Phan Minh Dung

AAAI Conference 2019 Conference Paper

On Structured Argumentation with Conditional Preferences

• Phan Minh Dung
• Phan Minh Thang
• Tran Cao Son

We study defeasible knowledge bases with conditional preferences (DKB). A DKB consists of a set of undisputed facts and a rule-based system that contains different types of rules: strict, defeasible, and preference. A major challenge in defining the semantics of DKB lies in determining how conditional preferences interact with the attack relations represented by rebuts and undercuts, between arguments. We introduce the notions of preference attack relations as sets of attacks between preference arguments and the rebuts or undercuts among arguments as well as of preference attack relation assignments which map knowledge bases to preference attack relations. We present five rational properties (referred to as regular properties), the inconsistency-resolving, effective rebuts, context-independence, attack monotonicity and link-orientation properties generalizing the properties of the same names for the case of unconditional preferences. Preference attack relation assignment are defined as regular if they satisfy all regular properties. We show that the set of regular assignments forms a complete lower semilattice whose least element is referred to as the canonical preference attack relation assignment. Canonical attack relation assignment represents the semantics of preferences in defeasible knowledge bases as intuitively, it could be viewed as being uniquely identified by the regular properties together with the principle of minimal removal of undesired attacks. We also present the normal preference attack relation assignment as an approximation of the canonical attack relation assignment.

AIJ Journal 2018 Journal Article

Fundamental properties of attack relations in structured argumentation with priorities

• Phan Minh Dung
• Phan Minh Thang

Due to a proliferation and diversity of approaches to structured argumentation with prioritized rules, several simple and intuitive principles for characterization and evaluation of the proposed attack relations have recently been introduced in [23]. While the proposed principles and properties are helpful, they do not identify unique attack relations. Any user of structured argumentation still faces a fundamental problem of determining an appropriate attack relation for her/his application and further principles that could help in identifying such attack relation. We argue that a key purpose of introducing priorities between defeasible rules is to remove undesired attacks while keeping the set of removed attacks to a minimum. This intuitive idea could be viewed as a kind of minimal-removal-principle. We show in this paper that the minimal-removal-principle together with a new simple and intuitive property of inconsistency-resolving and previously proposed properties indeed characterize a unique attack relation referred to as the canonical attack relation. We show that canonical attack relations could be characterized in three distinct ways, as the supremum of a complete upper-semilattice of regular attack relations, or by removing the undesired attacks from the basic attack relations where the undesired attacks are captured by a least-fixed point of an intuitive removal function, or as the normal attack relations introduced in an earlier paper for a class of well-prioritized knowledge bases. We start our study with a language consisting only of literals and two type of attacks, rebut and undercut. We then show that our approach can easily be scaled up by showing that all key results still hold for general underlying logical languages and the inclusion of assumptions. We apply our proposed approach to valued-based argumentation and show that it also leads to the canonical semantics.

AIJ Journal 2016 Journal Article

An axiomatic analysis of structured argumentation with priorities

• Phan Minh Dung

Several systems of semantics have been proposed for structured argumentation with priorities. As the proposed semantics often sanction contradictory conclusions (even for skeptical reasoners), there is a fundamental need for guidelines for understanding and evaluating them, especially their conceptual foundation and relationship. In this paper, we present an axiomatic analysis of the semantics of structured defeasible argumentation both with and without preferences by introducing a class of ordinary attack relations satisfying a set of simple and intuitive properties. We show that there exists a “normal form” for ordinary attack relations in the sense that stable extensions wrt any ordinary attack relation are stable extensions wrt the normal attack relations. We relate the ordinary semantics to other approaches, especially to the ASPIC+ framework and the prioritized approaches in logic programming.

ECAI Conference 2014 Conference Paper

An Axiomatic Analysis of Structured Argumentation for Prioritized Default Reasoning

• Phan Minh Dung

Several systems of argument-based and non-argument-based semantics have been proposed for prioritized default reasoning. As the proposed semantics often sanction contradictory conclusions (even for skeptical reasoners), there is a fundamental need for guidelines for understanding and evaluating them, especially their conceptual foundations and relationships. In this paper, we introduce several natural axioms for structural argumentation with preferences that capture both the consistency and closure postulates. We show that Aspic+semantics do not satisfy key axioms including the consistency postulate and propose a simple one satisfying all axioms. We show that the prescriptive non-argument-based approach to prioritized default reasoning is sound (and complete for a relevant class of knowledge bases) wrt our proposed simple semantics.

AILAW Journal 2011 Journal Article

The modular logic of private international law

• Phan Minh Dung
• Giovanni Sartor

Abstract We provide a logical analysis of private international law, a rather esoteric, but increasingly important, domain of the law. Private international law addresses overlaps and conflicts between legal systems by distributing cases between the authorities of such systems (jurisdiction) and establishing what rules these authorities have to apply to each case (choice of law). A formal model of the resulting interactions between legal systems is proposed based on modular argumentation. It is argued that this model may also be useful for governing the interactions between heterogeneous agents, belonging to different and differently regulated virtual societies, without recourse to a central regulatory agency. The model also provides for multiple interpretations concerning rules of private international law as well as substantive rules of the different legal systems.

IJCAI Conference 2009 Conference Paper

• Phan Minh Dung
• Phan Min Thang

We present an unified methodology for representation and development of dialectical proof procedures in abstract argumentation based on the notions of legal environments and dispute derivations. A legal environment specifies the legal moves of the dispute parties while a dispute derivation describes the procedure structure. A key insight of this paper is that the opponent moves determine the soundness of a dispute while the completeness of a dispute procedure depends on the proponent moves.

AILAW Journal 2009 Journal Article

Modular argumentation for modelling legal doctrines in common law of contract

• Phan Minh Dung
• Phan Minh Thang

Abstract To create a programming environment for contract dispute resolution, we propose an extension of assumption-based argumentation into modular assumption-based argumentation in which different modules of argumentation representing different knowledge bases for reasoning about beliefs and facts and for representation and reasoning with the legal doctrines could be built and assembled together. A distinct novel feature of modular argumentation in compare with other modular logic-based systems like Prolog is that it allows references to different semantics in the same module at the same time, a feature critically important for application of argumentation in legal domains like contract dispute resolution where the outcomes of court cases often depend on whether credulous or skeptical modes of reasoning were applied by the contract parties. We apply the new framework to model the doctrines of contract breach and mutual mistake.

AIJ Journal 2001 Journal Article

An argument-based approach to reasoning with specificity

• Phan Minh Dung
• Tran Cao Son

We present a new priority-based approach to reasoning with specificity which subsumes inheritance reasoning. The new approach differs from other priority-based approaches in the literature in the way priority between defaults is handled. Here, it is conditional rather than unconditional as in other approaches. We show that any unconditional handling of priorities between defaults as advocated in the literature until now is not sufficient to capture general defeasible inheritance reasoning. We propose a simple and novel argumentation semantics for reasoning with specificity taking the conditionality of the priorities between defaults into account. Since the proposed argumentation semantics is a form of stable semantics of nonmonotonic reasoning, it inherits a common problem of the latter where it is not always defined for every default theory. We propose a class of stratified default theories for which the argumentation semantics is always defined. We also show that acyclic and consistent inheritance networks are stratified. We prove that the argumentation semantics satisfies the basic properties of a nonmonotonic consequence relation such as deduction, reduction, conditioning, and cumulativity for well-defined and stratified default theories. We give a modular and polynomial transformation of default theories with specificity into semantically equivalent Reiter default theories.

LOPSTR Conference 1997 Conference Paper

Synthesis of Proof Procedures for Default Reasoning

• Phan Minh Dung
• Robert A. Kowalski
• Francesca Toni

Abstract We apply logic program development technology to define abstract proof procedures, in the form of logic programs, for computing the admissibility semantics for default reasoning proposed in [2]. The proof procedures are derived from a formal specification. The derivation guarantees the soundness of the proof procedures. The completeness of the proof procedures is shown by employing a technique of symbolic execution of logic programs to compute (an instance of) a relation implied by the specification.

AAAI Conference 1996 Conference Paper

Production Systems Need Negation as Failure

• Phan Minh Dung

We study action rule based systems with two forms of negation, namely classical negation and “negation as failure to find a course of actions”. We show by several examples that adding negation as failure to such systems increase their expressiveness, in the sense that real life problems can be represented in a natural and simple way. Then, we address the problem of providing a formal declarative semantics to these extended systems, by adopting an argumentation based approach, which has been shown to be a simple unifying framework for understanding the declarative semantics of various nonmonotonic formalisms. In this way, we naturally define the grounded (well-founded), stable and preferred semantics for production systems with negation as failure. Next, we characterize the class of stratified production systems, which enjoy the properties that the above mentioned semantics coincide and that negation as failure can be computed by a simple bottom-up operator.

AIJ Journal 1995 Journal Article

On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games

• Phan Minh Dung

The purpose of this paper is to study the fundamental mechanism, humans use in argumentation, and to explore ways to implement this mechanism on computers. We do so by first developing a theory for argumentation whose central notion is the acceptability of arguments. Then we argue for the “correctness” or “appropriateness” of our theory with two strong arguments. The first one shows that most of the major approaches to nonmonotonic reasoning in AI and logic programming are special forms of our theory of argumentation. The second argument illustrates how our theory can be used to investigate the logical structure of many practical problems. This argument is based on a result showing that our theory captures naturally the solutions of the theory of n-person games and of the well-known stable marriage problem. By showing that argumentation can be viewed as a special form of logic programming with negation as failure, we introduce a general logic-programming-based method for generating meta-interpreters for argumentation systems, a method very much similar to the compiler-compiler idea in conventional programming.

IJCAI Conference 1993 Conference Paper

On the Acceptability of Arguments and its Fundamental Role in Nonmonotonic Reasoning and Logic Programming

• Phan Minh Dung

TCS Journal 1992 Journal Article

On the relations between stable and well-founded semantics of logic programs

• Phan Minh Dung

We study the relations between stable and well-founded semantics of logic programs. 1. We show that stable semantics can be defined in the same way as well-founded semantics based on the basic notion of unfounded sets. Hence, stable semantics can be considered as “two-valued well-founded semantics”. 2. An axiomatic characterization of stable and well-founded semantics of logic programs is given by a new completion theory, called strong completion. Similar to the Clark's completion, the strong completion can be interpreted in either two-valued or three-valued logic. We show that ◦ Two-valued strong completion specifies the stable semantics. ◦ Three-valued strong completion specifies the well-founded semantics. 3. We study the equivalence between stable semantics and well-founded semantics. At first, we prove the equivalence between the two semantics for strict programs. Then we introduce the bottom-stratified and top-strict condition generalizing both the stratifiability and the strictness, and show that the new condition is sufficient for the equivalence between stable and well-founded semantics. Further, we show that the call-consistency condition is sufficient for the existence of at least one stable model.

ECAI Conference 1990 Conference Paper

Strong Circumscription Specifies Stable Semantics of Normal Logic Programs

• Phan Minh Dung