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.     

A theory of defeasible reasoning

Reasoning can lead not only to the adoption of beliefs, but also to the retraction of beliefs. In philosophy, this is described by saying that reasoning is defeasible. My ultimate objective is the construction of a general theory of reasoning and its implementation in an automated reasoner capable of both deductive and defeasible reasoning. the resulting system is named “OSCAR.” This article addresses some of the theoretical underpinnings of OSCAR. This article extends my earlier theory in two directions. First, it addresses the question of what the criteria of adequacy should be for a defeasible reasoner. Second, it extends the theory to accommodate reasons of varying strengths.     

The epistemic basis of defeasible reasoning

This article argues that: (i) Defeasible reasoning is the use of distinctive procedures for belief revision when new evidence or new authoritative judgment is interpolated into a system of beliefs about an application domain. (ii) These procedures can be explicated and implemented using standard higher-order logic combined with epistemic assumptions about the system of beliefs. The procedures mentioned in (i) depend on the explication in (ii), which is largely described in terms of a Prolog program, EVID, which implements a system for interactive, defeasible reasoning when combined with an application knowledge base. It is shown that defeasible reasoning depends on a meta-level Closed World Assumption applied to the relationship between supporting evidence and a defeasible conclusion based on this evidence. Thesis (i) is then further defended by showing that the EVID explication of defeasible reasoning has sufficient representational power to cover a wide variety of practical applications of defeasible reasoning, especially in the context of decision making.     

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 temporal modal defeasible logic for formalizing social commitments in dialogue and argumentation models

In this paper, we extend a temporal defeasible logic with a modal operator Committed to formalize commitments that agents undertake as a consequence of communicative actions (speech acts) during dialogues. We represent commitments as modal sentences. The defeasible dual of the modal operator Committed is a modal operator called Exempted. The logical setting makes the social-commitment based semantics of speech acts verifiable and practical; it is possible to detect if, and when, a commitment is violated and/or complied with. One of the main advantages of the proposed system is that it allows for capturing the nonmonotonic behavior of the commitments induced by the relevant speech acts.     

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     

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.     

On a rule-based interpretation of default conditionals

In nonmonotonic reasoning, a default conditional α→β has most often been informally interpreted as a defeasible version of a classical conditional, usually the material conditional. There is however an alternative interpretation, in which a default is regarded essentially as a rule, leading from premises to conclusion. In this paper, we present a family of logics, based on this alternative interpretation. A general semantic framework under this rule-based interpretation is developed, and associated proof theories for a family of weak conditional logics is specified. Nonmonotonic inference is easily defined in these logics. Interestingly, the logics presented here are weaker than the commonly-accepted base conditional approach for defeasible reasoning. However, this approach resolves problems that have been associated with previous approaches.      

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.     

Logical control of an elevator with defeasible logic

The elevator control program of Dyck and Caines (1995) can be implemented more concisely in d-Prolog, a defeasible logic programming system developed by Nute (1992, 1996, 1997). To demonstrate this, the program is recast, first into ordinary Prolog and then into d-Prolog. In defeasible logic, more specific rules take precedence over more general ones. Thus, the d-Prolog programmer can state general rules and then give explicit exceptions, just as humans do when explaining complex regularities to each other     

OSCAR: a general theory of rationality

Abstract

The enterprise is the construction of a general theory of rationality, and its implementation in an automated reasoning system named OSCAR. The paper describes a general architecture for rational thought. This includes both theoretical reasoning and practical reasoning, and builds in important interconnections between them. It is urged that a sophisticated reasoner must be an introspective reasoner, capable of monitoring its own reasoning and reasoning about it. An introspective reasoner is built on top of a non-introspective reasoner that represents the system's default reasoning strategies. The introspective reasoner engages in practical reasoning about reasoning in order to override these default strategies. The paper concludes with a discussion of some aspects of the default reasoner, including the manner in which reasoning is interest driven, and the structure of defeasible reasoning.     

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.     

A Categorical Linear Framework for Petri Nets

This paper presents a framework for giving a compositional theory of Petri nets using category theory. An integral part of our approach is the use of linear logic in specifying and reasoning about Petri nets. We construct categories of nets based on V. C. V. de Paiva′s dialectica category models of linear logic [in "Proc. Category Theory and Computer Science, Manchester" (D. H. Pitt, D. E. Rydeheard, P. Dybjer, A. M. Pitts, and A. Poigné, Eds.), Lecture Notes in Computer Science, Vol. 389, Springer-Verlag, Berlin/New York, 1989] and exploit the structure of de Paiva′s models to give constructions on nets. We compare our categories of nets with others in the literature, and show how some of the most widely-studied categories can be expressed within our framework. Taking a category of elementary nets as an example we show how this approach yields both existing and novel constructions on nets and discuss their computational interpretation.     

Defeasible inheritance with doubt index and its axiomatic characterization

This article introduces and uses a representation of defeasible inheritance networks where links in the network are viewed as propositions, and where defeasible links are tagged with a quantitative indication of the proportion of exceptions, called the doubt index. This doubt index is used for restricting the length of the chains of inference.The representation also introduces the use of defeater literals that disable the chaining of subsumption links. The use of defeater literals replaces the use of negative defeasible inheritance links, expressing “most A are not B”. The new representation improves the expressivity significantly.Inference in inheritance networks is defined by a combination of axioms that constrain the contents of network extensions, a heuristic restriction that also has that effect, and a nonmonotonic operation of minimizing the set of defeater literals while retaining consistency.We introduce an underlying semantics that defines the meaning of literals in a network, and prove that the axioms are sound with respect to this semantics. We also discuss the conditions for obtaining completeness.Traditional concepts, assumptions and issues in research on nonmonotonic or defeasible inheritance are reviewed in the perspective of this approach.     

Visualizing Semantic Web proofs of defeasible logic in the DR-DEVICE system

The Semantic Web aims at improving the current Web, by augmenting its content with semantics and encouraging the cooperation among human users and machines. Since the basic Semantic Web infrastructure is reaching sufficient maturity, research efforts are shifting towards logic, proof and trust and rule-based systems inevitably concentrate most of the attention. Nevertheless, in order for human users to trust system answers, they have to be presented with adequate explanations that justify the derived results. And, even more importantly, these explanations have to be presented in a user-comprehensible format. Consequently, the focus in this work is on humans and the research area called proof visualization that features three main approaches: tree-based, graphical and logical/textual. Since each of the approaches presents advantages and disadvantages, this article proposes a fourth, hybrid visualization approach that combines the pros of all three approaches and attempts to leverage the respective cons. The article also presents a software tool that implements the proposed hybrid approach. The tool is called VProof_H and visualizes defeasible logic proofs, offering multiple representations that adapt to user needs. Extensive scalability and user evaluation tests prove the software tool’s usability.     

Discovering rules to design newspapers: An inductive constraint logic programming approach

Inductive logic programming combines both machine learning and logic programming techniques. ILP uses first-order predicate logic restricted to Horn clauses as an underlying language. Thus, programs induced by an ILP system inherit the classical limitations of PROLOG programs. Constraint logic programming avoids some of the limitations of logic programming, and so ILP aims to induce programs that employ this paradigm. Current ILP systems that induce constrained logic programs extend systems based on the normal semantics ofILP. In this article we introduce IC-Log, a new system that induces constrained logic programs and relies on an extension ofa nonmonotonic semantics-based system. We then present an application of IC-Log in the field ofcomputer-aided publishing.     

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.     

Programming in temporal-nonmonotonic reasoning

Nonmonotonic reasoning has been proposed as an extension to classical first-order logic. Now people are interested in temporal reasoning with nonmonotonic logic [6]. We combine the monotonic logic [7] with a temporal logic to get a more general reasoning language. We discuss a monotonic logic TML which has predicate formulas, temporal formulas and a special modal formula, and give a completeness theorem of it. We use TH() to designate the set of theorems of a temporal-nonmonotonic theory which has the same language with TML. The completeness theorem of the temporal-nonmonotonic logic naturally arises. Like the relationship between predicate logic with a practical logic programming language PROLOG, we propose a useful temporal-nonmonotonic reasoning language TN for the temporal-nonmonotonic logic. As an appendix we supply an algorithm for the programming language TN.