note that the speci cation formalism in general in uences the model of media. In employing Rewriting Logic we obtain an abstract, yet operational model. We would like to stress that other formalisms could be employed as well. Throughout, our example is the NetAcademy, a medium for the scienti c community [4], [5]. Let us brie y describe the NetAcademy and exemplify hereby the characteristics of computational media:  The NetAcademy relies on the Internet technology as a means to provide access. Note, that it can be attended at www.netacademy.org.  It employs services provided by the carrier computer to process the information it carriers. It provides assistance in searching for information, in tracing relations between documents and in ensuring coherence of contents.  It implements the organization, scienti c communities have been developing in order to manage quality of the authentic knowledge of a community. It mirrors the roles of scienti c communities (e.g., editor, editorial board), supports and implements the processes of knowledge management (e.g., review processes).  A NetAcademy features the knowledge of a scienti c community with its particular view and its particular vocabulary to represent, categorize and systemize knowledge.  It encompasses several interrelated organizations for the knowledge it contains (1) as an encyclopedia it presents authentic knowledge, categorized and systematized. This aspect is implemented as

the glossary. (2) as a platform to stimulate scienti c discussion it presents publications that can be viewed (as in a journal) by publication date or (like in a conference) according to topic [5]. Those organizations distinguish themselves in the way they represent, process and organize knowledge.  A NetAcademy as a medium for a scienti c community is embedded in a Net of communicating NetAcademies. This Net features interdisciplinary research by mediating between the vocabularies of the di erent communities. This paper is organized as follows. Sect. 2 presents the general model of media in an informal way. In Sect. 3, we give the formal notion of a medium. In Sect. 4, we present the media framework, the method to design media and summarize the media components. Related work is discussed in Sect. 5. Sect. 6. concludes with a discussion of our approach. Rewriting Logic and Labelled Deductive Systems are presented in App. 6.

II. The Computational Metaphor

Media

The rst step towards building \new media" is a general model to envision, to structure and to describe them. We call our general model for media the computational media metaphor [1]. Media are envisioned as spheres for communities of agents and modeled as multi-agent systems. Our notion of a medium is depicted in Fig. 1. We consider ve characteristics of a

2. Agents to process knowledge. 3. Channels to transport knowledge over space and time. 4. Organization with roles to describe agents' liabilities and assents and protocols to describe ow of actions in media as well as the way a medium evolves. 5. Possible worlds to relate the description to actual and possible systems. Agents are humans as well as arti cial agents which themselves can be described according to the BeliefDesire Intention architecture of media [6]. The have belief which is the the representation of the outside world, as well as resources, modeled as information that with limited availability. Their intentions describe how they proceed, and which they signalize to the community of agents. Assets and liabilities describe their commitments and how they in uence their behavior. The agent Architecture is depicted in Fig. 2. Note, that media {provided they are adAgent Knowledge

Communication

Ressources

Exchange

Intentions

Signalization

Assets Liablilities

Negotiation

Desires

Fig. 2. Agents in the medium

equately organized{ can be considered as agents and as agents they are part of media. Media may share agents and channels and agents may be in various roles part in several media. Thus, our concept provides the notion of a medium being embedded in a net of interwoven media as depicted in Fig. 3.

Medium

III. A Formal Model of Media Medium

Communication Object

Agent

Fig. 1. Medium

medium: 1. Logic to represent knowledge.

The computational media metaphor, is concretized to a general, formal description of media. We employ Labelled Deductive Systems [3], Rewriting Logic [7] and Maude [7], an object-oriented speci cation language, which is based on Rewriting Logic in the notation supported by the CafeObj system [8]. Rewriting Logic and Maude are hereby our notation and labelled deductive systems a means to structure the media model. The formalisms are explained in App. 6. Let us give

M

M

Agent

M

M

Fig. 3. A net of interwoven media

a brief introduction into Rewriting Logic, Maude and Labelled Deductive Systems. Rewriting Logic describes the structure of the state of a distributed system by equational, order sorted speci cations and its behavior by transition rules. Equations and transition rules de ne a transition system with states and a state transition relation between states. A transition has two connotations (1) computational: the description of computational progress and (2) logical: the successor state is deduced from the predecessor state. Maude is an object-oriented concurrent speci cation language based on the paradigm of Rewriting Logic [7]. Hereby, the state is modeled as a multi-set of objects and messages. Distinguishing are Maude's general and very abstract mechanisms for coordination, synchronization and communication of objects, i.e., for an arbitrary, yet xed number of objects. The pattern at the left-hand side of a rule, comprising objects and messages describes which objects have to coordinate in order to perform a joint state transition as described in the rule. Hereby the pattern of objects and message is replaced in the speci cation of the global state by objects and messages computed at the right-hand side of the rule. Note, that the Rewriting Logic is a logic to model change, not a logic to reason about change [2]. The classical notion of a logic as a relation between sets of sentences is enhanced to a structured, distributed set of sentences and a deduction relation between those structured, distributed sets of sentences [3]. A labelled deductive system is constituted by a logic and an algebra. The labels that are elements of the algebra distinguish sets of sentences and predicates models the relations between those sets of sentences. Formally, a pair

l : S where l is a label and S a set of sentences from some logic is called declarative unit. Declarative units are structured in databases. A database is given by a triple (l; D; f ), where l is the distinguished label, D a diagram of labels, and f a function mapping labels to a set of sentences. The deduction relation is a relation between such databases. This formalism has several applications as [3], [9] suggest. Two of them are relevant in this context: (1) the relation of extra-logical domain and logic to model the possible worlds (2) distribution of formulas to model distributed knowledge. We present for each of the ve components of media a brief description, the formal characterization with logic and an illustrating example from the NetAcademy. Note, that for brevity, we present only fragments of speci cations.

A. Logic Logic represents information, i.e., facts as well as procedural information in a formal way such that it is subject to (mechanical) reasoning. Information about a domain of discourse, which the medium is intended to carry, as well as information about the medium with its structure has to be represented. We follow the approach of [7] and formalize a logic as a quintuple (Sign; sen; Mod; `; j=), where Sign is a class of signatures for which sen de nes the language to each signature. Mod relates each signature with a class of models, ` is a relation between sentences, particular to each signature and j= relates the models with the sentences which hold in them. In the NetAcademy, the domain of discourse is represented as a vocabulary in the Q-calculus [10]. The Q-calculus models objects, with attributes that are related to scales. Those scales are constituted by set of disjoint values and a relation between those values. Scales can be composed to complex scales. Querying allows not only a syntactic search but a semantic search on the bases of the relations on scales. This allows generalization, specialization and interactive re nement. This Q-calculus de nes a vocabulary and each of the NetAcademies has its vocabulary represented the terminology employed by a scienti c community in a structured way.

B. Agents Agents process information. Agents have the ability to store information as knowledge, to process knowledge, and to react to external and internal stimuli according to their abilities. Agents turn information into knowledge, i.e., internalized information that can be used in

order to act and react. Agents model humans as well as artifacts, as e.g., information systems. In our model, agents are characterized by their knowledge, i.e., by the facts as well as the procedural knowledge available to them. Thus, an agent is a set of rules of the logic employed to represent information on the medium. We specify agents as objects and agent types as classes. We introduce a class Agent from which the agents inherit their general structure, i.e., in particular the attribute knowledge carrying the agent's \knowledge". sort Knowledge class Agent { knowledge : Knowledge }

Note that, in Rewriting Logic, this knowledge of agents is modeled as a set of attribute value pairs with rules for manipulating those attribute value pairs. Note furthermore that those rules are common to all agents. Agents of the NetAcademy are, e.g., participants, the publication database, the registration database, the search engine and the documents in their representation as records of data about the publications. class Document [Agent] { authors : Namelist date : Date keywords : Vocabulary } class DocDatabase [Agent] { contents : (Document)Set }

We give as example two agent types, documents and A document carries the information about its authors, its publication date and keywords. The keywords, stem from the Vocabulary, i.e., the information about the domain of discourse a NetAcademy features. A DocDatabase carries a set of documents. A DocDatabase is capable to respond to request for documents. For brevity, we refrain from giving the speci cation of the behavior here.

DocDatabases.

C. Channels Channels transport information over time and space. Channels facilitate communication and they facilitate navigation of agents, moving along channels in the sphere. Examples for channels are the channels as employed in concurrent or distributed systems and hyperlinks. Note, that channels correspond to the traditional notion of a medium as a carrier of information.

We model channels as databases (in the sense of Labelled Deductive Systems, see App. 6), i.e., as a set of labels with relations between them, a distinguished label and a mapping, relating the labels to agents. For combining the agents with channels, we employ Labelled Deductive Systems. For modeling the channels, more precisely the algebra of labels in which the labels, they way they are computed and the relations between labels are given, we employ (again) Rewriting Logic. The transition rules ofthe form crl m1...m_n o1... on => o'1...o'm if p model, how diagrams evolve over time. The right-hand side and the left-hand side of the rule model both a class of diagrams - the ones that match the respective patterns. The left-hand side models a pattern of related labels which is prerequisite for communication and the right-hand side a pattern of related labels which is the result of the communication. Note, that those patterns describe a set of channels. Let us illustrate our notion of channels with examples of the NetAcademy. Channels inside a NetAcademy are the relations between di erent kinds of documents. Those relations are computed, as e.g., by the diagram modeling \all publications of an author", presents a collection of agents representing documents related by a channel to the documents themselves. These channels are computed and they implemented as hyperlinks. There are also cross-organization channels within a medium organizations encompassed in a NetAcademy: the glossary and the vocabulary are interrelated. Diagrams are, e.g., computed in the semantic search engine, which allows to semantically relate knowledge and use those diagrams to access semantically related documents. Let us rst explain how we model agents and channel in the NetAcademy. We model a NetAcademy as a declarative unit < Ni:NetAcademy | Atts > : < Ni:NetAcademy | Knowledge > with a label < Ni:NetAcademy | Atts > and an agent < Ni:NetAcademy | Knowledge >. Let us illustrate this with a particular example, the de nition of the channel for querying for contents in a Inter-NetAcademy search. Incoming queries are transformed by an agent into queries appropriate for the individual NetAcademies vocabularies. The result of the query is a collection of information objects. Let us give the respective speci cation of the channel. crl (to SE : search Topic : res to L) < SE : Searchengine | NAs = N1 N2 N3, map = M >

< < < =>
N2 : NetAcademy > N3 : NetAcademy >

SE : Searchengine | NAs = N1 N2 N3, map = M > < N1 : NetAcademy > < N2 : NetAcademy > < N3 : NetAcademy > ( to L res is R ) if (to N1 : search M(N1,N,Topic) : res to SE) < N1 : NetAcademy > ==> < N1 : NetAcademy > (to SE : res R1) and (to N2 : search M(N2,N,Topic) : res to SE) < N2 : NetAcademy > ==> < N2 : NetAcademy > (to SE : res R2) and (to N3 : search M(N3,N,Topic) : res to SE) < N3 : NetAcademy > ==> < N3 : NetAcademy > (to SE : res R3) and R1 R2 R3 == R .

Let us explain what this fragment of a speci cation models. It speci es a synchronous transition of four objects, the search-engine SE as well as the NetAcademies N1, N2, and N3. Thus, objects have to synchronize for searching in them, i.e., the search in all three NetAcademies is performed simultaneously and the whole search is considered to be an atomic action. The result of this search is collected in the variable R. This result is the concatenation of the search results of the queries in the three NetAcademies, and this is modeled as the rst literal. This rule is a conditional transition rule (keyword crl) and the condition consists of a conjunction of four transitions, three of them are transitions for the single NetAcademies, the forth models how the result of the three individual searches and the global search are related. Let us discuss the model of agents and channels. We model a state as a multi-set (or bag) of agents (or objects). This multiset does not discriminate physical locations and realizes hereby ubiquitous information objects. Only the channels de ne a structure on top of these agents, and de ne the equivalence of space through those channels. Note, that the concept of a channel is in contrast to, e.g., [11] implicit | there is no construct \channel": any of the ubiquitous information objects may communicate provided it is stated in the transition rules. Note, that our approach is compositional. Agents and

channels can be speci ed in di erent formalisms and can be composed to the declarative units. However, typically the way a medium evolves has to take both the agents and their channels into account, since the ability to coordinate typically depends on the relations between labels as well as the agents knowledge. Thus, the deduction relation has to be given at least partly as a relation between the databases.

D. Organization The organization speci es which agents, channels and which relations between agent channel combinations model a medium. Roles describe the agents with their liabilities and assets or obligations and rights constituting a medium. Protocols describe the ow of actions in this medium. An organization is speci ed by a set of roles and a set of protocols. Roles are an abstract and loose description of the agents a medium consists of and protocols are an abstract description of the ow of action and how the medium evolves. Thus, an organization is an abstract description of the collection of agents and channels and the way it evolves. To model this we distinguish the logical characterization of this relation and the way we model organization within the medium. Formally, let SpR be a speci cation of a role and  a role, let SpP a speci cation of protocols, a protocol SpM be a description of a medium and m a medium, then we require that

Mod(SpR)()  Mod(SpM )(m) Mod(SpP )( )  Mod(SpM )(m) Thus, we require that all roles and all protocols that constitute the organization hold in the medium. The organization of agents and protocols cannot only be considered at this abstract level. The organization is in our understanding of the medium an integral part of the medium itself. There are agents whose tacit knowledge encompasses (parts of) the organization. E.g., contracts are externalized protocols, i.e., abstract description of transactions to happen. Contracts are subject to negotiation and once they are settled, the agent has to perform as stated in the contract. Thus, the organization as described in the contract changes when the medium evolves and agents have capability to determine and reason about the organization. Let us describe how we model organization to be an integral part of a medium. Roles are abstract, loose descriptions of agents, their assets and liabilities, or their rights and obligations.

Those roles describe the behavior allowed for an agent as well as the behavior expected by an agent. Rewriting Logic provides us with a rather operational framework, and, thus, the role description is quite operational as well. However, more interesting is structure for integrating organization into channel agent combinations. In this particular, Rewriting logic in uenced model, we equip them with an identity, knowledge as well as the ability to act and react. Roles are more than mere descriptions of agents, they are part of the medium. When playing a role, the behavior of the agent playing the role may change. An agent can be viewed as a collection of the description of the abilities, or knowledge of the agents, with the roles, it is currently playing as well as a speci cation how the roles and the agent description are related. We model an agent playing roles as a labelled deductive systems, where the agent and roles are the logical part, and the algebra models the relation between agent and role. Thus, subject to speci cation are not only the role descriptions, but the relation between roles as protocols as well. Moreover, the agent role relation is subject to some of the agents in the knowledge, thus, it is not necessarily only part of the algebra, but of the logic itself. Let us give an example from the NetAcademy. Consider the relation between the role Editor and the agent type Participant: Participants may play the role \Editor". The Editor has its own identity | such that other objects may send submissions to the \editor". The editor is equipped with knowledge to store some information. For reviewing a paper the both the knowledge of agent and role is employed and the knowledge of the editor changes in the reviewing process. The relation itself is described with a predicate plays. Note, that the relation \plays" itself is not part of the channel system and channel speci cation, but knowledge of the agent Role-Agent-Management. Thus, we model here a NetAcademy capable of altering the plays relation with agents capable of managing the relations between agents and roles. crl (review P) < E : Editor > : KE < P : Participant > : KP < Role-Agent-Management > : plays(P,E) => < E : Editor > : KE' < P : Participant > : KP < Role-Agent-Management > : plays(P,E) if KE KP => KE' .

Let us brie y explain this transition rules. An Editor with knowledge KE and a Participant in KP are related by a channel of the Role-Agent-Management agents knows about a plays relation. The knowledge of the editor is additional information that can be employed by the agents to perform the requested review process, i.e. to react to the message review. This changes the participants knowledge while we have decided to let the knowledge of the Editor as well as the knowledge of the Role-Agent-Management with the respective plays relation unaltered. Protocols specify the ow of actions and the way an medium evolves. Thus, a protocol is an abstract loose description of the relations between agents { the channels{ and the relations between states {the databases. After describing the requirement that a medium has to obey the protocols above, let us model protocols as a component in a medium. Again our model is here heavily in uenced by Rewriting Logic. In any case, it is prerequisite, that a medium has the knowledge to ensure the compliance of communicating agents with the protocol. One way of modeling this is to have a protocol service agent, i.e., an agent with a tacit knowledge about protocols and the history of the medium (modeled as the predicate complies). Note that the relation between databases has to ensure that all transactions become reported to the protocol agent and that transaction only happen when they comply with the protocols of the protocol agent. a l1 : K1 l2 : K2 Protocol : H {P1 ... Pn} => l1 : K1' l2 : K2' Protocol : a;H {P1 ... Pn} if l1 : K1 l2 : K2 ==> l1 : K1' l2 : K2' and complies(a;H,{P1 ... Pn})

Thus, a transaction triggered by a message a takes place, if it complies with the protocols and it is possible, if it possible with the normal agents. The knowledge of the protocol agent encompasses the history of transitions as well as the protocol. Naturally the protocol agent has to have the knowledge how to interpret the \complies" relation.

E. Possible Worlds The Possible world relates a description to the real world, the medium is designed to represent. Within the media, information objects { externalized pieces of information { that are themselves not representable within the logical framework and accessible to processing have to be kept and have to be related to an representation in the medium. The relation between the logical description and the extra-logical domain has to be provided within the logical formalism of the medium. We model the extra-logical domain as labels in Labelled Deductive Systems. Note, that this suits into the formalism that we have established up to now. Those extra-logical labels are channels transporting information from outside the medium into the medium. Let us give an example from the NetAcademy. The publications themselves are not accessible to logic modeling or to processing. However, the metainformation comprising authors, publication data, and keywords, provided by the agent representing the extra-logical document within the formal world is subject to logic reasoning. The \extra-logical" document itself has to be kept in the model and has to be kept within the medium. The document itself is modeled as the label. Thus, we have declarative units of the form doc-file : < P : Document | authors = AList, publicationdate = D, keywords = KL >

The doc-file is the publication itself, which is represented as a le, whose contents cannot be formalized and whose le-format may not be accessible. It is represented by an agent of type Document, with some meta-information. Thus, the labels carry essential information and this information is relevant for us. Rewriting Logic provides a labeling discipline where the label contains all the information about the operations applied to a term. Without explaining this in detail let us mention that then the label carries all the information necessary to understand a term and relates the dual worlds of the formal model and its extra-logical \connotation" in the real world.

IV. Media Architecture The general model for media provides a structured description of media with ve components and how they

are related. This general notion can be concretized to a reference model for media, which is depicted in Fig. 4. Let us explain this reference model more Community View

Business Community (Roles, Protocols)

Implementation Processes

View

Transaction View

Information

Offers Demands

Contracting

Settlement

Infrastructure View

ICT- and Transaction Infrastructure

Knowledge

Intention

Contract

Settlement

Fig. 4. Media architecture

closely. We distinguish four phases (P1) the knowledge phase, where knowledge is gathered, (P2) the intention phase, where agents try compare their belief about the world to the goals they achieve and gain (P3) the contracting phase, where agents communicate in order to establish a relation and (P4) the settlement phase, where agents act according to the commitments. We distinguish furthermore four views: (V1) the community view, in which the roles as well as the protocols of a community are given and which describes the behavior expected from the participants in a community (V2) the process view, which implements the community view with the respective processes (V3) the transaction view, where services are provided as needed in the four phases, (V4) the Infrastructure view, which corresponds to the channels, i.e., which is responsible for communication. The views suggest how to design a medium. The roles and protocols as the most abstract notions of describing a medium with agents and and ow of action and only then the processes that implement those roles and processes. Only then the services requested by agents have to be modeled in a next step in the design. Those services have to be connected by channels transporting information between them. Note, that the four phases of the medium correspond to the agent architecture given in Sect. 2. The reference model structures a medium in phases and views and all those phases and views as well as the components we have developing are basically not more

than information, adequately in various formalisms structured. Let us summarize how we turn information into a medium and obtain a medium capable of carrying information. Information is turned to knowlComponent Information as Logic Information Agent Knowledge, i.e., tacit active information Channel Distributed, communicating knowledge Organization Valid Agent Channel Combination Possible World Relation to the real world. Medium Logic, Channel, Agent combination complying with the organization and related to the real world. Fig. 5. Information lifted to a medium

edge, i.e., active tacit information by the construct of agents. Channels distribute and relate agents and lift the knowledge of agents to distributed, related knowledge of agents. The Organization describe with agents, channel con gurations and which ways of evolving is possible within a medium, i.e., they lift the distributed related knowledge to an organized knowledge and possible world provide the relation to the extra world. Then, information is turned by agents, channels, organization and possible worlds into a medium. Let us discuss the expressiveness of our approach by describing components as they are typical for media in various applications within the medium framework. Contracts are externalized protocols in a medium, in which organization is part of the tacit knowledge of agents. They describe a number of roles for agents. For storing, observing compliance agents with the knowledge to understand the contracts and to check them against the behavior of agents are prerequisite. A repository is a combination of (1) an agent with a logic to represent and process information and possibly with a limited, structured understanding or the ability to abstract from the knowledge which is part of the medium and (2) a channel to transport the contents over space and time. A repository provides roles for the users, describing access privileges within the medium. A project management system is a repository together with an agent responsible for planning, for processing

the time constraints and for communicating with the users. This agent is capable of representing a schedule, acting according to the schedule and, possibly, of adapting the schedule according to constraints imposed by the environment. Those components illustrate how to model complex agents within our model of media.

V. Related Work The keyword \new media" is associated with multimedia [12], [13], with the design of information systems, or (distributed) arti cial intelligence [14], [15] with the respective agent architecture [6]. Those aspects have to be considered when re ning the general model to an implementation of the platform. While there are a number of computational media, there are only few, that employ computer science to describe the domain of discourse. Examples for such computational media are, e.g., the Encyclospace [16], the description, categorization and computer-based interpretation of music in [17]. Regarding the formalisms we refer to [18] for the use of Rewriting Logic in describing architectures for virtual distributed environments and to [19] for relations of Rewriting Logic with other formalisms. [3] presents an an introduction to Labelled Deductive systems. Multi-agent systems can be formalized at di erent levels of abstraction: the -calculus [11] models distributed systems as a collection of mobile agents, Troll [20], o  [21] are examples for object-oriented, formal approaches for describing distributed systems. Particular to our approach is the formalization not only of the domain of discourse to be represented on the medium, but also the medium with its structure as well, while other formal approaches restrict themselves often to processes. [22] employs temporal logic for modeling business processes, [23] deontic logic, [24], [25] Petri Nets. Modeling a system as multi-agent system, demands for reconsidering the services for representation, processing and communication to cope with distributed and heterogeneous structures. The Q-calculus is embedded in such a distributed system [10]. Recursive (product) catalogues [26], distributed planning systems [27] are examples for such key technologies. For an overview of the media for Electronic Commerce see [28] and for knowledge management [29].

VI. Concluding Remarks The trend to globalization and virtualization stimulates the demand for platforms for virtual communities in various application areas. The aspect we focus on in this paper is the information to be represented, processed and communicated on those media and how information is turned into a medium. This model provides a concise and unambiguous description of media and media components and de nes hereby a the notion of a medium in general or for a particular application. The descriptions are speci cations according to which the platforms can be built. Thus, the description covers a signi cant part of the design process. Moreover, a rigorous formal model for media allows to exploit the potential of the underlying technology w.r.t. processing of information - it turns information about the medium to knowledge. However, this model is more than an approach to describe a carrier of information established with a new technology. The media that we capture with this notion distinguish themselves from traditional carriers: The knowledge carried by the medium changes and evolves with the knowledge of the agents. Media are capable of processing the information they carry. Media carry knowledge, i.e., information active within the agents which is employed by the agents to act rather than mere externalized information. This knowledge encompasses not only the information to be transported by the medium | it includes knowledge about the medium, about its structure, its organization and of the means to access the information and to navigate through the medium. A medium is envisioned to be more than a mere and isolated carrier of information | a medium is part of an interwoven net of media. Distinguishing is our notion of a medium. A medium used to be considered as a mere carrier designed for transporting information over time and space [30]. We envision a medium to be more than a carrier: we consider a medium to be a means to structure the infosphere. To conclude let us relate our approach to the context of technology and environment. Modeling a medium as a multi-agent system seems to be adequate for the forthcoming media, since the Internet is clearly covered by this notion and more traditional carriers converge towards this super-medium. However, this approach suggest that the structure with its means to represent and process information must be truly distributed. Moreover, the amount of machine readable externalized information is increasing throughout and and this demands for making information machine

comprehensible, i.e., to increase the quality of information understood as well as for sophisticated intuitive structuring concepts. Thus, we expect expect that media after being empowered by technology to transport information now become empowered by logic to process information determined to change business and society as a whole [31]. Acknowledgments. The anonymous referees provided helpful comments. Martina Klose has proofread the paper and we are indebted to her for stimulating discussions. We gratefully acknowledge nancial support granted by the Grundlagenforschungsfonds of the University St. Gallen for Ulrike Lechner as well as nancial support granted by the Bertelsmann Foundation and the Heinz-Nixdorf Foundation for the MCM-Institute.

References

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Appendix We present the four rewriting rules for the unsorted case of unconditional rewrite rules. T (; X ) denotes the set of all terms over the signature  with free variables X . T E (; X ) is the same set partitioned into

equivalence classes by the equations in E . Re exivity. For each [ t ] 2 T E (; X ):

Transitivity.

[t] : [t] ! [t]

: [ t 1 ] ! [ t2 ] ; : [ t 2 ] ! [ t 3 ] [ ; ] : [ t1 ] ! [ t3 ] Congruence. For each (f : s1      sn ! s) 2 F 1 : [ t1 ] ! [ t01 ] : : : n : [ tn ] ! [ t0n ] f ( 1 ; : : : ; n ) : [ f (t1 ; : : : ; tn ) ] ! [ f (t01 ; : : : ; t0n ) ] Replacement. For each rewrite rule r : [ t(x1 ; : : : ; xn ) ] ! [ t0 (x1 ; : : : ; xn ) ] in R: 1 : [ w1 ] ! [ w10 ] : : : n : [ wn ] ! [ wn0 ] r( 1 ; : : : ; n ) : [ t(w=x) ] ! [ t0 (w0 =x) ]

De nition 1 (Labelled Deductive System) [3] Let A be a rst order language of the form A = (A; R1 ; : : : ; Rk ; f1; : : : ; fm ) where A is the set of terms of the algebra (individual variables and constants) and Ri are predicate symbols (on A, possibly binary) and f1 ; : : : ; fm are function symbols of various arities. A diagram of labels is a set M containing elements generated from A by the function symbols together with formulas of the form R(t1; : : : ; tk ) where ti 2 M and R is a predicate symbol of the algebra. Let L be a predicate language with connectives p1 ; : : : ; pn of various arities with quanti ers and with the same set of atomic terms A as the algebra. An atomic label is a term t 2 A. A label is any term generated form the atomic labels by the symbols f1 ; : : : ; fm A formula is any formula of L. A declarative unit is a pair t : A, where t is a label and A is a formula of L. A database is either a declarative unit or has the form ( ; M; f ), where M is a nite diagram of labels, 2 M is the distinguished label, and f is function associating with each label t in M either a database or a nite set of formulas. .