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A Logic-Based Artificial Intelligence Approach

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A Logic-Based Artificial Intelligence Approach ON THE FORMAL MODELING OF GAMES OF LANGUAGE AND ADVERSARIAL ARGUMENTATION Dissertation presented at Uppsala University to be publicly examined in Hö 2, Ekonomikum, Kyrkogårdsgatan 10, Uppsala, Friday, February 27, 2009 at 13:15 for the degree of Doctor of Philosophy. The examination will be conducted in English. Abstract Eriksson Lundström, J. S. Z. 2009. On the Formal Modeling of Games of Language and Adversarial Argumentation. A Logic-Based Artificial Intelligence Approach. 244 pp. Uppsala. ISBN 978-91-506-2055-9. Argumentation is a highly dynamical and dialectical process drawing on human cognition. Success- ful argumentation is ubiquitous to human interaction. Comprehensive formal modeling and analysis of argumentation presupposes a dynamical approach to the following phenomena: the deductive logic notion, the dialectical notion and the cognitive notion of justified belief. For each step of an argumentation these phenomena form networks of rules which determine the propositions to be allowed to make sense as admissible, acceptable, and accepted. We present a metalogic framework for a computational account of formal modeling and system- atical analysis of the dynamical, exhaustive and dialectical aspects of adversarial argumentation and dispute. Our approach addresses the mechanisms of admissibility, acceptability and acceptance of arguments in adversarial argumentation by use of metalogic representation, reflection, and Artifi- cial Intelligence-techniques for dynamical problem solving by exhaustive search. We elaborate on a common conceptual framework of board games and argumentation games for pursuing the alternatives facing the adversaries in the argumentation process conceived as a game. The analogy to chess is beneficial as it incorporates strategic and tactical operations just as argu- mentation. Drawing on an analogy to board games like chess, the state space representation, well researched in Artificial Intelligence, allows for a treatment of all possible arguments as paths in a directed state space graph. The traversal of the state space graph unravels and collates knowledge about the given situation/case under dispute. It will render a game leading to the most wins and fewest losses, identifying the most effective game strategy. As we model and incorporate the pri- vate knowledge of the two parties, the traversal results in an increased knowledge of the case and the perspectives and arguments of the participants. We adopt metalogic as formal basis; hence, arguments used in the argumentation, expressed in a non-monotonic defeasible logic, are encoded as terms in the logical argumentation analysis system. The advantage of a logical formalization of argumentation is that it provides a symbolic knowledge representation with a formally well-formed semantics, making the represented knowledge as well as the behavior of knowledge representation systems reasoning comprehensible. Computational logic as represented in Horn Clauses allows for expression of substantive propositions in a logical structure. The non-monotonic nature of defeasible logic stresses the representational issues, i.e. what is possible to capture in non-monotonic reasoning, while from the (meta)logic program, the sound computation on what it is possible to compute, and how to regard the semantics of this com- putation, are established. Keywords: Formal and computational models of argumentation, argumentation games, board game analogy, metalogic, logic-based Artificial Intelligence, game trees, dynamical and dialectical argu- mentation analysis, metareasoning, reflection Jenny S. Z. Eriksson Lundström, Department of Information Science, Box 513, Uppsala University, SE-751 20 Uppsala, Sweden © Jenny S. Z. Eriksson Lundström 2009 ISBN 978-91-506-2055-9 urn:nbn:se:uu:diva-9538 (http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-9538) Printed in Sweden by Universitetstryckeriet, Uppsala 2009. Jenny S. Z. Eriksson Lundström On the Formal Modeling of Games of Language and Adversarial Argumentation A Logic-Based Artificial Intelligence Approach Till minne av Thyra Amalia och Arthur Adrian, Albert Emanuel och Hilda Viktoria This dissertation supports the thesis: Argumentation is a highly dynamical and dialectical process drawing on human cognition. Successful argumentation is ubiquitous to human interaction. Comprehensive formal modeling and analysis of argumentation presupposes a dynamical approach to the following phenomena: the deductive logic notion, the dialectical notion and the cognitive notion of justified belief. For each step of an argumentation these phenomena form networks of rules which determine the propositions to be allowed to make sense as admissible, acceptable, and accepted. By means of explicit analogies to other human problem solving activities, and a metalogic representation drawing on Artificial Intelligence techniques, a flexible, and transparent, yet computational account of the above phenomena can be accommodated. In order to make this dissertation available to a broader audience, with the intent of facilitating the assessment and evaluation of our research, we focus on providing the tools for the examination of this work by the methods of research upon which it touches. Hence, to accommodate the reader who may be unfamiliar to some of these scientific methods, in the initial Chapters 1, 2, 3, 4 and 5, of the dissertation, we include a general introduction to the theories and methods upon which our scientific approach draws. Consequently, the expert reader may be well advised to skim these sections. ‘These’ is here to be understood as a parameter to be instantiated according to the reader’s field of expertise and liking. Contents Part I: Setup 1 Introduction . ......................................... 19 1.1 Human Problem Solving and Argumentation . ............. 19 1.2 Formal Argumentation . ........................... 20 1.3 Research in Formal Argumentation . .................... 21 1.4 Logic-Based Artificial Intelligence . ................... 22 1.5 Thesis and Contribution . ............................. 23 1.6 Research Approach . ................................ 24 1.7 Research Methods . .............................. 25 1.8 Outline of the Thesis . .............................. 26 Part II: Opening 2 Argumentation . .................................... 31 2.1 The Nature of Argumentation . ...................... 31 2.2 Justified Belief and Valid Arguments . ................... 32 2.2.1 Deductive Logic Validity . ...................... 33 2.2.2 Defeasible Arguments . .......................... 34 2.2.3 Dialectic Validity . ........................... 36 2.3 The Issue Under Dispute . ........................... 37 2.3.1 Cognitive Validity . ............................. 39 2.3.2 The Passing of Acceptance . ..................... 40 2.3.3 Rationality as Goals and Abilities . .............. 41 2.3.4 Human Error and Bounded Rationality . ........... 42 2.4 Meaningful Acceptable and Admissible Arguments . ..... 44 2.4.1 Meaningfulness . .............................. 44 2.4.2 Refutation and Acceptability . ................... 45 2.4.3 Admissible and Relevant Arguments . ............. 45 2.5 The Dynamics of Common Sense Reasoning . ............. 47 2.5.1 Dialectical Disputation . .......................... 47 2.5.2 Non-Monotonicity . ............................. 48 2.5.3 Exhaustive Search . ............................. 48 2.6 Demarcation . .................................... 49 2.7 Summing Up . .................................... 51 Part III: Middlegame 3 Layers of Logic-Based Argumentation . ................... 55 3.1 Five Layers of Argumentation . ...................... 55 3.2 Logical Layer: A Logic for Argumentation . ........... 56 3.2.1 Logic Reasoning in Natural Language . ........... 56 3.2.2 Propositional Logic . ........................... 58 3.2.3 First Order Predicate Logic . ..................... 64 3.2.4 Logic Reasoning in Classical Logic . ................ 68 3.2.5 Logic Programming . ........................... 69 3.2.6 A Tractable Non-Monotonic Logic . .............. 74 3.3 Dialectical Layer: Comparison of Arguments . ............. 80 3.3.1 Abstract Argumentation Semantics . ................ 80 3.3.2 Monological Argumentation Structures . ............. 82 3.3.3 Argumentation Semantics for Defeasible Reasoning . .... 83 3.4 The Procedural Layer . ........................... 85 3.4.1 Models of Dialogue Games . ..................... 85 3.4.2 Research on Adversarial Dialogue Games . ........ 86 3.5 Strategical Layer . ................................. 89 3.6 Relevance Layer . ................................. 90 3.7 Summing Up . .................................... 90 Part IV: Promotion 4 Graphs and Logical Games for Argumentation Decomposition . 93 4.1 Persuasion Dialogues as Board Games . ................ 93 4.2 Privacy Exhaustiveness and Dynamical Compu- tation . ..... 94 4.3 Adversarial Argumentation Games . .................... 95 4.3.1 A Basic Protocol . ........................... 95 4.3.2 Non-Monotonicity and Defeasible Arguments . ..... 96 4.4 Two-Person Perfect-Information Games . .............. 96 4.4.1 Terminal States for Board Games . ................ 96 4.5 AND/OR Graphs, Game Trees and Strategic Games . ..... 98 4.5.1 Strategic Analysis of Games . ................... 101 4.6 A Common Framework . ............................. 103 4.6.1 Procedural Layer Analogy . ....................... 103 4.6.2 Dialectical Layer Analogy . ....................... 104 4.6.3 Strategic Layer Analogy . ...................... 105 4.6.4
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