Self-defeating arguments

An argument is self-defeating when it contains defeaters for some of its own defeasible lines. It is shown that the obvious rules for defeat among arguments do not handle self-defeating arguments correctly. It turns out that they constitute a pervasive phenomenon that threatens to cripple defeasible reasoning, leading to almost all defeasible reasoning being defeated by unexpected interactions with self-defeating arguments. This leads to some important changes in the general theory of defeasible reasoning.     

Reconstructing Popov v. Hayashi in a framework for argumentation with structured arguments and Dungean semantics

In this article the argumentation structure of the court??s decision in the Popov v. Hayashi case is formalised in Prakken??s (Argument Comput 1:93?C124; 2010) abstract framework for argument-based inference with structured arguments. In this framework, arguments are inference trees formed by applying two kinds of inference rules, strict and defeasible rules. Arguments can be attacked in three ways: attacking a premise, attacking a conclusion and attacking an inference. To resolve such conflicts, preferences may be used, which leads to three corresponding kinds of defeat, after which Dung??s (Artif Intell 77:321?C357; 1995) abstract acceptability semantics can be used to evaluate the arguments. In the present paper the abstract framework is instantiated with strict inference rules corresponding to first-order logic and with defeasible inference rules for defeasible modus ponens and various argument schemes. The main techniques used in the formal reconstruction of the case are rule-exception structures and arguments about rule validity. Arguments about socio-legal values and the use of precedent cases are reduced to arguments about rule validity. The tree structure of arguments, with explicit subargument relations between arguments, is used to capture the dependency relations between the elements of the court??s decision.     

A conditional logic for defeasible beliefs

This paper provides a framework for representing beliefs by distinguishing between (i) the defeasible principles of a belief system, (ii) the propositions that are beyond reasonable doubt in a belief state, and (iii) the propositions ‘favored’ on the basis of defeasible principles and those propositions that are beyond reasonable doubt. Defeasible principles are interpreted semantically by means of a Lewis-style ranking of worlds (without the assumption that the actual world is among the ‘innermost’, or most highly ranked, worlds). The ‘favored closure’ (F-closure) of a set of defeasible principles and reasonable propositions is non-monotonic. Yet, given the concept of ‘pruning’ the default ranking relative to a set of worlds (determined by what is beyond reasonable doubt in a particular belief state) we provide a formal characterization of the conditions under which in inference to a favored conclusion on the basis of defeasible rules and reasonable propositions, is warranted. The adequacy of our representation of defeasible principles can be tested by considering a number of valid formulas that we list. We show that our concept of defeasible principle parallels but is not identical to the concept of ‘relatively high conditional probability’. An example of application of the formal language and semantics is given, and the final parts of the paper contain u     

Defeat among arguments: a system of defeasible inference

This paper presents a system of nonmonotonic reasoning with defeasible rules. The advantage of such a system is that many multiple extension problems can be solved without additional explicit knowledge; ordering competing extensions can be done in a natural and defeasible way, via syntactic considerations. The objectives closely resemble Poole's objectives.
But the logic is different from Poole's. The most important difference is that this system allows the kind of chaining that many other nonmonotonic systems allow. Also, the form in which the inference system is presented is quite unusual. It mimics an established system of inductive logic, and it treats defeat in the way of the epistemologist-philosophers.
The contributions are both of content and of form: (content) the kinds of defeat that are considered, and (form) the way in which defeat is treated in the rules of inference.     

Reasoning about preferences in argumentation frameworks

The abstract nature of Dung's seminal theory of argumentation accounts for its widespread application as a general framework for various species of non-monotonic reasoning, and, more generally, reasoning in the presence of conflict. A Dung argumentation framework is instantiated by arguments and a binary conflict based attack relation, defined by some underlying logical theory. The justified arguments under different extensional semantics are then evaluated, and the claims of these arguments define the inferences of the underlying theory. To determine a unique set of justified arguments often requires a preference relation on arguments to determine the success of attacks between arguments. However, preference information is often itself defeasible, conflicting and so subject to argumentation. Hence, in this paper we extend Dung's theory to accommodate arguments that claim preferences between other arguments, thus incorporating meta-level argumentation based reasoning about preferences in the object level. We then define and study application of the full range of Dung's extensional semantics to the extended framework, and study special classes of the extended framework. The extended theory preserves the abstract nature of Dung's approach, thus aiming at a general framework for non-monotonic formalisms that accommodate defeasible reasoning about as well as with preference information. We illustrate by formalising argument based logic programming with defeasible priorities in the extended theory.     

AN ARGUMENT-BASED APPROACH TO NONMONOTONIC REASONING*

We define an argument system to be a pair consisting of a set of inference rules and a set of completeness conditions. Inference rules are used to build arguments. Completeness conditions are used to define argument structures, which are sets of arguments supporting belief sets. We reformulate Reiter's default logic as special argument systems. This enables us, among other things, to apply the negation-as-failure rule to general default theories. We also speculate on some other potential uses of our argument systems.     

Agents that Learn How to Generate Arguments from Other Agents

Learning how to argue is a key ability for a negotiator agent. In this paper, we propose an approach that allows agents to learn how to build arguments by observing how other agents argue in a negotiation context. Particularly, our approach enables the agent to infer the rules for argument generation that other agents apply to build their arguments. To carry out this goal, the agent stores the arguments uttered by other agents and the facts of the negotiation context where each argument is uttered. Then, an algorithm for fuzzy generalized association rules is applied to discover the desired rules. This kind of algorithm allows us (a) to obtain general rules that can be applied to different negotiation contexts; and (b) to deal with the uncertainty about the knowledge of what facts of the context are taken into account by the agents. The experimental results showed that it is possible to infer argument generation rules from a reduced number of observed arguments.     

Quantum complementarity and logical indeterminacy

Whenever a mathematical proposition to be proved requires more information than it is contained in an axiomatic system, it can neither be proved nor disproved, i.e. it is undecidable, or logically undetermined, within this axiomatic system. I will show that certain mathematical propositions on a d-valent function of a binary argument can be encoded in d-dimensional quantum states of mutually unbiased basis (MUB) sets, and truth values of the propositions can be tested in MUB measurements. I will then show that a proposition is undecidable within the system of axioms encoded in the state, if and only if the measurement associated with the proposition gives completely random outcomes.     

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.     

A modular translation from defeasible nets to defeasible logics

Abstract

The sceptical inheritance nets introduced in Horty et al. [Proceedings of AAAI-87 (1987):358-363] are translated into a version of Nute's defeasible logic. Moreover this translation is modular in the sense of Thomason and Horty [Non-Monotonic Reasoning. Springer-Verlag (1989):234]. Apart from the importance of relating two nonmonotonic reasoning formalisms, this result shows that the reasoning mechanisms underlying defeasible logic and defeasible nets are the same. Yet they were invented independently and set in totally different contexts. This is perhaps some evidence that the underlying nonmonotonic reasoning mechanism is mainly correct. We also observe that since defeasible logics can contain both absolute and defeasible rules, they provided a uniform setting for considering nets which contain both strict and defeasible arcs.     

Abstract argumentation

In this paper we explore the thesis that the role of argumentation in practical reasoning in general and legal reasoning in particular is to justify the use of defeasible rules to derive a conclusion in preference to the use of other defeasible rules to derive a conflicting conclusion. The defeasibility of rules is expressed by means of non-provability claims as additional conditions of the rules.We outline an abstract approach to defeasible reasoning and argumentation which includes many existing formalisms, including default logic, extended logic programming, non-monotonic modal logic and auto-epistemic logic, as special cases. We show, in particular, that the admissibility semantics for all these formalisms has a natural argumentation-theoretic interpretation and proof procedure, which seem to correspond well with informal argumentation.In the admissibility semantics there is only one way for one argument to attack another, namely by undermining one of its non-provability claims. In this paper, we show how other kinds of attack between arguments, specifically how rebuttal and priority attacks, can be reduced to the undermining of non-provability claims.     

Artificial argument assistants for defeasible argumentation

The present paper discusses experimental argument assistance tools. In contrast with automated reasoning tools, the objective is not to replace reasoning, but to guide the user's production of arguments. Two systems are presented, and based on . The focus is on defeasible argumentation with an eye on the law. Argument assistants for defeasible argumentation naturally correspond to a view of the application of law as dialectical theory construction. The experiments provide insights into the design of argument assistants, and show the pros and cons of different ways of representing argumentative data. The development of the argumentation theories underlying the systems has culminated in the logical system that formalizes the interpretation of prima facie justified assumptions. introduces an innovative use of conditionals expressing support and attack. This allows the expression of warrants for support and attack, making it a transparent and flexible system of defeasible argumentation.     

Deliberation dialogues for reasoning about safety critical actions

In this paper we present the argument-based model proCLAIM, intended to provide a setting for heterogeneous agents to deliberate over safety critical actions. To achieve this purpose proCLAIM features a Mediator Agent with three main tasks: (1) guiding the participating agents in what their valid dialectical moves are at each stage of the dialogue; (2) deciding whether submitted arguments should be accepted on the basis of their relevance; and finally, (3) evaluating the accepted arguments in order to provide an assessment of whether the proposed action should or should not be undertaken. The main focus in this paper is the proposal of a set of reasoning patterns, represented in terms of argument schemes and critical questions, intended to automatise deliberations on whether a proposed action can safely be performed. We aim to motivate the importance of these schemes and critical questions for: (a) the Mediator Agent’s guiding task that allows for a highly focused deliberation; (b) the effective participation of heterogeneous agents; and (c) enabling the reuse of previous similar deliberations in order to evaluate arguments on an evidential basis.     

Abstract argumentation systems

In this paper, we develop a theory of abstract argumentation systems. An abstract argumentation system is a collection of “defeasible proofs”, called arguments, that is partially ordered by a relation expressing the difference in conclusive force. The prefix “abstract” indicates that the theory is concerned neither with a specification of the underlying language, nor with the development of a subtheory that explains the partial order. An unstructured language, without logical connectives such as negation, makes arguments not (pairwise) inconsistent, but (groupwise) incompatible. Incompatibility and difference in conclusive force cause defeat among arguments. The aim of the theory is to find out which arguments eventually emerge undefeated. These arguments are considered to be in force. Several results are established. The main result is that arguments that are in force are precisely those that are in the limit of a so-called complete argumentation sequence.     

Defeasible reasoning and logic programming

The general conditions of epistemic defeat are naturally represented through the interplay of two distinct kinds of entailment, deductive and defeasible. Many of the current approaches to modeling defeasible reasoning seek to define defeasible entailment via model-theoretic notions like truth and satisfiability, which, I argue, fails to capture this fundamental distinction between truthpreserving and justification-preserving entailments. I present an alternative account of defeasible entailment and show how logic programming offers a paradigm in which the distinction can be captured, allowing for the modeling of a larger range of types of defeat. This is possible through a natural extension of the declarative and procedural semantics of Horn clauses.     

Theorem Proving Modulo

Deduction modulo is a way to remove computational arguments from proofs by reasoning modulo a congruence on propositions. Such a technique, issued from automated theorem proving, is of general interest because it permits one to separate computations and deductions in a clean way. The first contribution of this paper is to define a sequent calculus modulo that gives a proof-theoretic account of the combination of computations and deductions. The congruence on propositions is handled through rewrite rules and equational axioms. Rewrite rules apply to terms but also directly to atomic propositions. The second contribution is to give a complete proof search method, called extended narrowing and resolution (ENAR), for theorem proving modulo such congruences. The completeness of this method is proved with respect to provability in sequent calculus modulo. An important application is that higher-order logic can be presented as a theory in deduction modulo. Applying the ENAR method to this presentation of higher-order logic subsumes full higher-order resolution. This revised version was published online in August 2006 with corrections to the Cover Date.     

t-DeLP: an argumentation-based Temporal Defeasible Logic Programming framework

The aim of this paper is to propose an argumentation-based defeasible logic, called t-DeLP, that focuses on forward temporal reasoning for causal inference. We extend the language of the DeLP logical framework by associating temporal parameters to literals. A temporal logic program is a set of basic temporal facts and (strict or defeasible) durative rules. Facts and rules combine into durative arguments representing temporal processes. As usual, a dialectical procedure determines which arguments are undefeated, and hence which literals are warranted, or defeasibly follow from the program. t-DeLP, though, slightly differs from DeLP in order to accommodate temporal aspects, like the persistence of facts. The output of a t-DeLP program is a set of warranted literals, which is first shown to be non-contradictory and be closed under sub-arguments. This basic framework is then modified to deal with programs whose strict rules encode mutex constraints. The resulting framework is shown to satisfy stronger logical properties like indirect consistency and closure.     

Defeasible Logic on an Embedded Microcontroller

Defeasible logic is a system of reasoning in which rules have exceptions, and when rules conflict, the one that applies most specifically to the situation wins out. This paper reports a successful application of defeasible logic to the implementation of an embedded control system. The system was programmed in d-Prolog (a defeasible extension of Prolog), and the inferences were compiled into a truth table that was encoded on a low-end PIC microcontroller.Advantages of defeasible logic include conciseness and correct handling of the passage of time. It is distinct from fuzzy logic and probabilistic logic, addressing a different set of problems.     

ANGLE: An autonomous, normative and guidable agent with changing knowledge

Some emerging computing systems (especially autonomic computing systems) raise several challenges to autonomous agents, including (1) how to reflect the dynamics of business requirements, (2) how to coordinate with external agents with sufficient level of security and predictability, and (3) how to perform reasoning with dynamic and incomplete knowledge, including both informational knowledge (observations) and motivational knowledge (for example, policy rules and contract rules). On the basis of defeasible logic and argumentation, this paper proposes an autonomous, normative and guidable agent model, called ANGLE, to cope with these challenges. This agent is established by combining beliefs-desires-intentions (BDI) architecture with policy-based method and the mechanism of contract-based coordination. Its architecture, knowledge representation, as well as reasoning and decision-making, are presented in this paper. ANGLE is characteristic of the following three aspects. First, both its motivational knowledge and informational knowledge are changeable, and allowed to be incomplete, inconsistent/conflicting. Second, its knowledge is represented in terms of extended defeasible logic with modal operators. Different from the existing defeasible theories, its theories (including belief theory, goal theory and intention theory) are dynamic (called dynamic theories), reflecting the variations of observations and external motivational knowledge. Third, its reasoning and decision-making are based on argumentation. Due to the dynamics of underlying theories, argument construction is not a monotonic process, which is different from the existing argumentation framework where arguments are constructed incrementally.     

Fast and scalable conflict detection for packet classifiers

Packet filters provide rules for classifying packets based on header fields. High speed packet classification has received much study. However, the twin problems of fast updates and fast conflict detection have not received much attention. A conflict occurs when two classifiers overlap, potentially creating ambiguity for packets that match both filters. For example, if Rule 1 specifies that all packets going to CNN be rate controlled and Rule 2 specifies that all packets coming from Walmart be given high priority, the rules conflict for traffic from Walmart to CNN. There has been prior work on efficient conflict detection for two-dimensional classifiers. However, the best known algorithm for conflict detection for general classifiers is the naive O(N²) algorithm of comparing each pair of rules for a conflict. In this paper, we describe an efficient and scalable conflict detection algorithm for the general case that is significantly faster. For example, for a database of 20 000 rules, our algorithm is 40 times faster than the naive implementation. Even without considering conflicts, our algorithm also provides a packet classifier with fast updates and fast lookups that can be used for stateful packet filtering.