基于可信度的辩论模型及争议评价算法

辩论是智能主体间为了消除分歧的一种基于言语的交互行为.由于知识的局限性,争议以及争议内部的陈述通常存在不确定性,因此在对辩论进行建模时需要考虑不确定信息处理问题.提出一种基于可信度的辩论模型（CFA）,该模型将争议表示为由若干前提和一个结论组成的可废止规则,并用对话树描述辩论推演过程.为了表示不确定性推理,引入可信度模型,将争议前提的不确定性和争议之间的攻击强度统一用可信度因子表示.在此基础上,提出计算陈述可信度的争议评价算法,并通过设定可信度阈值确定陈述的可接受性,得出最终辩论结果.最后,用一个实例说明该方法的有效性.该模型可以有效处理不确定信息条件下辩论推理过程,其辩论算法建立在数值计算基础之上,所得出的可接受陈述集在给定可信度阈值条件下是唯一的,可以克服Dung 的抽象辩论框架中扩充语义的不足.     

Is there a Burden of Questioning?

In some recent cases in Anglo-American law juries ruled contrary to an expert's testimony even though that testimony was never challenged, contradicted or questioned in the trial. These cases are shown to raise some theoretical questions about formal dialogue systems in computational dialectical systems for legal argumentation of the kind recently surveyed by Bench-Capon (1997) and Hage (2000) in this journal. In such systems, there is a burden of proof, meaning that if the respondent questions an argument, the proponent is obliged to offer some support for it give it up. But what should happen in a formal system of dialogue if the proponent puts forward an argument and the respondent fails to critically question it, and simply moves on to another issue? Is this some kind of fault that should have implications? Should it be taken to imply that, by default, the respondent has conceded the argument? What, if anything, should be the outcome of such a failure to question in a formal dialogue system of argumentation? These questions are considered by examining some legal cases of expert opinion testimony in relation rules for formal dialectical argumentation systems.     

A formal model of adjudication dialogues

This article presents a formal dialogue game for adjudication dialogues. Existing AI & law models of legal dialogues and argumentation-theoretic models of persuasion are extended with a neutral third party, to give a more realistic account of the adjudicator’s role in legal procedures. The main feature of the model is a division into an argumentation phase, where the adversaries plea their case and the adjudicator has a largely mediating role, and a decision phase, where the adjudicator decides the dispute on the basis of the claims, arguments and evidence put forward in the argumentation phase. The model allows for explicit decisions on admissibility of evidence and burden of proof by the adjudicator in the argumentation phase. Adjudication is modelled as putting forward arguments, in particular undercutting and priority arguments, in the decision phase. The model reconciles logical aspects of burden of proof induced by the defeasible nature of arguments with dialogical aspects of burden of proof as something that can be allocated by explicit decisions on legal grounds.

A model of argumentation and its application to legal reasoning

We present a computational model of dialectical argumentation that could serve as a basis for legal reasoning. The legal domain is an instance of a domain in which knowledge is incomplete, uncertain, and inconsistent. Argumentation is well suited for reasoning in such weak theory domains. We model argument both as information structure, i.e., argument units connecting claims with supporting data, and as dialectical process, i.e., an alternating series of moves by opposing sides. Our model includes burden of proof as a key element, indicating what level of support must be achieved by one side to win the argument. Burden of proof acts as move filter, turntaking mechanism, and termination criterion, eventually determining the winner of an argument. Our model has been implemented in a computer program. We demonstrate the model by considering program output for two examples previously discussed in the artificial intelligence and legal reasoning literature.     

A labelling framework for probabilistic argumentation

The combination of argumentation and probability paves the way to new accounts of qualitative and quantitative uncertainty, thereby offering new theoretical and applicative opportunities. Due to a variety of interests, probabilistic argumentation is approached in the literature with different frameworks, pertaining to structured and abstract argumentation, and with respect to diverse types of uncertainty, in particular the uncertainty on the credibility of the premises, the uncertainty about which arguments to consider, and the uncertainty on the acceptance status of arguments or statements. Towards a general framework for probabilistic argumentation, we investigate a labelling-oriented framework encompassing a basic setting for rule-based argumentation and its (semi-) abstract account, along with diverse types of uncertainty. Our framework provides a systematic treatment of various kinds of uncertainty and of their relationships and allows us to back or question assertions from the literature.     

Subjective logic and arguing with evidence

This paper introduces a subjective logic based argumentation framework primarily targeted at evidential reasoning. The framework explicitly caters for argument schemes, accrual of arguments, and burden of proof; these concepts appear in many types of argument, and are particularly useful in dialogues revolving around evidential reasoning. The concept of a sensor is also useful in this domain, representing a source of evidence, and is incorporated in our framework. We show how the framework copes with a number of problems that existing frameworks have difficulty dealing with, and how it can be situated within a simple dialogue game. Finally, we examine reasoning machinery that enables an agent to decide what argument to advance with the goal of maximising its utility at the end of a dialogue.     

An argumentation framework in default logic

This article presents a formal theory about nontrivial reasoning with inconsistent information, applicable, among other things, to defeasible reasoning. The theory, which is inspired by a formal analysis of legal argument, is based on the idea that inconsistency tolerant reasoning is more than revising an unstructural set of premises; rather it should be regarded as constructing and comparing arguments for incompatible conclusions. This point of view gives rise to two important observations, both pointing at some flaws of other theories. The first is that arguments should be compared as they are constructed, viz. step-by-step, while the second observation is that a knowledge representation language is needed with a defeasible conditional, since the material implication gives rise to arguments which are not constructed in actual reasoning. Accordingly, a nonmonotonic logic, default logic, is chosen as the formalism underlying the argumentation framework. The general structure of the framework allows for any standard for comparing pairs of arguments; in this study two such standards are investigated, based on specificity and on orderings of the premises.     

Twelve theses on argumentation systems

In this article we consider the partition of a set of statements P = P ^a ∪ P ^b ∪ P′, where P ^a , P ^b , P′ are, correspondingly, sets of statements only being argumented, both being argumented and argumenting, and only argumenting (basic statements). On P are defined two functions of argument and counter-argument selection forming the semantics for logics of argumentation. A four-valued logic of argumentation is proposed. By means of graph theory are formed trees of arguments (argument trees), wood, consisting of them, and some transformations of the wood, such that their result may be both planar and non-planar graph. Argument systems (systems of arguments) are defined together with their characterizations that use analytic tableaux. With the help of argument trees a specification of the idea of hermeneutic (“vicious”) circle is formalized.     

An argumentation model of forensic evidence in fine art attribution

In this paper, a case study is conducted to test the capability of the Carneades Argumentation System to model the argumentation in a case where forensic evidence was collected in an investigation triggered by a conflict among art experts on the attribution of a painting to Leonardo da Vinci. A claim that a portrait of a young woman in a Renaissance dress could be attributed to da Vinci was initially dismissed by art experts. Forensic investigations were carried out, and evidence was collected by art history experts and scientific experts. The expert opinions were initially in conflict, but new evidence shifted the burden of proof onto the side of the skeptics. This paper presents an analysis of the structure of the interlocking argumentation in the case using argument mapping tools to track the accumulation of evidence pro and con.     

Encoding deductive argumentation in quantified Boolean formulae

There are a number of frameworks for modelling argumentation in logic. They incorporate a formal representation of individual arguments and techniques for comparing conflicting arguments. A common assumption for logic-based argumentation is that an argument is a pair 〈Φ,α〉 where Φ is minimal subset of the knowledge-base such that Φ is consistent and Φ entails the claim α. Different logics provide different definitions for consistency and entailment and hence give us different options for argumentation. Classical propositional logic is an appealing option for argumentation but the computational viability of generating an argument is an issue. To better explore this issue, we use quantified Boolean formulae to characterise an approach to argumentation based on classical logic.     

Computing Arguments and Attacks in Assumption-Based Argumentation

Most computational frameworks for argumentation are based on abstract argumentation, which determines an argument's acceptability on the basis of its ability to counterattack all arguments attacking it. However, this view of argumentation doesn't address how to find arguments, identify attacks, and exploit premises. Assumption-based argumentation addresses these three issues. It's a refinement of abstract argumentation but remains general purpose, nonetheless. Rather than considering arguments to be a primitive concept, assumption-based argumentation defines them as backward deductions (using sets of rules in an underlying logic) supported by sets of assumptions. This approach reduces the notion of an attack against an argument to that of deduction of a contrary of an assumption.     

Extending abstract argumentation systems theory

In this paper, we extend the theory of abstract argumentation systems proposed by Vreeswijk (1997). This framework stands at a high abstraction level and provides a general model for argumentation activity. However, the theory reveals an inherent limitation in that the premises of the argumentation process are assumed to be indefeasible, and this introduces the need of an implicit constraint on the strength of the arguments, in order to preserve correctness. In many application contexts the information available to start reasoning is not guaranteed to be completely reliable, therefore it is natural to assume that premises can be discarded during the argumentation process. We extend the theory by admitting that premises can be defeated and relaxing the implicit assumption about their strength.Besides fixing the technical problems related to this hidden assumption (e.g., ensuring that warranted arguments are compatible), our proposal provides an integrated model for belief revision and defeasible reasoning, confirming the suitability of argumentation as a general model for the activity of intelligent reasoning in presence of various kinds of uncertainty.     

Dialectic proof procedures for assumption-based, admissible argumentation

We present a family of dialectic proof procedures for the admissibility semantics of assumption-based argumentation. These proof procedures are defined for any conventional logic formulated as a collection of inference rules and show how any such logic can be extended to a dialectic argumentation system.The proof procedures find a set of assumptions, to defend a given belief, by starting from an initial set of assumptions that supports an argument for the belief and adding defending assumptions incrementally to counter-attack all attacks.The proof procedures share the same notion of winning strategy for a dispute and differ only in the search strategy they use for finding it. The novelty of our approach lies mainly in its use of backward reasoning to construct arguments and potential arguments, and the fact that the proponent and opponent can attack one another before an argument is completed. The definition of winning strategy can be implemented directly as a non-deterministic program, whose search strategy implements the search for defences.     

A Reasoning Model Based on the Production of Acceptable Arguments

Argumentation is a reasoning model based on the construction of arguments and counter-arguments (or defeaters) followed by the selection of the most acceptable of them. In this paper, we refine the argumentation framework proposed by Dung by taking into account preference relations between arguments in order to integrate two complementary points of view on the concept of acceptability: acceptability based on the existence of direct counter-arguments and acceptability based on the existence of defenders. An argument is thus acceptable if it is preferred to its direct defeaters or if it is defended against its defeaters. This also refines previous works by Prakken and Sartor, by associating with each argument a notion of strength, while these authors embed preferences in the definition of the defeat relation. We propose a revised proof theory in terms of AND/OR trees, verifying if a given argument is acceptable, which better reflects the dialectical form of argumentation.     

Proof systems that take advice

One of the starting points of propositional proof complexity is the seminal paper by Cook and Reckhow [J. Symbolic Logic, 1979], where they defined propositional proof systems as poly-time computable functions which have all propositional tautologies as their range. Motivated by provability consequences in bounded arithmetic, Cook and Kraj?´?ek [J. Symbolic Logic, 2007] have recently started the investigation of proof systems which are computed by poly-time functions using advice.In this paper we concentrate on three fundamental questions regarding this new model. First, we investigate whether a given language L admits a polynomially bounded proof system with advice. Depending on the complexity of the underlying language L and the amount and type of the advice used by the proof system, we obtain different characterizations for this problem. In particular, we show that this question is tightly linked with the question whether L has small nondeterministic instance complexity.The second question concerns the existence of optimal proof systems with advice. For propositional proof systems, Cook and Kraj?´?ek gave a surprising positive answer which we extend to all languages.These results show that providing proof systems with advice yields a more powerful model, but this model is also less directly applicable in practice. Our third question therefore asks whether the usage of advice in propositional proof systems can be simplified or even eliminated. While in principle, the advice can be very complex, we show that propositional proof systems with logarithmic advice are also computable in poly-time with access to a sparse NP-oracle. Employing a recent technique of Buhrman and Hitchcock [CCC, 2008] we also manage to transfer the advice from the proof to the proven formula, which leads to a more practical computational model.     

Computing ideal sceptical argumentation

We present two dialectic procedures for the sceptical ideal semantics for argumentation. The first procedure is defined in terms of dispute trees, for abstract argumentation frameworks. The second procedure is defined in dialectical terms, for assumption-based argumentation frameworks. The procedures are adapted from (variants of) corresponding procedures for computing the credulous admissible semantics for assumption-based argumentation, proposed in [P.M. Dung, R.A. Kowalski, F. Toni, Dialectic proof procedures for assumption-based, admissible argumentation, Artificial Intelligence 170 (2006) 114–159]. We prove that the first procedure is sound and complete, and the second procedure is sound in general and complete for a special but natural class of assumption-based argumentation frameworks, that we refer to as p-acyclic. We also prove that in the case of p-acyclic assumption-based argumentation frameworks (a variant of) the procedure of [P.M. Dung, R.A. Kowalski, F. Toni, Dialectic proof procedures for assumption-based, admissible argumentation, Artificial Intelligence 170 (2006) 114–159] for the admissible semantics is complete. Finally, we present a variant of the procedure of [P.M. Dung, R.A. Kowalski, F. Toni, Dialectic proof procedures for assumption-based, admissible argumentation, Artificial Intelligence 170 (2006) 114–159] that is sound for the sceptical grounded semantics.     

一种基于时态的扩展值辩论框架

时间是用来描述辩论过程以及辩论活动变化的一个重要因素,在辩论框架中加入时间因素是积极的。本文结合Dung的标准辩论框架以及Bench-Capon的基于值的辩论框架,提出了基于时态的扩展值辩论框架。首先分析了Dung的辩论框架以及Bench-Capon的值辩论框架在时态以及辩论值方面描述的局限性及需求,然后结合这些需求提出了基于时态的扩展值辩论框架,给出了完整的框架结构和语义描述,证明了基于时态的扩展值辩论框架满足Dung提出的标准辩论框架的一些基本定理。     

The mathematics of patent claim analysis

In patent law most of the crucial legal questions such as patentability and infringement are linked to the patent claims. The European Patent Office regards patent claims as a set of independent features which are examined separately in a more or less formal way. The author has found that this approach allows for developing a simple mathematical model which treats patent claim features as logical statements and patent claims as compound statements wherein the individual statements are connected by logical connectives. The proposed mathematical model provides a uniform system for examining various legal questions that are dealt with separately under current case law, moreover, it allows for developing an expert system for resolving complex legal situations and for automating the evaluation of a large number of patent claim variants that is currently not possible.