Representing Epistemic Uncertainty by means of Dialectical Argumentation

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Representing Epistemic Uncertainty by means of
Dialectical Argumentation

• Peter McBurney and Simon Parsons
• Agent Applications, Research and Technology
  (Agent ART) Group
• Department of Computer Science
• University of Liverpool, Liverpool UK
• p.j.mcburney,s.d.parsons_at_csc.liv.ac.uk
• Presentation to
• Department of Computer Science
• University of Liverpool
• 6 February 2001

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Nature of the problem

• Problem Assessing the health risks of new
  chemicals and technologies
• Classical decision theory methods require
• Explicit delineation of all outcomes
• Quantification of uncertainties and consequences.
• But for most domains
• Scientific knowledge often limited (especially at
  outset)
• Experimental evidence ambiguous and conflicting
• No agreement on quantification.

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Types of evidence for chemical carcinogenicity

• Chemical structure comparison
• Mutagenic tests on tissue cultures
• Animal bioassays
• Human epidemiological studies
• Explication of biomedical causal pathways.
• These different sources of evidence may conflict.
  
• E.g. Formaldehyde.

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Risk Assessment for chemical X
Are there adverse health effects from exposure
to chemical X ?
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Argumentation to represent uncertainty

• Two meanings of argument
• A case for a claim (a tentative proof)
• A debate between people about a claim.
• Our degree of certainty in a claim depends on the
  cases for and against it.
• The more and stronger cases against , the less
  certainty.
• A consensus in favour of a claim indicates the
  greatest certainty.
• We can therefore represent uncertainty by means
  of dialectical argumentation.
• We also require a mechanism for generating
  inferences from the dialectical status of a
  claim.

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Philosophical underpinning

• We have adopted an explicit philosophy of
  science
• Peras (1994) model of science as a 3-person
  game
• The Experimenter Nature The Scientific
  Community.
• Feyerabends (1971) philosophy of science as
  epistemological anarchism
• There are no absolute standards which distinguish
  science from non-science
• Standards differ by time, by discipline and by
  context.
• We see two principles as necessary for an
  activity to be called science
• All claims are contestable by anyone (in the
  community)
• All claims are defeasible, with reasoning always
  to the best explanation.

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Peras Philosophy of Science
Experimenter
Nature
Scientific Community
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To model these, we need

• A theory of rational discourse between
  reasonable, consenting participants
• Hitchcocks (1991) principles of rational mutual
  inquiry
• The discourse ethics of Habermas and Alexy
  (1978).
• A model for an argument
• Toulmins (1958) argument schema.
• A means to formalize complex dialogues
• Walton and Krabbes (1995) characterization of
  different types of dialogues
• Formal dialogue-games of Hamblin (1970, 1971) and
  MacKenzie (1979, 1990).

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Hitchcocks Principles

• 18 Principles of rational mutual discourse, for
  example
• Dialectification The content and methods of
  dialogue should be decided by the participants.
• Mutuality no statement becomes a commitment of
  a participant unless he or she specifically
  accepts it.
• Orderliness one issue is raised and discussed
  at a time.
• Logical pluralism both deductive and
  non-deductive inference is permitted.
• Rule-consistency there should be no situation
  where the rules prohibit all acts, including the
  null act.
• Realism the rules must make agreement between
  participants possible.
• Retraceability participants must be free at all
  times to supplement, change or withdraw previous
  tentative commitments.
• Role reversability the rules should permit the
  responsibility for initiating suggestions to
  shift between participants.

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Alexys Discourse Rules

• Rules for discourse over moral and ethical
  questions, for example
• Freedom of assembly
• Common language
• Freedom of speech
• Freedom to challenge claims
• Arguments required for claims
• Freedom to challenge arguments
• Freedom to disagree over modalities
• Requirement for clarification and precization
• Proportionate defence
• No self-contradictions permitted.

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Toulmins Argument Schema
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Walton and Krabbes Typology of Dialogues

• Information-seeking dialogues
• One participant seeks the answer to a question.
• Inquiries
• All participants collaborate to find the answer
  to a question.
• Persuasions
• One participant seeks to persuade other(s) of the
  truth of a proposition.
• Negotiations
• Participants seek to divide a scarce resource.
• Deliberations
• Participants collaborate to decide a course of
  action in some situation.
• Eristic dialogues
• Participants quarrel verbally as a substitute for
  physical fighting.

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Risk Assessment for chemical X
Are there adverse health effects from exposure
to chemical X ?
What is the likelihood and size of impact?
Scientific Dialogues
What should be done about chemical X ?
Regulatory Dialogue
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Risk Assessment Dialogues

• Scientific dialogues
• Does exposure (in a certain way at certain dose
  levels) to chemical X lead to adverse health
  effects? If so, what is the likelihood and
  magnitude of impact?
• A mix of
• Inquiries
• Persuasion dialogues.
• A regulatory dialogue
• What regulatory actions (if any) should be taken
  regarding chemical X ?
• A mix of
• Inquiries
• Deliberations
• Negotiations
• Persuasion dialogues.

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Dialogue Games

• Games between 2 players where each moves by
  uttering a locution.
• Developed by philosophers to study fallacious
  reasoning.
• Used in agent dialogues (Parsons Amgoud),
  software development (Stathis), modeling legal
  reasoning (Bench-Capon et al., Prakken).
• Rules define circumstances of
• Commencement of the dialogue
• Permitted locutions
• Combinations of locutions
• e.g. cannot assert a proposition and its negation
• Commitment
• When does a player commit to some claim?
• Termination of the dialogue.

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The Risk Agora

• A formal framework for representing dialogues
  concerning carcinogenic risk of chemicals.
• Represent the arguments for and against a
  chemical being a carcinogen.
• Represent the current state of scientific
  knowledge, including epistemic uncertainty.
• Enable contestation and defence of clains and
  arguments.
• Enable comparison and synthesis of arguments for
  specific claims.
• Enable summary snapshots of the debate at any
  time.
• We have fully specified the locutions and rules
  for a dialogue-game for scientific discourses.

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Speaking in the Agora

• Participants can
• Propose or assert claims, arguments, grounds,
  inference-rules, consequences
• Modify each with modalities
• Question or contest others proposals or
  assertions
• Accept others proposals or assertions.
• Examples of locutions
• propose ( participant 1 (claim, modality) )
• assert ( participant 1 (claim, modality) )
• show_arg ( participant 1 (arg_for_claim,
  modalities) )
• contest ( participant 2 propose ( participant
  1 (claim, modality) ) )
• etc.

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Representing uncertainty in the Agora

• We represent the degree of uncertainty in a claim
  by means of its dialectical argument status in
  the Agora.
• We use a dictionary of labels due to Krause, Fox
  et al. (1998).
• We have modified definitions slightly to allow
  for counter-counter-arguments.
• This is an example, and other modality
  dictionaries could be defined.
• A claim is
• Open - no arguments presented yet for it or
  against it.
• Supported - at least one grounded argument
  presented for it .
• Plausible - at least one consistent, grounded
  argument presented for it.
• Probable - at least one consistent, grounded
  argument presented and no rebuttals or undercuts
  presented.
• Accepted - at least one consistent, grounded
  argument presented for it and any rebuttals or
  undercuts have been attacked with
  counter-arguments.

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Debating experimental tests of claims

• We also permit debate on
• The validity of experiments to test scientific
  claims.
• The results of valid experiments.
• An experimental test of a claim is
• Open - no evidence either way.
• Invalid test - the scientific experiment is
  not accepted by the participants as a valid test
  of the claim
• Inconclusive test - the test is accepted as
  valid, but the results are not accepted as
  statistically significant support for the claim
  or against it.
• Disconfirming instance - the test is accepted as
  evidence against the claim.
• Confirming instance - the test is accepted as
  evidence for the claim.

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Experimental status of claims

• Claims are then assigned labels according to the
  extent that debate in the Agora accepts
  experimental evidence for and against them.
• A claim is
• Untested
• Inconclusive
• Refuted
• Confirmed.
• Experimental evidence in favour of a claim can be
  presented as an argument for the claim.

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Inference from the Agora

• We define a claim as (defeasibly) true at time t
• if and only if it is Accepted in the Agora at
  time t.
• Otherwise, it is not (defeasibly) true at time t.
• This notion of truth depends on the opinions of
  the participants in the Agora, which may change
  over time.
• As more evidence is obtained and further
  arguments presented to the Agora, the truth
  status of a claim may change.
• Such changes may be non-monotonic.

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Formal properties of the Agora

• The Agora dialogue-game rules comply with
• Alexys discourse rules
• 15 of Hitchcocks 18 Principles.
• Acceptability of claims is a game-theoretic
  semantics (Hintikka 1968)
• Truth of a proposition depends on a participant
  in the Agora having a strategy to defeat any
  opponent in the dialogue-game associated with the
  proposition.
• Inference from finite snap-shots to the long-run
  is well-founded
• We can place probabilistic bounds on the
  possibility of errors of inference from finite
  snapshots to values at infinity.
• This is analogous to the Neyman-Pearson (1928)
  theory of statistical inference.

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Inference from snapshots to infinite status
(With apologies to Jackson Pollock)
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TheoremStability of labels in absence of new
information.

• Let P be a claim. Suppose that
• A(P) is a consistent argument for P such that all
  rebuttals and undercuts against A(P) are
  themselves attacked by other arguments,
• All arguments pertaining to P using the initial
  information and inference rules are eventually
  articulated by participants within the Agora, and
• No new information concerning P is received by
  participants following commencement.
• Then
• The uncertainty label for P converges to
  Accepted as time goes to infinity.

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Key Theorem Probability of Inference Errors is
bounded.

• Consider a claim P. Suppose that
• The uncertainty label for P converges to a limit
  at infinity,
• A snapshot is taken at a time t after all
  relevant arguments related to P have been
  presented,
• The uncertainty label of P at time t is
  Accepted, and
• The probability of new information relevant to P
  arising after time t is less than ?, for some 0
  lt ? lt 1.
• Then
• The probability that the uncertainty label for
  claim P at infinity is also Accepted is at
  least 1 - ?.

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Example

• Assumptions
• K1 The chemical X is produced by the human
  body naturally (it is endogenous).
• K2 X is endogeneous in rats.
• K3 An endogenous chemical is not carcinogenic.
• K4 Bioassays of X on rats show significant
  carcinogenic effects.
• Rules of inference
• R1 (And Introduction) From P and Q, infer (P
  Q).
• R2 (Modus Ponens) From P and (P implies Q)
  infer Q.
• R3 If a chemical is carcinogenic in an animal
  species, infer that it is also carcinogenic in
  humans.

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Example (cont) A dialogue concerning the
statement P X is carcinogenic to humans

• Snapshot status of Claim P Open
• assert (Participant 1 (P, confirmed) )
• query (Participant 2 assert (Participant 1
  (P, confirmed)))
• show_arg (Participant 1 (K4, R3, P,
  (Confirmed, Valid, Confirmed))
• Snapshot status of Claim P Accepted
• contest (Participant 2 assert (Participant 1
  (P, confirmed)))
• query Participant 3 contest (Participant 2
  assert (Participant 1 (P, confirmed))))
• propose (Participant 2 (not-P, Plausible))
• query Participant 1 propose (Participant 2
  (not-P, Plausible))
• show_arg (Participant 2 ((K1, K3) , R2, not-P,
  (Confirmed, Probable, Valid, Plausible)))
• Snapshot status of Claim P Plausible

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Whats next

• A model of a deliberation dialogue
• Dialogues about what action(s) to take.
• Have proposed a model based on Wohlrapps (1998)
  retroflexive argumentation, a model of
  non-deductive inference (joint work with David
  Hitchcock).
• Locutions specific to regulatory domain
• Have proposed a first set using Habermas (1981)
  Theory of Communicative Action.
• A means to combine different types of dialogue
• Have proposed a formalism using Parikhs (1985)
  Game Logic, a version of Dynamic Modal Logic (the
  modal logic of processes).
• A qualitative decision theory
• Will draw on Fox and Parsons (1998).

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Other formal properties under exploration

• Can we automate these dialogues?
• Will automated dialogues ever terminate?
• Under what circumstances?
• After how many moves? (Computational complexity).
• When are two dialogues the same?
• How do we assess the quality of a dialogue
  system?
• How sensitive is the framework to changes in the
  game rules?

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Thanks to

• EPSRC
• Grant GR/L84117 Qualitative Decision Theory
• Grant GR/N35441/01 Symposium on Argument and
  Computation
• Phd Studentship.
• European Union Information Society Technologies
  Programme (IST)
• Sustainable Lifecycles in Information Ecosystems
  (SLIE) (IST-1999-10948).
• Trevor Bench-Capon, Computer Science Dept,
  University of Liverpool.
• John Fox, Advanced Computation Laboratory,
  Imperial Cancer Research Fund, London.
• David Hitchcock, Philosophy Dept, McMaster
  University, Hamilton, Ontario.
• Anonymous referees (UAI, GTDT, AMAI).