Multiagent argumentation systems and their logics

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Multi-agent argumentation systems and their logics

• Slavian Radev
• Politechnika Bialostocka

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Argumentation system ASP,A,R,E

• P set of propositions
• A set of argumentations
• RA?PxFIN(P) relations for argumentation names
• EP ?0,1 evaluation
• XaY means X is a-argument for Y
• E(X) 1 accept, E(X)0 reject

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Logical connectivies

• If XaY and ZaT then (XoZ)a(YoT) for every logical
  connective o
• For simplicity we consider only set
  connectivies ?,?,?

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Evaluation of formulae E

• If E(X) 1 for every X?a(Y) then E(Y)1
• If E(X) 0 for every X?a(Y) then E(Y)0
• Otherwise E(Y) ?

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Agents a,b and operations over argumentations

• There are a lot of possibilities for operations
  over argumentations of agents
• Union R R(a)?? R(b)
• Intersection R R(a)?? R(b)
• Attack-defence
• Question-answering
• ...

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Union

• Even if all the argumentation systems of a and b
  are consistent and 2-valued we obtain the third
  value ? in the union
• The logic is of the form of Lukasiewicz-Post
• (Note that we consider only 3 values and only set
  connectivies)

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Intersection

• Even if all the argumentation systems are
  nonempty (fro every Y and every a the set a(Y) is
  nonempty) we may obtain empty argumentation hence
  new value
• There are two ways to treat the third value
  Kleene approach and Lukasiewicz-Post approach

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Attack-defence

• In the literature on argumentation systems very
  popular is attack-defence model in which
• The first agent (Proposer) proposes the thesis
• The second agent (Oponent) proposes the
  opposition (contraargument)
• The game continue till they reach an evaluated
  formula
• If the formula is 1 then the thesis is accepted

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Attack-defence

• Now not for all formulas but for a single formula
  we define the AD-operation over the relations
• The semantics is
• The opponent choses the argument
• The proponent choses the argument for the
  argument of the opponent
• And so on
• Proposition is accepted if 1 is reached, rejected
  if 0

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Attack-defence

• Again third value may appear. Now it is a
  circle the same player uses two times the same
  argument
• Or more dangerous the original system has a
  circle (f.i. If argumentation is of all formulas
  s.t. A?B then A is an argument for A)

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Question-answering

• The other player may ask what means the
  proposition X. In that case the proponent have to
  eliminate X (substitute all occurences of X with
  sinonimous X')
• In that case again circle may appear, f.i. simple
  idiotical equations XX?Y, YX?Y
• The game semantics of Hintikka allows us to
  choose X1 and Y0 in that case
• But in the case X?Y, Y?X we have infinite
  change the place and thus third value