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 analyze their beliefs; thus, unlike other computationally reasoning systems, argumentation offers an intellectually friendly alternative to other defeasible reasoning systems. LogicProgrammingisacomputationalparadigmthathasproducedcompu- tationallyattractivesystemswithremarkablesuccessinmanyapplications. 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 in applications. (shrink)

In this paper we show how defeasible logic could formally account for the non-monotonic properties involved in motivational attitudes like intention and obligation. Usually, normal modal operators are used to represent such attitudes wherein classical logical consequence and the rule of necessitation comes into play, i.e., ⊢A/⊢ □A, that is from ⊢A derive ⊢ □A. This means that such formalisms are affected by the Logical Omniscience problem. We show that policy-based intentions exhibit non-monotonic behaviour which could be captured (...) through a non-monotonic system like defeasible logic. To this end we outline a defeasible logic of intention that specifies how modalities can be introduced and manipulated in a non-monotonic setting without giving rise to the problem of logical omniscience. In a similar way we show how to add deontic modalities defeasibly and how to integrate them with other motivational attitudes like beliefs and goals. Finally we show that the basic aspect of the BOID architecture is captured by this extended framework. (shrink)

Most of the theories on formalising intention interpret it as a unary modal operator in Kripkean semantics, which gives it a monotonic look. We argue that policy-based intentions exhibit non-monotonic behaviour which could be captured through a non-monotonic system like defeasible logic. To this end we outline a defeasible logic of intention. The proposed technique alleviates most of the problems related to logical omniscience. The proof theory given shows how our approach helps in the maintenance of (...) intention-consistency in agent systems like BDI. (shrink)

This is a title on the foundations of defeasible logic, which explores the formal properties of everyday reasoning patterns whereby people jump to conclusions, reserving the right to retract them in the light of further information. Although technical in nature the book contains sections that outline basic issues by means of intuitive and simple examples. This book is primarily targeted at philosophers interested in the foundations of defeasible logic, logicians, and specialists in artificial intelligence and theoretical (...) computer science. (shrink)

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. (shrink)

In this paper, the Carneades argumentation system is extended to represent a procedural view of inquiry in which evidence is marshalled to support or defeat claims to knowledge. The model is a sequence of moves in a collaborative group inquiry in which parties take turns making assertions about what is known or not known, putting forward evidence to support them, and subjecting these moves to criticisms. It is shown how this model of evaluating evidence in an inquiry is based on (...) a defeasible logic using forms of argument that admit exceptions. It is contended that reasoning from absence of knowledge is as important to inquiry as positive reasoning from evidence to knowledge. The philosophical conflict between this view of reasoning about knowledge and the true-belief-plus view is explored by airing objections and replies on both sides. (shrink)

In this paper we propose an extension of Defeasible Logic to represent and compute different concepts of defeasible permission. In particular, we discuss some types of explicit permissive norms that work as exceptions to opposite obligations or encode permissive rights. Moreover, we show how strong permissions can be represented both with, and without introducing a new consequence relation for inferring conclusions from explicit permissive norms. Finally, we illustrate how a preference operator applicable to contrary-to-duty obligations can be (...) combined with a new operator representing ordered sequences of strong permissions. The logical system is studied from a computational standpoint and is shown to have linear computational complexity. (shrink)

Thinking about misleading higher-order evidence naturally leads to a puzzle about epistemic rationality: If one’s total evidence can be radically misleading regarding itself, then two widely-accepted requirements of rationality come into conflict, suggesting that there are rational dilemmas. This paper focuses on an often misunderstood and underexplored response to this (and similar) puzzles, the so-called conflicting-ideals view. Drawing on work from defeasible logic, I propose understanding this view as a move away from the default metaepistemological position according to (...) which rationality requirements are strict and governed by a strong, but never explicitly stated logic, toward the more unconventional view, according to which requirements are defeasible and governed by a comparatively weak logic. When understood this way, the response is not committed to dilemmas. (shrink)

Conciliatory views of disagreement say, roughly, that it’s rational for you to become less confident in your take on an issue in case you find out that an epistemic peer’s take on it is the opposite. Their intuitive appeal notwithstanding, there are well-known worries about the behavior of conciliatory views in scenarios involving higher-order disagreements, which include disagreements over these views themselves and disagreements over the peer status of alleged epistemic peers. This paper does two things. First, it explains how (...) the core idea behind conciliatory views can be expressed in a defeasible logic framework. The result is a formal model that’s particularly useful for thinking about the behavior of conciliatory views in cases involving higher-order disagreements. And second, the paper uses this model to resolve three paradoxes associated with disagreements over epistemic peerhood. (shrink)

For Tarski logics, there are simple criteria that enable one to conclude that two premise sets are equivalent. We shall show that the very same criteria hold for adaptive logics, which is a major advantage in comparison to other approaches to defeasible reasoning forms. A related property of Tarski logics is that the extensions of equivalent premise sets with the same set of formulas are equivalent premise sets. This does not hold for adaptive logics. However a very similar criterion (...) does. We also shall show that every monotonic logic weaker than an adaptive logic is weaker than the lower limit logic of the adaptive logic or identical to it. This highlights the role of the lower limit for settling the adaptive equivalence of extensions of equivalent premise sets. (shrink)

In this paper we investigate how to represent and reason about legal abrogations and annulments in Defeasible Logic. We examine some options that embed in this setting, and in similar rule-based systems, ideas from belief and base revision. In both cases, our conclusion is negative, which suggests to adopt a different logical model. This model expresses temporal aspects of legal rules, and distinguishes between two main timelines, one internal to a given temporal version of the legal system, and (...) another relative to how the legal system evolves over time. Accordingly, we propose a temporal extension of Defeasible Logic suitable to express this model and to capture abrogation and annulment. We show that the proposed framework overcomes the difficulties discussed in regard to belief and base revision, and is sufficiently flexible to represent many of the subtleties characterizing legal abrogations and annulments. (shrink)

This work formalizes an informant-based structured argumentation approach in a multi-agent setting, where the knowledge base of an agent may include information provided by other agents, and each piece of knowledge comes attached with its informant. In that way, arguments are associated with the set of informants corresponding to the information they are built upon. Our approach proposes an informant-based notion of argument strength, where the strength of an argument is determined by the credibility of its informant agents. Moreover, we (...) consider that the strength of an argument is not absolute, but it is relative to the resolution of the conflicts the argument is involved in. In other words, the strength of an argument may vary from one context to another, as it will be determined by comparison to its attacking arguments (respectively, the arguments it attacks). Finally, we equip agents with the means to express reasons for or against the consideration of any piece of information provided by a given informant agent. Consequently, we allow agents to argue about the arguments’ strength through the construction of arguments that challenge (respectively, defeat) or are in favour of their informant agents. (shrink)

Relevant to philosophy, law, management, and artificial intelligence, these papers explore the applicability of nonmonotonic or defeasible logic to normative reasoning. The resulting systems purport to solve well-known deontic paradoxes and to provide a better treatment than classical deontic logic does of prima facie obligation, conditional obligation, and priorities of normative principles.

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. (shrink)

The notions of defeasibility and defeasible reasoning have generated a great deal of interest in various research communities. Here I want to focus on their use in logic and argumentation studies. I will approach these topics from the perspective of an informal logician who finds himself struggling with some issues that surround the idea of and the deployment of the concept of defeasibility. My intention is to make those struggles as clear as I can.

While defeasibility in legal reasoning has been the subject of recent scholarship, it has yet to be studied in the context of judicial opinion. Yet, being subject to appeal, judicial decisions can default for a variety of reasons. Prakken (2001) argued that the defeasibility affecting reasoning involved in adversarial legal argumentation is best analysed as procedural rather than logical. In this paper we argue that the defeasibility of ratio decendi is similarly best explained and modeled in a procedural and dialectical (...) framework. We propose that appeals are best understood as meta-dialogues about the reasoned dialogue occurring in the initial trial. (shrink)

After the seminal work of Kraus, Lehmann and Magidor (formally known as the KLM approach) on conditionals and preferential models, many aspects of defeasibility in more complex formalisms have been studied in recent years. Examples of these aspects are the notion of typicality in description logic and defeasible necessity in modal logic. We discuss a new aspect of defeasibility that can be expressed in the case of temporal logic, which is the normality in an execution. In (...) this contribution, we take Linear Temporal Logic (LTL) as case study for this defeasible aspect. LTL has found extensive applications in Computer Science and Artificial Intelligence, notably as a formal framework for representing and verifying computer systems that vary over time. However, some systems may presents exceptions at some innocuous time points where they can be tolerated, or conversely, exceptions at other crucial time points where they need to be addressed. In order to ensure the reliability of such systems, we study a preferential extension of LTL, called defeasible linear temporal logic (LTL ~ ). In the first part of this paper, we show how semantics of KLM's preferential models can be integrated with LTL. We also discuss the addition of non-monotonic temporal operators as a way to formalise defeasible properties of these systems. The second part of this paper is a study of the satisfiability problem of LTL ~ sentences. Based on Sistla and Clarke's work on the complexity of the classical LTL language, we show the bounded-model property of two fragments of LTL ~ language. Moreover, we provide a procedure to check the satisfiability of sentences in both of these fragments. (shrink)

In the 1980s, Pollock’s work on default reasons started the quest in the AI community for a formal system of defeasible argumentation. The main goal of this paper is to provide a logic of structured defeasible arguments using the language of justification logic. In this logic, we introduce defeasible justification assertions of the type t : F that read as “t is a defeasible reason that justifies F”. Such formulas are then interpreted as (...) arguments and their acceptance semantics is given in analogy to Dung’s abstract argumentation framework semantics. We show that a large subclass of Dung’s frameworks that we call “warranted” frameworks is a special case of our logic in the sense that Dung’s frameworks can be obtained from justification logic-based theories by focusing on a single aspect of attacks among justification logic arguments and Dung’s warranted frameworks always have multiple justification logic instantiations called “realizations”. We first define a new justification logic that relies on operational semantics for default logic. One of the key features that is absent in standard justification logics is the possibility to weigh different epistemic reasons or pieces of evidence that might conflict with one another. To amend this, we develop a semantics for “defeaters”: conflicting reasons forming a basis to doubt the original conclusion or to believe an opposite statement. This enables us to formalize non-monotonic justifications that prompt extension revision already for normal default theories. Then we present our logic as a system for abstract argumentation with structured arguments. The format of conflicting reasons overlaps with the idea of attacks between arguments to the extent that it is possible to define all the standard notions of argumentation framework extensions. Using the definitions of extensions, we establish formal correspondence between Dung’s original argumentation semantics and our operational semantics for default theories. One of the results shows that the notorious attack cycles from abstract argumentation cannot always be realized as justification logic default theories. (shrink)

In this paper we present an embedding of abstract argumentation systems into the framework of Barwise and Seligmans logic of information flow. We show that, taking P.M. Dungs characterization of argument systems, a local logic over states of a deliberation may be constructed. In this structure, the key feature of non-monotonicity of commonsense reasoning obtains as the transition from one local logic to another, due to a change in certain background conditions. Each of Dungs extensions of argument (...) systems leads to a corresponding ordering of background conditions. The relations among extensions becomes a relation among partial orderings of background conditions. This introduces a conceptual innovation in Barwise and Seligmans representation of commonsense reasoning. (shrink)

This book presents adaptive logics as an intuitive and powerful framework for modeling defeasible reasoning. It examines various contexts in which defeasible reasoning is useful and offers a compact introduction into adaptive logics. The author first familiarizes readers with defeasible reasoning, the adaptive logics framework, combinations of adaptive logics, and a range of useful meta-theoretic properties. He then offers a systematic study of adaptive logics based on various applications. The book presents formal models for defeasible reasoning (...) stemming from different contexts, such as default reasoning, argumentation, and normative reasoning. It highlights various meta-theoretic advantages of adaptive logics over other logics or logical frameworks that model defeasible reasoning. In this way the book substantiates the status of adaptive logics as a generic formal framework for defeasible reasoning. (shrink)

Does the law contain implicit exceptions to its own rules? If so, what consequence does that have for understanding the relationship between law and morality? This collection gathers leading legal philosophers to analyse the logical structure of legal norms, advancing the understanding of the general philosophy of law.

The purpose of the paper is to present a logical framework that allow to formalize a kind of prima facie duties, defeasible conditional duties, indefeasible conditional duties and actual (indefeasible) duties, as well as to show their logical interconnections.

This work explores some ways in which logics for defeasible reasoning can be applied to questions in epistemology. It's naturally thought of as developing four applications: The first is concerned with simple epistemic rules, such as "If you perceives that X, then you ought to believe that X" and "If you have outstanding testimony that X, then you ought to believe that X." Anyone who thinks that such rules have a place in our accounts of epistemic normativity must explain (...) what happens in cases where they come into conflict —such as one where you perceive a red object and are told that it is blue. The literature has gone in two directions: The first suggests that rules have built-in unless-clauses specifying the circumstances under which they fail to apply; the second that rules do not specify what attitudes you ought to have, but only what counts in favor or against having those attitudes. I express these two different ideas in a defeasible logic framework and demonstrate that there's a clear sense in which they are equivalent. The second application uses a defeasible logic to solve an important puzzle about epistemic rationality, involving higher-order evidence, or, roughly, evidence about our capacities for evaluating evidence. My solution has some affinities with the so-called conflicting-ideals view. The third application, then, is a characterization of this view in logical terms: I suggest that it should be thought of as an unconventional metaepistemological view, according to which epistemic requirements are not exceptionless, but defeasible and governed by a comparatively weak logic. Finally, the fourth application is in the burgeoning debate about the epistemic significance of disagreement. The intuitive conciliatory views say, roughly, that you ought to become less confident in your take on some question X, if you learn that an epistemic equal disagrees with you about X. I propose to think of conciliationism as a defeasible reasoning policy, develop a mathematically precise model of it, and use it to solve one of the most pressing problems for conciliatory views: Given that there are disagreements about these views themselves, they can self-defeat and issue inconsistent recommendations. (shrink)

ABSTRACT Inspired by legal reasoning, this paper presents a semantics and proof theory of a system for defeasible argumentation. Arguments are expressed in a logic-programming language with both weak and strong negation, conflicts between arguments are decided with the help of priorities on the rules. An important feature of the system is that these priorities are not fixed, but are themselves defeasibly derived as conclusions within the system. Thus debates on the choice between conflicting arguments can also be (...) modelled. The semantics of the system is given with a fixpoint definition, while its proof theory is stated in dialectical style, where a proof takes the form of a dialogue between a proponent and an opponent of an argument: an argument is shown to be justified if the proponent can make the opponent run out of moves in whatever way the opponent attacks. (shrink)

The Logic of Legal Requirements. Essays on Defeasibility, edited by Jordi Ferrer Beltrán and Giovanni Battista Ratti, and published by Oxford University Press in 2012, is a very much welcome contribution to one of the most discussed topics in the contemporary legal theory and philosophy. Defeasibility is connected to many essential issues such as the nature of legal reasoning, the structure of legal norms and legal system, the concept of legal validity, as well as the mechanisms and limits of..

The study of defeasible reasoning unites epistemologists with those working in AI, in part, because both are interested in epistemic rationality. While it is traditionally thought to govern the formation and (with)holding of beliefs, epistemic rationality may also apply to the interrogative attitudes associated with our core epistemic practice of inquiry, such as wondering, investigating, and curiosity. Since generally intelligent systems should be capable of rational inquiry, AI researchers have a natural interest in the norms that govern interrogative attitudes. (...) Following its recent coinage, we use the term ``zetetic'' to refer to the properties and norms associated with the capacity to inquire. In this paper, we argue that zetetic norms can be modeled via defeasible inferences to and from questions---a.k.a erotetic inferences---in a manner similar to the way norms of epistemic rationality are represented by defeasible inference rules. We offer a sequent calculus that accommodates the unique features of ``erotetic defeat" and that exhibits the computational properties needed to inform the design of zetetic agents. The calculus presented here is an improved version of the one presented in Millson (2019), extended to cover a new class of defeasible erotetic inferences. (shrink)

In this article, we present an analysis of defeasible generalizations -- generalizations which are essentially exception-laden, yet genuinely explanatory -- in terms of various notions of privileged conditions. We argue that any plausible epistemology must make essential use of defeasible generalizations so understood. We also consider the epistemic significance of the sort of understanding of context that is required for understanding of explanatory defeasible generalizations on any topic.

Defeasible rules are said to allow for the following two-staged sequence, viz., that p → q and yet p & r → not-q. This is puzzling because in the logic of conditionals the sufficiency of p for q cannot normally be undermined if one adds to the antecedent a further proposition r. Critics argue that the better approach to comprehending defeasibility is explicitly to represent the limiting factor r in a single-stage articulation of the rule, viz., as p (...) & not-r → q. This is a more complete statement of the rule; where the old rule announced, confidently and without qualification, that in circumstances or class of cases p consequence q follows, the new rule admits from the outset that q only follows if we add the qualifier that limits the antecedent circumstances to the smaller class of cases p & not-r. This is not only more complete, the critics argue, it is also a more accurate or truthful statement of the rule. The rule p → q, articulated at the first stage of the defeasible process, is only a pretender encountered along the way to this more complete truth. In this paper I show how, and why, contrary to the critics, the process of private law adjudication supports the multi-staged structure and representation of defeasible legal rules. What matters when one party makes a claim against another party is not so much that the claim is true (or even that it is advanced as a legitimate claim under the rule that is most likely to be true), but rather that the claim is of the sort that the party can justifiably say is true. The latter, at least, is what carries the plaintiff past the initial burden of proof, and what calls for the defendant to reply if the plaintiff is not to carry the day. I illustrate the argument by way of the court’s reluctance in a tort case to entertain a purely statistical basis for a plaintiff’s claim that the defendant has caused her injury. Rather, the court will insist on direct evidence that appears to arise out of the particular circumstances of the case as the plaintiff alleges them to be, and even if, as a purely statistical matter, the latter sort of claim is less likely to be true than the claim grounded in pure statistical likelihood. I relate this argument for defeasible rules (and against rules that are more truthful) to some important arguments offered by the philosopher Stephen Darwall in his recent book The Second Person Viewpoint. Private law’s defeasible rules, I argue, capture the special respect (and interpersonal accountability) that attaches only to rights arising out of “second personal” claiming (and counterclaiming) and which are not realizable merely as a matter of “third personal” (moral) truth. (shrink)

According to informal logic, the possibilities of deductive logic as a tool for analysing and evaluating ordinary arguments are very limited. While I agree with this claim in general, I question it in the case of the argument from cause to effect. In this paper I first show, on the basis of carefully chosen examples, that we usually react differently to falsification of the conclusion of the argument from cause to effect than we do to the falsification of (...) the conclusion of other defeasible arguments. I then identify general conditions and assumptions under which the causal argument from cause to effect can be reconstructed as deductive. Finally, I compare the causal argument with the expert argument, which is a typical example of a defeasible argument in the narrower sense. (shrink)

This paper points out some problems with two recent logical systems – one due to Prakken and Sartor, the other due to Kowalski and Toni – designedfor the representation of defeasible arguments in general, but with a specialemphasis on legal reasoning.

This paper builds on a previous discussion of Stephen Mumford’s rejection of what he takes to be David Best’s argument for a distinction between purposive and aesthetic sports. That discussion concluded that Mumford’s argument misses its target, but closed by introducing a possible alternative argument, not made by Mumford, that might be thought to have the potential to secure Mumford’s conclusion. This paper considers that alternative argument, namely, the thought that the ascription of psychological predicates conceived of in terms of (...) defeasible criteria that constitute logically good evidence could preserve Best’s claim to be making a logical point while allowing a place for intention in relation to aims and purposes in sport. It is argued that the relationship between rules and intention is such that this alternative argument cannot secure Mumford’s conclusion. (shrink)