Defeasible Rules Research Articles

Defeasible logic programming: DeLP-servers, contextual queries, and explanations for answers

Argumentation represents a way of reasoning over a knowledge base containing possibly incomplete and/or inconsistent information, to obtain useful conclusions. As a reasoning mechanism, the way an argumentation reasoning engine reaches these conclusions resembles the cognitive process that humans follow to analyse their beliefs; thus, unlike other computationally reasoning systems, argumentation offers an intellectually friendly alternative to other defeasible reasoning systems. Logic Programming is a computational paradigm that has produced computationally attractive systems with remarkable success in many applications. Merging ideas from both areas, Defeasible Logic Programming offers a computational reasoning system that uses an argumentation engine to obtain answers from a knowledge base represented using a logic programming language extended with defeasible rules. This combination of ideas brings about a computationally effective system together with a human-like reasoning model facilitating its use ...

A THEORETICAL FRAMEWORK FOR TRUST-BASED NEWS RECOMMENDER SYSTEMS AND ITS IMPLEMENTATION USING DEFEASIBLE ARGUMENTATION

Although the importance of trust in recommender systems is widely recognized, the actual mechanisms of trust propagation and trust preservation are poorly understood. This is partly due to the fact that trust is a complex notion, which is typically context dependent, subjective, dynamic and not always transitive or symmetrical. This paper presents a theoretical analysis of the notion of trust in news recommendation and discusses the advantages of modeling this notion using Defeasible Logic Programming, a general-purpose defeasible argumentation formalism based on logic programming. In the proposed framework, users can express explicit trust statements on news reports, news sources and other users. Trust is then modeled and propagated using a dialectical process supported by a Defeasible Logic Programming interpreter. A set of basic postulates for trust and their representation by means of defeasible rules is presented. The suitability of the approach is investigated with a set of illustrative examples and then analyzed from a formal perspective. The obtained results indicate that the proposed framework provides a solid foundation for building trust-based news recommendation services.

A formalization of argumentation schemes for legal case-based reasoning in ASPIC+

In this article we offer a formal account of reasoning with legal cases in terms of argumentation schemes. These schemes, and undercutting attacks associated with them, are formalized as defeasible rules of inference within the ASPIC+ framework. We begin by modelling the style of reasoning with cases developed by Aleven and Ashley in the CATO project, which describes cases using factors, and then extend the account to accommodate the dimensions used in Rissland and Ashley's earlier HYPO project. Some additional scope for argumentation is then identified and formalized.

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---124; 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---357; 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.

Well-founded semantics for defeasible logic

Fixpoint semantics are provided for ambiguity blocking and propagating variants of Nute’s defeasible logic. The semantics are based upon the well-founded semantics for logic programs. It is shown that the logics are sound with respect to their counterpart semantics and complete for locally finite theories. Unlike some other nonmonotonic reasoning formalisms such as Reiter’s default logic, the two defeasible logics are directly skeptical and so reject floating conclusions. For defeasible theories with transitive priorities on defeasible rules, the logics are shown to satisfy versions of Cut and Cautious Monotony. For theories with either conflict sets closed under strict rules or strict rules closed under transposition, a form of Consistency Preservation is shown to hold. The differences between the two logics and other variants of defeasible logic—specifically those presented by Billington, Antoniou, Governatori, and Maher—are discussed.

A Preliminary Reification of Argument Theory Change

In this article we introduce the basics for understanding the mechanisms of Argument Theory Change. In particular we reify it using Defeasible Logic Programming. In this formalism, knowledge bases are represented through defeasible logic programs. The main change operation we deflne over a defeasible logic program is a special kind of revision that inserts a new argument and then modifles the resulting program seeking for the argument's warrant. Since the notion of argument refers to a set of defeasible rules, we generalize this technique in order to handle extended arguments, i.e., arguments containing also strict rules. Hence, revision using extended arguments allows us to consider program-independent arguments, which brings about new issues. A single notion of minimal change is analyzed, which refers to keep the contents of the program as much as possible. Finally, a brief discussion about the relation between our approach and the basic theory of belief revision is exposed, along with a description of other possible (more complex) minimal change principles.

A logic programming framework for possibilistic argumentation: Formalization and logical properties

In the last decade defeasible argumentation frameworks have evolved to become a sound setting to formalize commonsense, qualitative reasoning. The logic programming paradigm has shown to be particularly useful for developing different argument-based frameworks on the basis of different variants of logic programming which incorporate defeasible rules. Most of such frameworks, however, are unable to deal with both explicit uncertainty and vague knowledge, as defeasibility is directly encoded in the object language. This paper presents possibilistic defeasible logic programming (P-DeLP), a new logic programming language which combines features from argumentation theory and logic programming, incorporating as well the treatment of possibilistic uncertainty. Such features are formalized on the basis of PGL, a possibilistic logic based on Gödel fuzzy logic. One of the applications of P-DeLP is providing an intelligent agent with non-monotonic, argumentative inference capabilities. In this paper we also provide a better understanding of such capabilities by defining two non-monotonic operators which model the expansion of a given program by adding new weighed facts associated with argument conclusions and warranted literals, respectively. Different logical properties for the proposed operators are studied.

On the evaluation of argumentation formalisms

Argumentation theory has become an important topic in the field of AI. The basic idea is to construct arguments in favor and against a statement, to select the “acceptable” ones and, finally, to determine whether the original statement can be accepted or not. Several argumentation systems have been proposed in the literature. Some of them, the so-called rule-based systems, use a particular logical language with strict and defeasible rules. While these systems are useful in different domains (e.g. legal reasoning), they unfortunately lead to very unintuitive results, as is discussed in this paper. In order to avoid such anomalies, in this paper we are interested in defining principles, called rationality postulates, that can be used to judge the quality of a rule-based argumentation system. In particular, we define two important rationality postulates that should be satisfied: the consistency and the closure of the results returned by that system. We then provide a relatively easy way in which these rationality postulates can be warranted for a particular rule-based argumentation system developed within a European project on argumentation.

DR-Prolog: A System for Defeasible Reasoning with Rules and Ontologies on the Semantic Web

Nonmonotonic rule systems are expected to play an important role in the layered development of the semantic Web. Defeasible reasoning is a direction in nonmonotonic reasoning that is based on the use of rules that may be defeated by other rules. It is a simple, but often more efficient approach than other nonmonotonic rule systems for reasoning with incomplete and inconsistent information. This paper reports on the implementation of a system for defeasible reasoning on the Web. The system 1) is syntactically compatible with RuleML, 2) features strict and defeasible rules, priorities, and two kinds of negation, 3) is based on a translation to logic programming with declarative semantics, 4) is flexible and adaptable to different intuitions within defeasible reasoning, and 5) can reason with rules, RDF, RDF Schema, and (parts of) OWL ontologies

Rules for Reasoning from Knowledge and Lack of Knowledge

In this paper, the traditional view that argumentum ad ignorantiam is a logical fallacy is challenged, and lessons are drawn on how to model inferences drawn from knowledge in combination with ones drawn from lack of knowledge. Five defeasible rules for evaluating knowledge-based arguments that apply to inferences drawn under conditions of lack of knowledge are formulated. They are the veridicality rule, the consistency of knowledge rule, the closure of knowledge rule, the rule of refutation and the rule for argument from ignorance. The basic thesis of the paper is that knowledge-based arguments, including the argument from ignorance, need to be evaluated by criteria for epistemic closure and other evidential rules that are pragmatic in nature, that need to be formulated and applied differently at different stages of an investigation or discussion. The paper helps us to understand practical criteria that should be used to evaluate all arguments based on knowledge and/or ignorance.

Research on negotiating agent development

The paper presents a flexible and effective method of development of negotiating agents. A strategy specification, which is specified by a state chart and defeasible rules, can be dynamically inserted into an agent shell incorporating a state chart interpreter and a defeasible logic inference engine, in order to yield a desirable agent. The set of desirable criteria and rules is required to be justified with different context of the application.

DefLog: on the Logical Interpretation of Prima Facie Justified Assumptions

Assumptions are often not considered to be definitely true, but only as prima facie justified. When an assumption is prima facie justified, there can for instance be a reason against it, by which the assumption is not actually justified. The assumption is then said to be defeated. This requires a revision of the standard conception of logical interpretation of sets of assumptions in terms of their models. Whereas in the models of a set of assumptions, all assumptions are taken to be true, an interpretation of prima facie justified assumptions must distinguish between the assumptions that are actually justified in the interpretation and those that are defeated. In the present paper, the logical interpretation of prima facie justified assumptions is investigated. The central notion is that of a dialectical interpretation of a set of assumptions. The basic idea is that a prima facie justified assumption is not actually justified, but defeated when its so-called dialectical negation is justified. The properties of dialectical interpretation are analysed by considering partial dialectical interpretations, or stages, and by establishing the notion of dialectical justification. The latter leads to a characterization of the existence and multiplicity of the dialectical interpretations of a set of assumptions. Since dialectical interpretations are a variant of stable semantics, the results are relevant for existing work on nonmonotonic logic and defeasible reasoning, on which the present work builds. Instead of focusing on defeasible rules or arguments, the present approach is sentence-based. A particular innovation is the use of a conditional that is prima facie justified (just like other assumptions) instead of an inconclusive conditional.

Computing Generalized Specificity

Most formalisms for representing common-sense knowledge allow incomplete and potentially inconsistent information. When strong negation is also allowed, contradictory conclusions can arise. A criterion for deciding between them is needed. The aim of this paper is to investigate an inherent and autonomous comparison criterion, based on specificity as defined in [POO 85, SIM 92]. In contrast to other approaches, we consider not only defeasible, but also strict knowledge. Our criterion is context-sensitive, i. e., preference among defeasible rules is determined dynamically during the dialectical analysis. We show how specificity can be defined in terms of two different approaches: activation sets and derivation trees. This allows us to get a syntactic criterion that can be implemented in a computationally attractive way. The resulting definitions may be applied in general rulebased formalisms. We present theorems linking both characterizations. Finally we discuss other frameworks for defeasible reasoning in which preference handling is considered explicitly.

Computational Dialogic Defeasible Reasoning

This article begins with an introduction to defeasible (nonmonotonic) reasoning and a brief description of a computer program, EVID, which can perform such reasoning. I then explain, and illustrate with examples, how this program can be applied in computational representations of ordinary dialogic argumentation. The program represents the beliefs and doubts of the dialoguers, and uses these propositional attitudes, which can include commonsense defeasible inference rules, to infer various changing conclusions as a dialogue progresses. It is proposed that computational representations of this kind are a useful tool in the analysis of dialogic argumentation, and, in particular, demonstrate the important role of defeasible reasoning in everyday arguments using commonsense reasoning.

A formal approach to negotiating agents development

This paper presents a formal and executable approach to capture the behaviour of parties involved in a negotiation. A party is modeled as a negotiating agent composed of a communication module, a control module, a reasoning module, and a knowledge base. The control module is expressed as a statechart, and the reasoning module as a defeasible logic program. A strategy specification therefore consists of a statechart, a set of defeasible rules, and a set of initial facts. Such a specification can be dynamically plugged into an agent shell incorporating a statechart interpreter and a defeasible logic inference engine, in order to yield an agent capable of participating in a given type of negotiations. The choice of statecharts and defeasible logic with respect to other formalisms is justified against a set of desirable criteria, and their suitability is illustrated through concrete examples of bidding and multi-lateral bargaining scenarios.

Relating defeasible and normal logic programming through transformation properties

This paper relates the Defeasible Logic Programming ( DeLP) framework and its semantics SEM DeLP to classical logic programming frameworks. In DeLP, we distinguish between two different sorts of rules: strict and defeasible rules. Negative literals ( ∼A) in these rules are considered to represent classical negation. In contrast to this, in normal logic programming ( NLP), there is only one kind of rules, but the meaning of negative literals ( not A) is different: they represent a kind of negation as failure, and thereby introduce defeasibility. Various semantics have been defined for NLP, notably the well-founded semantics (WFS) (van Gelder et al., Proceedings of the Seventh Symposium on Principles of Database Systems, 1988, pp. 221–230; J. ACM 38 (3) (1991) 620) and the stable semantics Stable (Gelfond and Lifschitz, Fifth Conference on Logic Programming, MIT Press, Cambridge, MA, 1988, pp. 1070–1080; Proceedings of the Seventh International Conference on Logical Programming, Jerusalem, MIT Press, Cambridge, MA, 1991, pp. 579–597). In this paper we consider the transformation properties for NLP introduced by Brass and Dix (J. Logic Programming 38(3) (1999) 167) and suitably adjusted for the DeLP framework. We show which transformation properties are satisfied, thereby identifying aspects in which NLP and DeLP differ. We contend that the transformation rules presented in this paper can help to gain a better understanding of the relationship of DeLP semantics with respect to more traditional logic programming approaches. As a byproduct, we obtain the result that DeLP is a proper extension of NLP.

Propositional defeasible logic has linear complexity

Defeasible logic is a rule-based nonmonotonic logic, with both strict and defeasible rules, and a priority relation on rules. We show that inference in the propositional form of the logic can be performed in linear time. This contrasts markedly with most other propositional nonmonotonic logics, in which inference is intractable.

Default reasoning from conditional knowledge bases: Complexity and tractable cases

Conditional knowledge bases have been proposed as belief bases that include defeasible rules (also called defaults) of the form “ φ→ψ”, which informally read as “generally, if φ then ψ”. Such rules may have exceptions, which can be handled in different ways. A number of entailment semantics for conditional knowledge bases have been proposed in the literature. However, while the semantic properties and interrelationships of these formalisms are quite well understood, about their computational properties only partial results are known so far. In this paper, we fill these gaps and first draw a precise picture of the complexity of default reasoning from conditional knowledge bases: Given a conditional knowledge base KB and a default φ→ψ, does KB entail φ→ψ? We classify the complexity of this problem for a number of well-known approaches (including Goldszmidt et al.'s maximum entropy approach and Geffner's conditional entailment), where we consider the general propositional case as well as natural syntactic restrictions (in particular, to Horn and literal-Horn conditional knowledge bases). As we show, the more sophisticated semantics for conditional knowledge bases are plagued with intractability in all these fragments. We thus explore cases in which these semantics are tractable, and find that most of them enjoy this property on feedback-free Horn conditional knowledge bases, which constitute a new, meaningful class of conditional knowledge bases. Furthermore, we generalize previous tractability results from Horn to q-Horn conditional knowledge bases, which allow for a limited use of disjunction. Our results complement and extend previous results, and contribute in refining the tractability/intractability frontier of default reasoning from conditional knowledge bases. They provide useful insight for developing efficient implementations.

On Resolving Conflicts Between Arguments

Argument systems are based on the idea that one can construct arguments for propositions; i.e., structured reasons justifying the belief in a proposition. Using defeasible rules, arguments need not be valid in all circumstances, therefore, it might be possible to construct an argument for a proposition as well as its negation. When arguments support conflicting propositions, one of the arguments must be defeated, which raises the question of \emph{which (sub-)arguments can be subject to defeat}? In legal argumentation, meta-rules determine the valid arguments by considering the last defeasible rule of each argument involved in a conflict. Since it is easier to evaluate arguments using their last rules, \emph{can a conflict be resolved by considering only the last defeasible rules of the arguments involved}? We propose a new argument system where, instead of deriving a defeat relation between arguments, \emph{undercutting-arguments} for the defeat of defeasible rules are constructed. This system allows us, (\textit{i}) to resolve conflicts (a generalization of rebutting arguments) using only the last rules of the arguments for inconsistencies, (\textit{ii}) to determine a set of valid (undefeated) arguments in linear time using an algorithm based on a JTMS, (\textit{iii}) to establish a relation with Default Logic, and (\textit{iv}) to prove closure properties such as \emph{cumulativity}. We also propose an extension of the argument system that enables \emph{reasoning by cases}.

Scientia Iuris - An Unsolved Philosophical Problem

Legal dogmatics in Continental European law (scientia iuris, Rechtswissenschaft) consists of professional legal writings whose task is to systematize and interpret valid law. Legal dogmatics pursues knowledge of the existing law, yet in many cases it leads to a change of the law. Among general theories of legal dogmatics, one may mention the theories of negligence, intent, adequate causation and ownership. The theories produce principles and they also produce defeasible rules. By means of production of general and defeasible theories, legal dogmatics aims at obtaining a system of law that is both internally coherent and harmonized with its background in morality and (political) philosophy. Legal dogmatics is necessary in the context of constitutional constraints on the majority rule. Only if the courts act on the basis of Reason they can be a legitimate counterpart of the majority rule. And Reason cannot be exhausted by particular decision making. It also needs a more abstract deliberation, given by expert jurists. However, legal dogmatics has been a target of several kinds of criticism: empirical, morally-political, epistemological, logical, and ontological. The position taken in this article is to answer such criticism by mutually adjusting philosophy and the practices of the law.