Interactive Complex Granules

Abstract

Information granules (infogranules, for short) are widely discussed in the literature. In particular, let us mention here the rough granular computing approach based on the rough set approach and its combination with other approaches to soft computing. However, the issues related to interactions of infogranules with the physical world and to perception of interactions in the physical world by infogranules are ? This work was supported by the Polish National Science Centre grants 2011/01/B/ ST6/03867, 2011/01/D/ST6/06981, and 2012/05/B/ST6/03215 as well as by the Polish National Centre for Research and Development (NCBiR) under the grant SYNAT No. SP/I/1/77065/10 in frame of the strategic scienti c research and experimental development program: \Interdisciplinary System for Interactive Scienti c and Scienti c-Technical Information" and the grant No. O ROB/0010/ 03/001 in frame of the Defence and Security Programmes and Projects: \Modern engineering tools for decision support for commanders of the State Fire Service of Poland during Fire & Rescue operations in the buildings"

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As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.

{ Albert Einstein ([ 2 ]) not well elaborated yet. On the other hand the understanding of interactions is the critical issue of complex systems. We propose to model complex systems by interactive computational systems (ICS) created by societies of agents. Computations in ICS are based on complex granules (c-granules, for short). In the paper we concentrate on some basic issues related to interactive computations based on c-granules performed by agents in the physical world. 1

Introduction

Granular Computing (GC) is now an active area of research (see, e.g., [ 16 ]). Objects we are dealing with in GC are information granules (or infogranules, for short). Such granules are obtained as the result of information granulation [ 26, 28 ]:

Information granulation can be viewed as a human way of achieving data compression and it plays a key role in implementation of the strategy of divide-and-conquer in human problem-solving.

The concept of granulation is rooted in the concept of a linguistic variable introduced by Lot Zadeh in 1973 [ 25 ]. Information granules are constructed starting from some elementary ones. More compound granules are composed of ner granules that are drawn together by indistinguishability, similarity, or functionality [ 27 ].

Computations on granules should be interactive. This requirement is fundamental for modeling of complex systems [ 3 ]. For example, in [ 13 ] this is expressed as follows

[...] interaction is a critical issue in the understanding of complex systems of any sorts: as such, it has emerged in several well-established scienti c areas other than computer science, like biology, physics, social and organizational sciences.

Interactive Rough Granular Computing (IRGC) is an approach for modeling interactive computations (see, e.g., [17, 19{23]). Computations in IRGC are progressing by interactions represented by interactive information granules. In particular, interactive information systems (IIS) are dynamic granules used for representing the results of the agent interaction with the environments. IIS can be also applied in modeling of more advanced forms of interactions such as hierarchical interactions in layered granular networks or generally in hierarchical modeling. The proposed approach [17, 19{23] is based on rough sets but it can be combined with other soft computing paradigms such as fuzzy sets or evolutionary computing, and also with machine learning and data mining techniques. The notion of the highly interactive granular system is clari ed as the system in which intrastep interactions [ 4 ] with the external as well as with the internal environments take place. Two kinds of interactive attributes are distinguished: perception attributes, including sensory ones and action attributes.

In this paper we extend the existing approach by introducing complex granules (c-granules) making it possible to model interactive computations performed by agents. Any c-granule consists of three components, namely soft suit, link suit and hard suit. These components are making it possible to deal with such abstract objects from soft suit as infogranules as well as with physical objects from hard suit. The link suit of a given c-granule is used as a kind of c-granule interface for expressing interaction between soft suit and and hard suit. Any agent operates in a local world of c-granules. The agent control is aiming to control computations performed by c-granules from this local world for achieving the target goals. Actions (sensors or plans) from link suits of c-granules are used by the agent control in exploration and/or exploitation of the environment on the way to achieve their targets. C-granules are also used for representation of perception by agents of interactions in the physical world. Due to the bounds of the agent perception abilities usually only a partial information about the interactions from physical world may be available for agents. Hence, in particular the results of performed actions by agents can not be predicted with certainty.

In Section 2 a general structure of c-granules is described and some illustrative examples are included. Moreover, some preliminary concepts related to agents performing computations on c-granules are discussed. In Section 3 the agent architecture is outlined. Societies of agents and communication languages are discussed shortly in Section 4.

This paper is a step in the realization of the Wisdom Technology (WisTech) programme [6{8]. 2

Complex Granules and Physical World We de ne the basic concepts related to c-granule relative to a given agent ag. We assume that the agent ag has access to a local clock making it possible to use the local time scale. In this paper we consider discrete linear time scale.

We distinguish several kinds of objects in the environment in which the agent ag operates: { physical objects (called also as hunks of matter, or hunks, for short) [ 5 ] such as physical parts of agents or robots, speci c media for transmitting information; we distinguish hunks called as artifacts used for labeling other hunks or stigmergic markers used for indirect coordination between agents or actions [ 9 ]; note that hunks may change in time and are perceived by the agent ag as dynamic (systems) processes; any hunk h at the local time t of ag is represented by the state sth(t); the results of perception of hunk states by agent ag are represented by value vector of relevant attributes (features); { complex granules (c-granules, for short) consisting of three parts: soft suit, link suit, and hard suit (see Figure 1); c-granule at the local time t of ag is denoted by G; G receives some inputs and produces some outputs; inputs and outputs of c-granule G are c-granules of the speci ed admissible types; input admissible type is de ned by some input preconditions and the output admissible type is de ned by some output postconditions, there are distinguished inputs (outputs) admissible types which receive (send) c-granules from (to) the agent ag control;

G soft suit consists of 1. G name, describing the behavioral pattern description of the agent ag corresponding to the name used by agent for identi cation of the granule, 2. G type consisting of the types of inputs and outputs of G c-granule, 3. G status (e.g., active, passive), 4. G information granules (infogranules, for short) in mental imagination of the agent consisting, in particular of G speci cation, G implementation and manipulation method(s); any implementation distinguished in infogranule is a description in the agent ag language of transformation of input c-granules of relevant types into output c-granules of relevant types, i.e., any implementation de nes an interactive computation which takes as input c-granules (of some types) and produces some c-granules (of some types); inputs for c-granules can be delivered by the agent ag control (or by other c-granules), we also assume that the outputs produced by a given c-granule depend also on interactions of hunks pointed out by link suite as well as some other hunks from the environment - in this way the semantics of c-granules is established; G link suit consists of 1. a representation of con guration of hunks at time t (e.g., mereologies of parts in the physical con gurations perceived by the agent ag); 2. links from di erent parts of the con guration to hunks; 3. G links and G representations of elementary actions; using these links the agent ag may perform sensory measurement or/and actions on hunks; in particular, links are pointing to the sensors or e ectors in the physical world used by the considered c-granule; using links the agent ag may, e.g., x some parameters of sensors or/and actions, initiate sensory measurements or/and action performance; we also assume that using these links the agent ag may encode some information about the current states of the observed hunks by relevant information granules; G hard suit is created by the environment of interacting hunks encoding G soft suit, G link suit and implementing G computations; soft suit and link suit of G are linked by G links for interactions between the G hunk con guration representation and G infogranules; link suit and hard suit are linked by G links for interactions between the G hunk con guration representation and hunks in the environment.

The interactive processes during transforming inputs of c-granules into outputs of c-granules is in uenced by 1. interaction of hunks pointed out by link suit; 2. interaction of pointed hunks with relevant parts of con guration in link suit.

Agent can establish, remember, recognize, process and modify relations between c-granules or/and hunks.

A general structure of c-granules is illustrated in Figure 1.

agent behavioral pattern description used by agent for c-granule identification

c-GRANULE G (at the local agent ag time)

G links between G hunk configuration representation and G infogranules type defined by

acceptance postconditions

G soft_suit output c-granule of admissible output type G link_ suit

G hard_suit G links between hunks and their configurations) input type defined by acceptance preconditions input c-granule of admissible input type

input/output c-granules (of control type) G name G status G type

G infogranules (e.g., G specification, G implementation and manipulation method(s))

G infogranular representation of hunk

configurations + G links + representations of G elementary actions

environment of interacting hunks encoding G soft_suit, G link_suit and

implementing G computations G interactions with environments operational semantics: implementation and manipulation method(s) of admisssible nacamsees, oi-fointtyeprperse,teaxtipoenc(timedplseemmenatnattiicosn) of interactive computations with goals specified by specisfipcaetcioifnic(aatbiostnra,cotpseermaatinotnicas)l,si.eem., parnotcicesdures for performing interactive computations by the agent ag control; this includes checking the expected properties of I/O/C c-granules and other conditions, specification e.g., after sensory measurements and/or action realisation using links to hunk configuration(s) with the structure defined by G link_suit; possible cases of interpretation are often defined relative to different universes of c-granules and hunks)

In Figure 2 we illustrate how the abstract de nition of operation from soft link interacts with other suits of c-granule. It is necessary to distinguish two cases. In the rst case, the results of operation realized by interaction of hunks are consistent with the speci cation in the suit link. In the second case, the result speci ed in the soft suit can be treated only as an estimation of the real one which may be di erent due to the unpredictable interactions in the hard suit. Figure 3 illustrates c-granules corresponding to sensory measurement. Note that in this case, the parameters xed by the agent control may concern sensor selection, selection of the object under measurement by sensor and selection of sensor parameters. They are interpreted as actions selected from the link suit. In the perception of con guration of hunks of c-granule are distinguished infogranules representing sensor, object under measurement and the con guration itself. The links selected by the agent control represent relations between states of hunks and infogranules corresponding to them in the link suit. h2

G1 ‘G1’  …

G1 G2 ‘G1 G2’ h1 … h infogranues in soft_suit corresponding to specification and implementation of operation  programs, actions or plans implementing 

representation of configuration of hunks for  consisting of representations of arguments of , programs for computing , etc. links for reading a representation of

G1 G2 from h Figure 4 illustrates how an interactive information (decision) system is created and updated during running of c-granule implementation according to scenario(s) de ned in the soft suit and related G links. Such information (decision) systems are used for recording information about the computation steps during c-granule implementation run. Note that the structure of this information system is di erent from the classical de nition [ 14, 15, 18 ]. In particular, this system is open because of links to physical objects as well as interactions are changing (often in unpredictable way) in time. In our approach, the agent can be also interpreted as c-granule. However, this is a c-granule of higher order with embedded control. One can also consider another situation when the c-granules are autonomous but this is out of scope of this article. Instead of this one can consider interactions in societies of agents. We assume that for any agent ag there is distinguished a family of elementary c-granules and constructions on c-granules leading to more compound c-granules. The agent ag is using the constructed granules for modeling attention and interaction with the environment. Note that for any new construction on elementary granules (such as network of c-granules) should be de ned the corresponding c-granule. This c-granule should have appropriate soft suit, link suit and hard suit so that the constructed c-granule will satisfy the conditions of the new c-granule construction speci cation. Note that one of the constraints on such construction may follow from the interactions which the agent ag will have at the disposal in the uncertain environment.

input: perform the sensory measurement by sensor s in the hunk configuration h (i) establish links with the sensor and the hunk under measurement, (ii) in interaction with link_suit select the relevant action ac and parameters p for the action relevant for initiation the sensory measurement, (iii) record in the corresponding information system the results of sensory measurements on the basis of the properties of the states of sensor during the measurement process.

c-granule soft_suit specification implementation scenario

s hard_suit: dynamic hunk configuration h in the environment with the physical sensor s specification given by input

output: information system representing the sensory measurement process by sensor s

link_suit: with the representation of the dynamic hunk configuration h

and links from sensor representation to the physical sensor s labeled by selected ac(p) (action ac with relevant parameters p) initiating the sensory measurement and the

hunk on which the measurement is performed Agents may be treated as generalized c-granules with embedded control structure.

Any agent ag is de ned over several classes of c-granules. Among them are: { senbot (sensory bot) - class of c-granules representing possible states of the agent sensory measurements with at most one distinguished c-granule at the local time moment t of agent ag; { imbot (imagination bot)- class of all possible c-granules which can be constructed by the agent ag from sensory measurements with at most one distinguished c-granule at the local time moment t of agent ag; { embot (emotional bot)- subclass of imbot class representing emotional concepts of the agent ag; { nebot (needs bot)- subclass of imbot class representing concepts of the agent ag needs; { enabot (environment action bot) - subclass of imbot class specifying the agent ag elementary actions in the environment; { imobot (imagination operation bot) - subclass of imbot class specifying the agent ag elementary operations (di erent from elementary actions) on cgranules from imbot; link_suit consisting of hunk configuration representation at time t together with links to hunks (labeled by elementary actions or /and plans); input c-granules for the considered c-granule are defined, e.g., by some parts of the configuration representation or values of control paremeters S(t) values of control parameters at time t

for conditional attributes values of conditional (hierarchical) attributes at time t‘ >t representing curent results of measurements

decisions values of decision attributes at time

t’’>t’ corresponding to output c-granules

for the considered cgranule row of decision system corresponding to implementation of c-granule links (labeled by actions or /and plans) at time t represent relations between infogranules and hunks defined by representation of hunk configuration of the

global state S(t) defined by the agent control system { abot (attention bot) - subclass of imbot class representing c-granules currently under attention by the agent ag; { activebot - subclass of imbot class representing c-granules currently active; { passivebot - subclass of imbot class representing c-granules currently passive; { metbot (method bot) - subclass of imbot representing methods of manipulation on c-granules (construction, destruction, modi cation, join, classi ers construction); { metabot (method adaptation bot) subclass of imbot representing c-granules used for adaptation or/and modi cation of the given methods of manipulation on c-granules.

The language of c-granule names consists of { set of names of existing c-granules; { set of names of new generated c-granules.

Types of objects relative to c-granules in imbot: { set of types of existing c-granules; { set of types of new generated c-granules.

There are some distinguished c-granules of the agent ag: { Meaning relation (Mean) - a distinguished c-granule representing a relation between c-granules and their names. { Type relation (TypeMean) - a distinguished c-granule representing a relation between c-granules and their types. { Reference relation (Ref) - a distinguished c-granule representing a relation between c-granules and 'related' names. { Jbot (Judgment bot) - a distinguished c-granule representing actual collection of strategies of approximate reasoning used by the agent ag for judgment and risk assessment in the current environment and agent situation. { Cobot (control bot) - a distinguished c-granule representing actual collection of strategies of approximate reasoning used by the agent ag for control, adaptation, and modi cation of all the agent ag c-granules. { Metacobot (meta-control bot) - a distinguished c-granule representing actual collection of strategies of approximate reasoning used by the agent ag for cobot control, adaptation, and modi cation.

The generalized c-granules corresponding to agents are de ned using also the above classes of c-granules for de ning corresponding suits of such generalized c-granules. The details of such construction will be presented in our next papers. Here, we would like to note only that there is a quite general approach for de ning new c-granules from the simpler already de ned.

Figure 5 illustrates an idea of transition relation related to a given agent ag. The relation is de ned between con gurations of ag at time t and the measurement time next to t. A con guration of ag at time t consists of all con gurations of c-granules existing at time t. A con guration of c-granule G at time t consists of G itself as well as all c-granules selected on the basis of links in the link suit of G at time t. These are, in particular all c-granules pointed by links corresponding to the c-granules stored in the computer memory during the computation process realised by c-granule as well as c-granules corresponding to perception at time t of the con guration of hunks at time t.

agent configuration at

time t (with a predicted granule’s structure at the time unit next to t) agent configuration at the time unit next to t (not necessarily satisfying the predicted results):

the result of interactions caused by undertaken actions

and unpredicted interactions with the

environment (parallel) realization by the agent of selected actions, sensory measurements, new information granule construction/destruction,

etc.

Fig. 5. Transiton relation of the agent ag

Societies of Agents and Communication Languages We assume that the agents can perceive behavioral patterns of other agents of their groups and based on this they can try to exchange some messages [ 10 ]. It is worthwhile to mention that at the beginning agents do not have common understanding of the meaning of such messages. In the consequence, this leads to misunderstanding, not comfortable situation for agents (in terms of hierarchy of their needs represented by nebot). However, after series of trials they have a chance to set up common meaning of some behavioral patterns. In other words, they start to create common c-granules which use agreed links to other hunks or infogranules and also descriptions of some details about actions related to meaning or methods of implementation of the infogranule contents. For example, at the beginning the messages could be linked to warning situations or to identi cations of some sources for satis ability of some agent needs. This kind of simple messages could be passed by very simple behavioral pattern. Next, based on these very simple behavioral patterns the agents can develop more compound messages related to c-granules corresponding to common plans of cooperation of group of agents or/and competition with other groups of agents. This very general framework could be implemented in many ways using di erent AI paradigms. Especially, many models from Natural Computing could be quite helpful (e.g., modi cation of cellular automata or evolutionary programming). However, our proposal is to implement this general scheme by agents having soft suit and link suit built up on the hierarchies of interactive information (decision) systems linked to con gurations of hunks. Starting from the simplest case when we have just one attribute and one message to be passed up to quite complex system this approach based on rough sets is quite convenient for implementation by computers well prepared for manipulation on tables of data.

It has to be underlined that the behavioral patterns are complex vague concepts. Hence, some advanced methods for approximation of these concepts should be used. Usually these methods are based on hierarchical learning (see, e.g., [ 11, 1 ]). Note that often in satis ability checking for vague concept, actions or/and plans are used. In the rough set approach it is important to remember that the attribute values are given only for some examples from reality. Moreover, if we use a large number of attributes or/ and hierarchical learning this will not guarantee the exact description of reality in terms of perceived vague concepts.

Languages of agents consist of partial descriptions of situations (or their indiscernibility or similarity classes) perceived by agents as well as description of approximate reasoning schemes about the situations and their changes by actions and /or plans. The situations may be represented in hierarchical modeling by structured objects (e.g., relational structures over attribute value vectors or/and indiscernibility (similarity classes) of such structures). In reasoning about the situation changes one should take into account that the predicted actions or/and planes may depend not only on the changes of past situations but also on the performed actions and plane in the past. This is strongly related to the idea of perception pointed out in [ 12 ]:

The main idea of this book is that perceiving is a way of acting. It is something we do. Think of a blind person tap-tapping his or her way around a cluttered space, perceiving that space by touch, not all at once, but through time, by skillful probing and movement. This is or ought to be, our paradigm of what perceiving is.

Note that the expression of the language may be used without its 'support' in corresponding link suit and hard suit of c-granules under the assumption that there are xed coding methods between expressions and hunks by the agent. However, the languages should contain more general expressions for communication usually requiring the usage of expressions representing classes of hunks rather than single hunks. This follows from the fact that the agents have bounded abilities for discernibility of perceived objects. In our approach the situations and reasoning schemes about situations are represented by c-granules.

Note that di erent behavioral patterns may be indiscernible relative to the set of attributes used by the agent. Hence, it follows that the agents perceive objects belonging to the same indiscernibility or/and similarity class in the same way. This is an important feature making it possible to use generalization by agents. For example, the situations classi ed by a given set of characteristic functions of induced classi ers (used as attributes) may be indiscernible. On the other hand, a new situation unseen so far may be classi ed to indiscernibility classes which allows agents to make generalizations. The new names created by agents are names of new structured objets or their indiscernibility (similarity) classes.

Agents should be equipped with adaptation strategies for discovery of new structured objects and their features (attributes). This is the consequence of the fact that the agents are dealing with vague concepts. Hence, the approximations of these concepts represented by the induced classi ers evolve with changes in uncertain data and imperfect knowledge.

Conclusions and Future Research

The outlined research on the nature of interactive computations is crucial for understanding complex systems. Our approach is based on complex granules (c-granules) performing computations through interaction with physical objects (hunks). Computations of c-granules are controlled by the agent control. More compound c-granules create agents and societies of agents. Other issues outlined in this paper such as interactive computations performed by societies for agents, especially communication language evolution and risk management in interactive computations will be discussed in more detail in our next papers.

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