1. An argument-based framework to model an agent's beliefs in a dynamic environment Marcela Capobianco Carlos I. Chesñevar Guillermo R. Simari Dept. of Computer Science and Engineering U NIVERSIDAD N ACIONAL DEL S UR ARGENTINA

2. ArgMAS 2004 - New York2 Outline  Motivation  The Argumentation Framework  Potential Arguments  Conclusions

3. ArgMAS 2004 - New York3 Introduction  In this presentation we will show how a Logic Programming approache to argumentation may be suitable for applications in MAS.  Here, we present ODeLP which is an argument- based formalism for knowledge representation and reasoning in dynamic environments.  ODeLP uses defeasible argumentation to decide between conflicting goals.  We will begin presenting the general framework of DeLP of which ODeLP is a restriction.

4. ArgMAS 2004 - New York4 Deafeasible Logic Programming: DeLP A Defeasible Logic Program ( dlp ) is a set of facts, strict and defeasible rules denoted  = ( ,  ) bird ( X )  chicken ( X ) chicken ( tina ) bird ( X )  penguin ( X ) penguin ( opus )  flies ( X )  penguin ( X ) scared ( tina ) flies ( X )  bird ( X )  flies ( X )  chicken ( X ) flies ( X )  chicken ( X ), scared ( X ) Strict Rules Facts Defeasible Rules  

5. ArgMAS 2004 - New York5 Argument Def: Let L be a literal and   ( ,  ) be a program.  , L  is an argument for L, if  is a set of rules in  such that: 1)There exists a defeasible derivation of L from    ; 2)The set    is non contradictory; and 3)  is minimal, that is, there is no proper subset  of  such that  satisfies 1) and 2).

6. ArgMAS 2004 - New York6 An example poor_perf ( john ). sick ( john ). poor_perf ( peter ). unruly ( peter ). suspend ( X )   responsible ( X ). suspend ( X )  unruly ( X ).  suspend ( X )  responsible ( X ).  responsible ( X )  poor_perf ( X ). responsible ( X )  good_perf ( X ). responsible ( X )  poor_perf ( X ), sick ( X ). ?- suspend ( john ).

7. poor_perf ( john ). sick ( john ). good_perf ( peter ). unruly ( peter ) suspend ( X )   responsible ( X ). suspend ( X )  unruly ( X ).  suspend ( X )  responsible ( X ).  responsible ( X )  poor_perf ( X ). responsible ( X )  good_perf ( X ). responsible ( X )  poor_perf ( X ), sick ( X ).  {  suspend ( john )  responsible ( john )., responsible ( john )  poor_perf ( john ), sick ( john ).},  suspend ( john )   suspend ( john ) responsible ( john ) poor_perf ( john ) sick ( john ) poor_perf ( john ) An argument for  suspend ( john ) built from the program

8.  suspend ( john ) responsible ( john ) poor_perf ( john ) sick ( john ) poor_perf ( john )  , Q  is a subargument of  , L  if  is an argument for Q and     = { responsible ( john )  poor_perf ( john ), sick ( john ).}  = {  suspend ( john )  responsible ( john )., responsible ( john )  poor_perf ( john ), sick ( john ).}

9. Counter-arguments   { suspend ( john )  suspend ( john )}  suspend ( john ) responsible ( john ) poor_perf ( john ) sick ( john ) poor_perf ( john ) poor_perf ( john ). sick ( john ). good_perf ( peter ). unruly ( peter ) suspend ( X )   responsible ( X ). suspend ( X )  unruly ( X ). suspend ( X )   responsible ( X ).  suspend ( X )  responsible ( X ).  responsible ( X )  poor_perf ( X ). responsible ( X )  good_perf ( X ). responsible ( X )  poor_perf ( X ), sick ( X ). responsible ( john ) poor_perf ( john ) sick ( john ) poor_perf ( john )   { responsible ( john ),  responsible ( john )} suspend ( john )  responsible ( john ) poor_perf ( john )

10. ArgMAS 2004 - New York10 An argument  , P  is a proper defeater for  , L  if  , P  is a counter-argument  , L  that atacks a subargument  , Q  de  , L  and  , P  is better than  , Q  (by some comparison criterion). Proper Defeater responsible ( john ) poor_perf ( john ) sick ( john ) poor_perf ( john ) suspend ( john )  responsible ( john ) poor_perf ( john )

11. ArgMAS 2004 - New York11 An argument  , P  is a proper defeater for  , L  if  , P  is a counter-argument  , L  that atacks a subargument  , Q  de  , L  and  , P  is not comparable to  , Q  (by some comparison criterion) Blocking Defeater suspend ( john ) unruly ( john )  suspend ( peter ) responsible ( peter ) good_perf ( peter )

12. 00 11 22 33 22 33 44 33 44 55 11 22 Dialectical Tree Given a program  = ( ,  ), a literal L will be warranted if there is an argument  , L  built from , and that argument has a dialectical tree whose root node is marked U. That is, argument  , L  is an argument for which all the possible defeaters have been defeated. We will say that  is a warrant for L.   , L 

13.  *  , L  Marking of a Dialectical Tree  U U D U U U U U D D D D

14. ArgMAS 2004 - New York14 Answers in DeLP Given a program  = ( ,  ), and a query for L the posible answers are: YES, if L is warranted. NO, if  L is warranted. UNDECIDED, if neither L nor  L are warranted. UNKNOWN, if L is not in the language of the program.

15. ArgMAS 2004 - New York15 Observation based DeLP  In ODeLP we will restrict the program that represents the agent’s knowledge base  to a set  of facts and a set  of defeasible rules.  We will denote the knowledge base     The restriction of the non-defeasible part of  to facts, eliminating strict rules, is a change that has no effect in the capabilities of the system but makes belief revision coming for new observations easier.

16. ArgMAS 2004 - New York16 Beliefs and Perception  The set of agent’s beliefs is formed by the warranted literals, i.e., those that are supported by an undefeated argument.  From agent’s new perceptions, beliefs could change.  Our view of perception is simple and relies on the assumption that observations are correct.  If new perceptions are in conflict with old ones, new perceptions are always preferred.

17. ArgMAS 2004 - New York17        (    )   { O 1, …, O n }  Beliefs and Perception  If new perceptions are in conflict with old ones, new perceptions are always preferred.  If  is the set of new perceptions, the revision of the set of facts is done as follows: { O 1, …, O n }     

18. ArgMAS 2004 - New York18 Change in Beliefs  New observations lead to change in what the agent should believe.  Because the process of calculating the new warrants is computationally hard we have developed a system to integrate precompiled knowledge in ODeLP to address real time constrains.  Our goal is to avoid recomputing arguments.  A condition is that the precompiled knowledge should be independent from the observations.

19. ArgMAS 2004 - New York19 Dialectical Database  The Dialectical Database of a defeasible logic program is a graph from which every dialectical tree can be obtained.  Potential arguments, to be defined next, use schematic rules and are the nodes in this structure.  The arcs in the graph represent the defeat relation among them.  We have developed algorithms for the construction and use of dialectical databases.

20. ArgMAS 2004 - New York20 Potential Arguments Def: Let  be a set of defeasible rules. A subset A of  is a potential argument for a literal Q, noted  A, Q  if there is a noncontradictory set of literals  and an instance  of the rules in A such that  , Q  is an argument with respect to program ( ,  ).

21. ArgMAS 2004 - New York21 An example poor_perf ( john ). sick ( john ). poor_perf ( peter ). unruly ( peter ). suspend ( X )   responsible ( X ). suspend ( X )  unruly ( X ).  suspend ( X )  responsible ( X ).  responsible ( X )  poor_perf ( X ). responsible ( X )  good_perf ( X ). responsible ( X )  poor_perf ( X ), sick ( X ).

22. ArgMAS 2004 - New York22 Some Potential arguments B 1 ={ suspend ( X )   responsible ( X ).} B 2 ={ suspend ( X )   responsible ( X ).,  responsible ( X )  poor_perf ( X ).} B 3 ={  suspend ( X )  responsible ( X ).} B 4 ={  suspend ( X )  responsible ( X )., responsible ( X )  good_perf ( X ).} B 5 ={  suspend ( X )  responsible ( X )., responsible ( X )  poor_perf ( X ), sick ( X ).} C 1 ={ responsible ( X )  good_perf ( X ).} C 2 ={  responsible ( X )  poor_perf ( X ).} C 3 ={  responsible ( X )  poor_perf ( X ), sick ( X ).}

23. ArgMAS 2004 - New York23 Graph for the DD C1C1 C2C2 C3C3 B3B3 B4B4 B5B5 B1B1 B2B2 The defeat relation among potential arguments (proper and blocking) is also recorded.

24. ArgMAS 2004 - New York24 ODeLP-based agent architecture Dialectical base ODeLP inference engine Updating mechanism perceptions queries answers Observations Defeasible rules

25. ArgMAS 2004 - New York25 Conclusions  Solid theoretical foundations for agent design should be based on proper formalisms for KR&R.  Real time issues are critical when modeling agent interaction in a MAS setting.  Dialectical databases could help deal with these constrains.  Defeasible Logic Programming: An Argumentative Approach, A. J. García, G.R. Simari, Theory and Practice of Logic Programming. Vol 4(1) pp 95-138, 2004.

26. ArgMAS 2004 - New York26 Work in Progress  Extending the analysis of ODeLP properties.  Complexity analysis of the ODeLP system.  Implementing applications wich use ODeLP as the knowledge representation and reasoning formalism.