formal modelling of reactive agents as an aggregation of simple behaviours

Formal Modelling of Reactive Formal Modelling of Reactive Agents as an aggregation of Agents as an aggregation of

Simple BehavioursSimple Behaviours

P.Kefalas

Dept. of Computer Science13 Tsimiski Str.

546 24 ThessalonikiGreece

[email protected]

TOPICS OF PRESENTATIONTOPICS OF PRESENTATION

Introduction to Formal Modelling

Motivation Modelling Component X-Machines

Building a Communicating X-Machine System

Evaluation

Conclusion

P.Kefalas, CITY Liberal Studies

FORMAL MODELLINGFORMAL MODELLING

Agents, as highly dynamic systems, are concerned with:

(i) a set of appropriate environmental stimuli or inputs,

(ii) a set of internal states of the agent, and

(iii) a set of rules that relate the two above and determines what the agent state will change to if a particular stimulus arrives while the agent is in a particular state.


Although Agent-Oriented Software Engineering aims to manage the inherent complexity of software systems, there is still no evidence to suggest that any methodology proposed so far leads towards correct systems.

It is argued that Formal Methods can (to some extend) solve the problem, under the following conditions: they can deal successfully with complexity of single or

multi agent systems, and they are practical.

Agent Oriented Software EngineeringAgent Oriented Software Engineering


Formal MethodsFormal Methods

Z

VDM

Finite State Machines

Petri Nets

Modelling of data typesModelling of data types

Modelling of controlModelling of control


The Challenge is to develop The Challenge is to develop agent models and implementationsagent models and implementations

that are correctthat are correct

Criteria for correctness: the initial agent model should match with the requirements

the agent model should satisfy any necessary properties in order to meet its design objectives

the implementation should pass all tests constructed using a complete functional test generation method.

MODELLING

VERIFICATION

TESTING


FORMAL MODELLING OF AGENTSFORMAL MODELLING OF AGENTS

In order to be useful to modelling of intelligent agents a formal method should be able:

to model both the data and the changes of an agent, to model separately the behaviours of an agent and the

ways the behaviours interact with each other,

to be intuitive, practical and effective towards implementation of an agent, and

to facilitate development of correct agents.


A FSM-like model A FSM-like model seems to capture most of seems to capture most of

the requirementsthe requirements

space

obstacle

AT BASE

MOVING AT OBJECT

AT OBSTACLE

base

space

base

object

object

space

space

object

obstacle

obstacle

… … but no data, no separate behavioursbut no data, no separate behavioursP.Kefalas, CITY Liberal Studies

X-MACHINESX-MACHINES

X-Machines is:

A General Computational Machine Based on Finite State Machines, but also:

it has a MEMORY structure its transitions are labeled with FUNCTIONS

Therefore:

X-Machines is a formal method which employs a diagrammatic approach to modelling and is capable ofmodelling both DATA and CONTROL of a system.


σ γ

S1

S2

S3

S4

M=(m1, m2, …, mn)

φ1

φ3φ2

φ5 φ4

φ4 φ2

X-MachineX-Machine

Diagrammatical NotationDiagrammatical Notation


COMMUNICATING X-MACHINESCOMMUNICATING X-MACHINESX-Machines can also communicate with each other:

Functions can read an input from a communication input stream, i.e. a “message” sent by the annotated model name

Functions can writes a “message” to the communication input stream of machine with the annotated model name. The “message” is sent after all the output parameters are instantiated.

Therefore:

X-Machines is a formal method can be used to separatelymodel behaviours of an agent system that communicate.


Communicating X-MachineCommunicating X-Machine

Diagrammatical NotationDiagrammatical Notation


xm-1 xm-2

Channel for receiving message

from xm-1

Channel for sending

message to xm-2

σ γ

S1 S2

M=(m1, m2, …, mn)

φ1

S3 S4φ2

Formal DefinitionFormal Definition

X-Machines is a 8-tuple

M = (Σ, Γ, Q, M, Φ, F, q0, m0) Σ, Γ is the input and output finite alphabet respectively Q is the finite set of states M is the (possibly) infinite set called memory Φ is the type of the machine M, a finite set of partial functions φ that map an input and a memory state to an output and a new memory state, φ: Σ M Γ M

F is the next state partial function that given a state and a function from the type Φ, denotes the next state. F is often described as a transition state diagram, F:QΦQ

q0, m0 are the initial state and memory respectively.P.Kefalas, CITY Liberal Studies

Example:Example:

A reactive agent that collects objects, A reactive agent that collects objects, records any objects found on its way and records any objects found on its way and sets up its goal according to the list of sets up its goal according to the list of objects found.objects found.

drop find_base

move

AT BASE

GOING BACK

SEARCHING DIRECTED TO OBJECT

AT OBSTACLE

move

move_back

find_base

lift_object lift_object

find_object

direct_move direct_move

find_obstacle

find_obstacle avoid_obstacle

avoid_obstacle

find_obstacle

avoid_obstacle

do_nothing

find_obstacle

M = (OBJECT{none}, (COORDCOORD), seq (COORDCOORD))

REACTIVE AGENT


Formal DefinitionFormal Definition

Σ = ({space, base}OBSTACLEOBJECT)COORDCOORD

Γ={"moving freely", "moving to base", "dropping food", ...}.

Q={At Base, Searching, At Obstacle, Going Back, Directed to Object}

M = (OBJECT{none}) (COORD COORD) seq (COORD COORD)

m0 = (none, (0,0), nil)

q0 = "At Base"

…lift_object( (obj,x,y),(none,(x,y),objectlist) )

("lifting object",(obj,(x,y),<(x,y) :: objectlist>)), if objOBJECT

find_object( (obj,x,y),(item,(x,y),objectlist) ) ("record object position",(item,(x,y),<(x,y) :: objectlist>)), if itemnone objOBJECT (x,y) objectlist

…P.Kefalas, CITY Liberal Studies

Agents as an aggregation of behavioursAgents as an aggregation of behaviours

identification of the individual behaviours,

modeling of individual behaviours,

aggregation of behaviours in order to construct the whole agent model

Methodology:


Behaviour 1

Behaviour 2

Behaviour 3

Behaviour 4

Com

mu

nication

Agent type 1

Behaviour 1

Behaviour 4

Com

mu

nication

Agent type 2

Com

mu

nication

Multi-Agent System

The methodology is useful for building multi-agent The methodology is useful for building multi-agent systems in which agents have common behaviourssystems in which agents have common behaviours


Example:Example:The same reactive agent as before but The same reactive agent as before but with a set of distinct behaviourswith a set of distinct behaviours

(a) searching for an object,

(b) moving directly to an object,

(c) lifting and dropping objects,

(d) avoiding obstacles

(e) traveling back to the base,

(f) building a map of the environment

Step 1:Step 1:

Identifying individual behaviours:


Step 2:Step 2:

Modelling individual behaviours:

WAITING FOR GOAL

receive_goal

STARTING SEARCH

MOVING

DIRECTLY

move_to_object

get_back

move_to_object receive_goal

BUILDING MAP

find_object

set_goal

M = (seq COORDCOORD) M = (agent_position, object_position)

MD BEM

moving directly to an object building map of the environment


Step 3 (a):Step 3 (a):

Communication of individual behaviours:

WAITING FOR GOAL

receive_goal

STARTING SEARCH

MOVING

DIRECTLY

move_to_object

get_back

move_to_object receive_goal

BUILDING MAP

find_object

set_goal

M = (seq COORDCOORD) M = (agent_position, object_position)

MD

MD BEM

BEM

BEM

moving directly to an object building map of the environment


Step 3 (b):Step 3 (b):

Aggregation of behaviours:

AGENT SEARCHING FOR OBJECT

MOVING TO OBJECT

LIFTING AND DROPPING

AVOIDING OBSTACLES

TRAVELLING TO BASE

BUILDING MAP OF THE

ENVIRONMENT

PERCEPTING

detect_space

detect_obstacle

detect_base

detect_object

PERCEPTOR

PRO-ACTIVE BEHAVIOURS


X-Machines is a FORMAL METHOD but also it

INTUITIVE and EXPRESSIVE as well as PRACTICAL


DISCUSSION AND EVALUATIONDISCUSSION AND EVALUATION

XMDL (X-Machine Description Language) is a declarative mark-up language, which permits the designer to write ASCII code in order to describe a X-machine model.

XMDLmodel

XMDLcommunication

+ =CommunicatingXMDL model

The approach has several advantages for the developer who:

does not need to model a communicating system from scratch, can re-use existing models (behaviours),

can consider modelling and communication as two separate distinct activities in the development of a communicating system based on behaviours,

can use existing tools for both stand-alone and communicating X-machines.

… … Discussion and Evaluation …Discussion and Evaluation …


a COMPLETE TESTING strategy that guarantees to find all faults in the implementation

a MODEL CHECKING strategy that guarantees to verify that specific properties hold (XmCTL)

X-Machines is supported by:

… … Discussion and Evaluation …Discussion and Evaluation …


CONCLUSIONSCONCLUSIONS

X-Machine is a suitable formal method for specifying and building correct reactive agents.

Tools are continuously built in order to facilitate agent development based around X-Machines.

Communicating X-Machines encourage the modular development of agents based on an aggregation of behaviours.

Communicating X-Machines lead towards the specification of large scale multi-agent systems.


Formal Modelling of Reactive Formal Modelling of Reactive Agents as an aggregation of Agents as an aggregation of

Simple BehavioursSimple Behaviours

P.Kefalas

Dept. of Computer Science13 Tsimiski Str.

546 24 ThessalonikiGreece

[email protected]

formal modelling of reactive agents as an aggregation of simple behaviours

Documents