Luís Moniz Pereira Centro de Inteligência Artificial - CENTRIA Universidade Nova de Lisboa [email protected] Pierangelo Dell’Acqua Dept. of Science and

Luís Moniz Pereira

Centro de Inteligência Artificial - CENTRIA

Universidade Nova de Lisboa

[email protected]

Pierangelo Dell’Acqua

Dept. of Science and Technology

Linköping University

[email protected]

Our agents

We propose a LP approach to agents that can:

Reason and React to other agentsPrefer among possible choices Intend to reason and to actUpdate their own knowledge, reactions, and goals Interact by updating the theory of another agentDecide whether to accept an update depending on the

requesting agent

Framework

This framework builds on the works:

Updating Agents - P. Dell’Acqua & L. M. Pereira MAS’99

Updates plus Preferences - J. J. Alferes & L. M. Pereira

JELIA’00

Enabling agents to update their KB

Updating agent: a rational, reactive agent that can dynamically change its own knowledge and goals

makes observations reciprocally updates other agents with goals and rules thinks (rational) selects and executes an action (reactive)

Agent’s language

Atomic formulae:

A objective atoms

not A default atoms

i:C projects

updatesiC

Formulae: Li is an atom, an update or a negated update

active rule

generalized rules

Zj is a project

integrity constraint

false L1 Ln Z1 Zm

A L1 Ln

not A L1 Ln

L1 Ln Z

Projects and updates

A project j:C denotes the intention of some agent i of proposing the updating the theory of agent j with C.

denotes an update proposed by i of the current theory of some agent j with C .

wilma:C

iC

fredC

Example: active rules

money maria : not work

beach maria : goToBeach

travelling pedro : bookTravel

Consider the following active rules in the theory of Maria.

Agent’s language

A project i:C can take one of the forms:

Note that a program can be updated with another program, i.e., any rule can be updated.

i : ( A L1 Ln )

i : ( L1 Ln Z )

i : ( ?- L1 Ln )

i : ( not A L1 Ln )

i : ( false L1 Ln Z1 Zm )

Agents’ knowledge states

Knowledge states represent dynamically evolving states of agents’ knowledge. They undergo change due to updates.

Given the current knowledge state Ps , its successor knowledge state Ps+1 is produced as a result of the occurrence of a set of

parallel updates.

Update actions do not modify the current or any of the previous knowledge states. They only affect the successor state: the precondition of the action is evaluated in the current state and the postcondition updates the successor state.

Enabling agents to prefer

city not mountain not beachnot travelling

work

vacation not work

mountain not city not beachnot travellingmoney

beach not city not mountainnot travellingmoney

travelling not city not mountainnot beachmoney

Let the underlying theory of Maria be:

Since the theory has a unique two-valued model:

M={city, work}

Maria decides to live in the city.

Enabling agents to prefer

If we add the fact ”money” to the theory of Maria, then the theory has 4 models:

M1={city, money, work} M2= {mountain, money, work}

M3= {beach, money, work} M4= {travelling, money, work}

Therefore, Maria is unable to decide where to live.

To select among alternative choices, Maria needs the ability of preferring.

Updates plus preferences

A logic programming framework that combines two distinct forms of reasoning: preferring and updating.

Updates create new models, while preferences allow us to select among pre-existing models

The priority relation can itself be updated.

A language capable of considering sequences of logic programs that result from the consecutive updates of an initial program, where it is possible to define a priority relation among the rules of all successive programs.

Preferring agents

Agents can express preferences about their own rules.

Preferring agent: an agent that is able to prefer beliefs and reactions when several alternatives are possible.

Preferences are expressed via priority rules.

Preferences can be updated, possibly on advice from others.

Priority rules

Let < be a binary predicate symbol whose set of constants includes all the generalized rules:

r1 < r2 means that the rule r1 is preferred to rule r2 .

A priority rule is a generalized rule defining < .

A prioritized LP is a set of generalized rules (possibly, priority rules) and integrity constraints.

Example: a prioritized LP

(1) city not mountain not beachnot travelling

(2) work

(3) vacation not work

(4) mountain not city not beachnot travellingmoney

(5) beach not city not mountainnot travellingmoney

(6) travelling not city not mountainnot beachmoney

1<4 work 4<6 vacation


1<6 work 6<1 vacation M={city, money, work}

If we add ”money” to the theory, then there is a unique model:

If work is false, then vacation holds:

M1={mountain, money, vacation} M2={beach, money, vacation}

Agent theory

The initial theory of an agent is a pair (P,R):- P is an prioritized LP.- R is a set of active rules.

An updating program is a finite set of updates.

Let S be a set of natural numbers. We call the elements sS states.

An agent at state s , written s , is a pair (T,U):

- T is the initial theory of .

- U={U1,…, Us} is a sequence of updating programs.

Multi-agent system

A multi-agent system M={1s ,…, n

s } at state s is a

set of agents 1,…,n at state s.

M characterizes a fixed society of evolving agents.

The declarative semantics of M characterizes the relationship among the agents in M and how the system evolves.

The declarative semantics is stable models based.

Example: happy story


(2) work




(6) travelling not city not mountainnot beachmone







Let the initial theory (P,R) of Maria be:

U={ }

State: 0



(2) work











At state 0 Maria receives l money

U={ } U1={ }l money

State: 1



(2) work











State: 2

Then, Maria receives maria not work

U={ } U1={ }, U2={ }l money marianot work



(2) work




(6) travelling not city not mountainnot beachmoney







State: 3

Then, Maria receives f (5<4vacation)

U={ }U1={ }, U2={ }, U3={ }lmoney marianot work f (5<4vacation)

Future work

The approach can be extended in several ways: Non synchronous, dynamic multi-agent system.

Other rational abilities can be incorporated, e.g., learning.

Development of a proof procedure for updating and preferring reasoning.

Documents

Luís Moniz Pereira Centro de Inteligência Artificial - CENTRIA Universidade Nova de Lisboa [email protected] Pierangelo Dell’Acqua Dept. of Science and