From Classical Logic to Computational Argumentation

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1 From Classical Logic to Computational Argumentation Massimiliano Giacomin DII - Dipartimento di Ingegneria dell Informazione Università degli Studi di Brescia (Italy)

How many kinds of reasoning? http://feedyoursoul.

2 How many kinds of reasoning? A rough classification Epistemic reasoning - Deductive reasoning - Inductive reasoning - Abductive reasoning Practical reasoning 2

Epistemic vs Practical reasoning EPISTEMIC PRACTICAL EPISTEMIC REASONING: Reasoning about what to believe PRACTICAL REASONING: Reasoning about

3 Epistemic vs Practical reasoning EPISTEMIC PRACTICAL EPISTEMIC REASONING: Reasoning about what to believe PRACTICAL REASONING: Reasoning about what to do NB: Practical reasoning is influenced from epistemic reasoning, epistemic reasoning should not be influenced by practical reasoning 3

4 Deductive, abductive, inductive reasoning Deductive reasoning: the conclusion follows validly from the premises Inductive reasoning: the premises point several cases of some pattern, and the conclusion states that this pattern will hold in general Abductive reasoning: A reasoning that (i) points out a certain fact, (ii) points out that if a certain hypothesis were true, we would get this fact, and so (iii) concludes that that hypothesis is indeed true. 4

5 Informal examples Deductive reasoning Premises All the beans from this bag are white These beans are from this bag Conclusion These beans are white Inductive reasoning Premises These beans are white These beans are from this bag Conclusion All the beans from this bag are white Abductive reasoning Premises All the beans from this bag are white These beans are white Conclusion These beans are from this bag 5

6 Inductive and abductive reasoning in H&W Inductive reasoning in H&W domain Conclusions from clinical trials Abductive reasoning in H&W domain Diagnostic reasoning In both cases, we cannot be completely sure of the conclusion, even if the premises are certain! 6

7 Epistemic Reasoning: example (1) Norwegians are good cross-country skiers People having a paunch are not good cross-country skiers 7

8 Epistemic Reasoning: example (2) Norwegians are good cross-country skiers People having a paunch are not good cross-country skiers Petter is norwegian Norwegians are good cross-country skiers Petter is a good cross-c.try skier 8

9 Epistemic Reasoning: example (3) Norwegians are good cross-country skiers People having a paunch are not good cross-country skiers Petter is norwegian Norwegians are good cross-country skiers Petter is a good cross-c.try skier Petter has a punch People having a paunch are not good cross-country skiers Petter is not a good cross-c.try skier 9

10 Epistemic Reasoning: example (4) Norwegians are good cross-country skiers People having a paunch are not good cross-country skiers Petter is norwegian Norwegians are good cross-country skiers Petter is a good cross-c.try skier CONFLICTING CONCLUSIONS Petter has a punch People having a paunch are not good cross-country skiers Petter is not a good cross-c.try skier 10

11 Practical Reasoning: example I want to enjoy some free time If I go to the mountains for cross country ski, I will enjoy some free time So, I will go to the mountains for cross country ski CONFLICTING ACTIONS I want to enjoy some free time If I go to the pub for a beer, I will enjoy some free time So, I will go to the pub for a beer 11

12 Practical Reasoning: normative reasoning I should prepare a lesson to teach tomorrow CONFLICTING OBLIGATIONS I should complete my review for Artificial Intelligence Journal, since I have made a commitment with the editor and the deadline is today 12

13 Lessons learned Reasoning is not necessarily deductive: - rules are not always strict (see e.g. inductive and abductive reasoning + examples) - inference can be drawn from incomplete information (see e.g. examples) Arguments are not always valid even if they are good (and important) ones! Conflicts arise in real world! (conflicting conclusions from inductive and abductive reasoning, conflicting possible actions, ) 13

14 Reasoning in a context of disagreement Properties Emergent conflicts due to different reasons Defeasibility of conclusions Possible Subjectivity of conclusions Contexts Individual reasoning Dialogue (negotiation, persuasion, ) Solution Reasoning must be non-monotonic - conclusions may be retracted in the light of new information 14

15 Why classical logic is not a solution (1) MONOTONIC NOTION OF LOGICAL CONSEQUENCE F 1,, F n C F 2 F n C F 1 Adding facts (premises) yields a smaller sets of models è conclusions cannot be retracted! 15

16 Why classical logic is not a solution (2) EX FALSO (SEQUITUR) QUODLIBET F 1,, F n Q F n F 2 Q F 1 Everything follows from inconsistency! 16

17 even if the consequences can be desirable! EX FALSO (SEQUITUR) QUODLIBET PN: Petter is Norwegian PP: Petter has a Punch PG: Petter is a good cross-country ski M: AC Milan will win Champions League PN PP PN PG PP PG PN PN PG PP PP PG PG PG M PG M 17

18 Why classical logic is not a solution (3) LISTING ALL EXCEPTIONS IS IMPRACTICAL PN: Petter is Norwegian PP: Petter has a Punch PG: Petter is a good cross-country ski M: AC Milan will win Champions League PN PP PN PP PG PP PG PN PN PG PP PP PG PG PG M PG M It is impossible to exhaustively list all exceptions in an open context What if I don t know whether PP (Petter has a punch)? 18

19 So what? A SOLUTION Consider explicitly ARGUMENTS instead of PROOFS Manage contradictions EXPLICITLY COMPUTATIONAL ARGUMENTATION 19

20 INTRODUCTION TO COMPUTATIONAL ARGUMENTATION

21 ARGUMENTATION THEORY Argumentation is a verbal and social activity of reason aimed at increasing (or decreasing) the acceptability of a controversial standpoint for the listener or reader, by putting forward a constellation of propositions intended to justify (or refute) the standpoint before a rational judge. 21

ARGUMENTATION THEORY Argumentation is a verbal and social activity of reason aimed at increasing (or decreasing) the acceptability of a controversial standpoint for the listener or reader,

22 ARGUMENTATION THEORY Argumentation is a verbal and social activity of reason aimed at increasing (or decreasing) the acceptability of a controversial standpoint for the listener or reader, by putting forward a constellation of propositions intended to justify (or refute) the standpoint before a rational judge. 22

23 Many views of Argumentation Philosophical Argumentation - Philosophical Roots: Aristotle - Toulmin (1958) Natural argumentation (and natural language argumentation) Argumentation in Psychology Argumentation in Artificial Intelligence [Prakken 2011] Argumentation is the process of supporting claims with grounds and defending them against attack. - proposed as a framework for practical and uncertain reasoning able to cope with partial and/or inconsistent knowledge - first papers in AI: R.P. Loui (1987), J. Pollock (1987), G. Simari & Loui (1992) 23

24 An informal example (1) Vaccinating babies should be mandatory The conclusion Vaccines prevent previously devastating diseases Preventing diseases increase publich health The reason We are justified in believing that vaccination should be mandatory 24

25 An informal example (2) Vaccinating babies should be mandatory The conclusion Vaccines prevent previously devastating diseases Preventing diseases increase publich health The reason We are justified in believing that vaccination should be mandatory BUT In Argumentation (and in real life as well): - reasons are not necessary conclusive (they don t logically entail conclusions) - arguments and conclusions can be retracted in front of new information, i.e. counterarguments 25

26 An informal example (3) Vaccinating babies should be mandatory VB should not be mandatory Vaccines prevent previously devastating diseases Preventing diseases increase publich health Vaccines may cause autism Individual health is important We are NOT justified in believing that vaccination should be mandatory 26

27 An informal example (4) Vaccinating babies should be mandatory VB should not be mandatory Vaccines prevent previously devastating diseases Preventing diseases increase publich health Vaccines may cause autism Individual health is important Vaccines don t cause autism All scientific studies concluded vaccines don t cause it We are again justified in believing that vaccination should be mandatory 27

28 An informal example (5) Vaccinating babies should be mandatory VB should not be mandatory Vaccines prevent previously devastating diseases Preventing diseases increase publich health Vaccines may cause autism Individual health is important There is a study supporting correlation Vaccines don t cause autism Paper by A. Wakefield et al., Lancet 1998 All scientific studies concluded vaccines don t cause it We are again NOT justified in believing that vaccination should be mandatory 28

29 An informal example (6) Vaccinating babies should be mandatory VB should not be mandatory Vaccines prevent previously devastating diseases Preventing diseases increase publich health Vaccines may cause autism Individual health is important There is a study supporting correlation Vaccines don t cause autism Paper by A. Wakefield et al., Lancet 1998 All scientific studies concluded vaccines don t cause it That paper is fraudolent Results not reproduced; conflicts of interest Now we are again justified in believing that vaccination should be mandatory 29

30 5-layers model of Argumentation Systems DEFINITION OF ARGUMENT STATUS DEFINITION OF ATTACK DEFINITION OF CONFLICT DEFINITION OF ARGUMENT UNDERLYING LANGUAGE (and consequence) [PRAKKEN & VREESWIJK 1999] 30

31 The underlying language SEVERAL FRAMEWORKS WITH DIFFERENT UNDERLYING LANGUAGES Classical logic (deductive argumentation) Logic Programming (defeasible logic programming) Classical logic + assumptions (assumption-based argumentation) Any language (ASPIC+) DEFINITION OF ARGUMENT STATUS DEFINITION OF ATTACK DEFINITION OF CONFLICT DEFINITION OF ARGUMENT UNDERLYING LANGUAGE A LANGUAGE COMES WITH A NOTION OF CONSEQUENCE 31

32 Definition of Argument DEFINITION OF ARGUMENT STATUS WHAT AN ARGUMENT IS Corresponds to a proof in the underlying logic DEFINITION OF ATTACK DEFINITION OF CONFLICT DEFINITION OF ARGUMENT UNDERLYING LANGUAGE BACK TO THE INFORMAL EXAMPLE consequence relation language Vaccinating babies should be mandatory Vaccines prevent previously devastating diseases Preventing diseases increase publich health ARGUMENT 32

33 Definition of conflict between arguments DEFINITION OF ARGUMENT STATUS WHEN ARE TWO ARGUMENTS IN CONFLICT? - e.g. they have contradictiory conclusions - the conclusion of an argument contradicts a premise of an another argument - DEFINITION OF ATTACK DEFINITION OF CONFLICT DEFINITION OF ARGUMENT UNDERLYING LANGUAGE BACK TO THE INFORMAL EXAMPLE Vaccinating babies should be mandatory VB should not be mandatory Vaccines prevent previously devastating diseases Preventing diseases increase publich health Vaccines may cause autism Individual health is important 33

34 Definition of attack DEFINITION OF ARGUMENT STATUS ATTACK (also called DEFEAT) BETWEEN ARGUMENTS i.e. when does an argument win the conflict? DEFINITION OF ATTACK DEFINITION OF CONFLICT DEFINITION OF ARGUMENT UNDERLYING LANGUAGE BACK TO THE INFORMAL EXAMPLE Vaccinating babies should be mandatory VB should not be mandatory Vaccines prevent previously devastating diseases Preventing diseases increase publich health Vaccines may cause autism Individual health is important 34

35 On the relation of attack SYMMETRIC ATTACK It will be dry in London It will be wet in London BBC forecast sunshine CNN forecast rain ASYMMETRIC ATTACK It will be dry in London It will be wet in London London service forecast sunshine CNN forecast rain 35

36 Definition of argument status DEFINITION OF ARGUMENT STATUS DEFINITION OF ATTACK DEFINITION OF CONFLICT DEFINITION OF ARGUMENT UNDERLYING LANGUAGE GIVEN A SET OF ARGUMENTS RELATED BY A CONFLICT AND ATTACK RELATION, WHAT ABOUT THE STATUS OF EACH ARGUMENT? IN PARTICULAR, WHICH ARGUMENTS ARE JUSTIFIED? 36

37 An informal example: back again Vaccinating babies should be mandatory VB should not be mandatory Vaccines prevent previously devastating diseases Preventing diseases increase publich health Vaccines may cause autism Individual health is important There is a study supporting correlation Vaccines don t cause autism Paper by A. Wakefield et al., Lancet 1998 All scientific studies concluded vaccines don t cause it That paper is fraudolent Results not reproduced; conflicts of interest 37

38 STRUCTURED VS ABSTRACT ARGUMENTATION DEFINITION OF ARGUMENT STATUS ABSTRACT ARGUMENTATION DEFINITION OF ATTACK DEFINITION OF CONFLICT DEFINITION OF ARGUMENT STRUCTURED ARGUMENTATION UNDERLYING LANGUAGE (and consequence) 38

Wason's Cards: What is Wrong?

Wason's Cards: What is Wrong? Pei Wang Computer and Information Sciences, Temple University This paper proposes a new interpretation