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

ArgMAS New York2 Outline  Motivation  The Argumentation Framework  Potential Arguments  Conclusions

ArgMAS 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.

ArgMAS 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  

ArgMAS 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).

ArgMAS 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 ).

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

 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 ).}

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 )

ArgMAS 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 )

ArgMAS 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 )

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 

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

ArgMAS 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.

ArgMAS 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.

ArgMAS 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.

ArgMAS 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 }     

ArgMAS 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.

ArgMAS 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.

ArgMAS 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 ( ,  ).

ArgMAS 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 ).

ArgMAS 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 ).}

ArgMAS 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.

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

ArgMAS 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 , 2004.

ArgMAS 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.