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)

There is a common understanding among logicians today that nonmonotonic types of reasoning, such as defeasible or presumptive, can clearly warrant a rational acceptance of its conclusion. Recognition of the significance and legitimacy of these forms of arguments, which were considered for long as fallacious, is believed to be very recent and many logicians tended to reject any discussions around it within the tradition of logic after Aristotle. In contrast, Islamic jurisprudence (fiqh), since medieval age, has recognised the (...) validity and importance of non-deductive forms of reasoning, analysed the structures of such arguments and demonstrated how the conventionally understood fallacies are not essentially fallacies. Qiyās – generally represents analogical reasoning – is taken here as a case of defeasible reasoning in Islamic argumentation. This paper will show through works of two emblematic medieval Muslim jurist-logicians, al-Juwainī and al-Ghazzālī, that understanding the legitimacy and the structure of non-deductive forms of arguments is at the core of Islamic legal theories (usūl al-fiqh), and that they recognised its legitimacy and proposed a dialectical method (jadal) of approaching it. Les logiciens comprennent généralement que les types de raisonnement non monotones peuvent justifier l’acceptation rationnelle des conclusions. L’importance et la légitimité de ces formes d’arguments, qui ont longtemps été considérées comme fallacieuses, ont été controversées parmi les logiciens de la tradition logique aristotélicienne. En revanche, la jurisprudence islamique (fiqh) a depuis longtemps reconnu l’importance des formes de raisonnement non déductives et a démontré que les sophismes conventionnellement compris ne sont pas essentiellement des sophismes. Le qiyās – qui représente généralement le raisonnement analogique – est un exemple de raisonnement réfutable dans l’argumentation islamique. Je montre à travers les travaux de deux juristes-logiciens musulmans médiévaux emblématiques, al-Juwainī et al-Ghazzālī, que la compréhension de la légitimité des formes d’arguments non déductives est au cœur des théories juridiques islamiques (usūl al-fiqh), qui ont proposé une méthode d’approche dialectique (jadal). (shrink)

In defeasible reasoning, initially drawn conclusions can be withdrawn in light of new information. In this paper, we examine how the conclusions drawn from conditionals describing positive or negative situations can be defeated by subsequent negative or positive information, respectively. Participants were confronted with conditionals of the form “If [situation], then I am happy/sad” which were either followed by no additional information or by additional information describing situations of the same or the opposite valence. The participant's task was (...) to decide on a question asking for a possible conclusion (“Am I happy?” vs. “Am I sad?”). We found a negativity bias in defeasible reasoning: negative information defeated positively charged conclusions more strongly than positive information defeated negatively charged conclusions. We discuss our results in relation to the new psychology of reasoning. (shrink)

The question addressed in this paper is how the degree of justification of a belief is determined. A conclusion may be supported by several different arguments, the arguments typically being defeasible, and there may also be arguments of varying strengths for defeaters for some of the supporting arguments. What is sought is a way of computing the “on sum” degree of justification of a conclusion in terms of the degrees of justification of all relevant premises and the strengths of (...) all relevant reasons. (shrink)

There was a long tradition in philosophy according to which good reasoning had to be deductively valid. However, that tradition began to be questioned in the 1960’s, and is now thoroughly discredited. What caused its downfall was the recognition that many familiar kinds of reasoning are not deductively valid, but clearly confer justification on their conclusions. Here are some simple examples.

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. (shrink)

We present a mathematical approach to defeasible reasoning based on arguments. This approach integrates the notion of specificity introduced by Poole and the theory of warrant presented by Pollock. The main contribution of this paper is a precise, well-defined system which exhibits correct behavior when applied to the benchmark examples in the literature. It aims for usability rather than novelty. We prove that an order relation can be introduced among equivalence classes of arguments under the equi-specificity relation. We (...) also prove a theorem that ensures the termination of the process of finding the justified facts. Two more lemmas define a reduced search space for checking specificity. In order to implement the theoretical ideas, the language is restricted to Horn clauses for the evidential context. The language used to represent defeasible rules has been restricted in a similar way. The authors intend this work to unify the various existing approaches to argument-based defeasible reasoning. (shrink)

Modeling legal argumentation is one of the most important research in AI and Law, and a lot of models have been proposed. However, most research has not treated value judgement and debate. In this paper, we introduce a legal reasoning model which covers various aspects of legalreasoning such as making argument, selecting argument and debate.Furthermore, we present how criminal law is described and reasoned inthis model.

In this paper we show that any reasoning process in which conclusions can be both fallible and corrigible can be formalized in terms of two approaches: (i) syntactically, with the use of defeasible reasoning, according to which reasoning consists in the construction and assessment of arguments for and against a given claim, and (ii) semantically, with the use of partial structures, which allow for the representation of less than conclusive information. We are particularly interested in the (...) formalization of scientific reasoning, along the lines traced by Lakatos’ methodology of scientific research programs. We show how current debates in cosmology could be put into this framework, shedding light on a very controversial topic. (shrink)

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. (shrink)

According to the Reasoning View, a normative reason to φ is a premise in a pattern of sound reasoning leading to the conclusion to φ. But how should the Reasoning View account for reasons that are outweighed? One very promising proposal is to appeal to defeasible reasoning. On this proposal, when a reason is outweighed, the associated pattern of sound reasoning is defeated. Both Jonathan Way and Sam Asarnow have recently developed this idea in (...) different ways. I argue that this appeal to defeasible reasoning faces a challenge, since reasons can be both outweighed and disabled. Way's view generates good predictions about outweighed reasons, but not about disabled reasons. Asarnow's view generates good predictions about disabled reasons, but not about outweighed reasons. We want a version of the Reasoning View that can generate good predictions about both. I present a version of the Reasoning View that can meet the challenge. (shrink)

One of the most important developments over the last twenty years both in logic and in Artificial Intelligence is the emergence of so-called non-monotonic logics. These logics were initially developed by McCarthy [10], McDermott & Doyle [13], and Reiter [17]. Part of the original motivation was to provide a formal framework within which to model cognitive phenomena such as defeasible inference and defeasible knowledge representation, i.e., to provide a formal account of the fact that reasoners can reach conclusions (...) tentatively, reserving the right to retract them in the light of further information. (shrink)

This paper argues that some traditional fallacies should be considered as reasonable arguments when used as part of a properly conducted dialog. It is shown that argumentation schemes, formal dialog models, and profiles of dialog are useful tools for studying properties of defeasible reasoning and fallacies. It is explained how defeasible reasoning of the most common sort can deteriorate into fallacious argumentation in some instances. Conditions are formulated that can be used as normative tools to judge (...) whether a given defeasible argument is fallacious or not. It is shown that three leading violations of proper dialog standards for defeasible reasoning necessary to see how fallacies work are: (a) improper failure to retract a commitment, (b) failure of openness to defeat, and (c) illicit reversal of burden of proof. (shrink)

This is a reply to a paper by Graham Oppy in the July, 1999 issue of this journal, “Koons’ Cosmological Argument.” Recent work in defeasible or nonmonotonic logic means that the cosmological argument can be cast in such a way that it does not presuppose that every contingent situation, without exception, has a cause. Instead, the burden of proof is shifted to the skeptic, who must produce positive reasons for thinking that the cosmos is an exception to the (...) class='Hi'>defeasible law of causality. I show how Oppy’s critique can be turned into a plausible rebuttal of my argument. However, this rebuttal can be set aside when the original argument is supplemented by a plausible account of the nature of causal priority. Several independent lines of argument in support of this account are outlined. (shrink)

Heuristics can be regarded as justifying the actions and beliefs of problem-solving agents. I use an analysis of heuristics to argue that a symbiotic relationship exists between traditional epistemology and contemporary artificial intelligence. On one hand, the study of models of problem-solving agents usingquantitative heuristics, for example computer programs, can reveal insight into the understanding of human patterns of epistemic justification by evaluating these models'' performance against human problem-solving. On the other hand,qualitative heuristics embody the justifying ability of defeasible (...) rules, the understanding of which is provided by traditional epistemology. (shrink)

One of the most striking characteristics of human beings is their ability to function successfully in complex environments about which they know very little. In light of our pervasive ignorance, we cannot get around in the world just reasoning deductively from our prior beliefs together with new perceptual input. As our conclusions are not guaranteed to be true, we must countenance the possibility that new information will lead us to change our minds, withdrawing previously adopted beliefs. In this sense, (...) our reasoning is “defeasible”. The question arises how defeasible reasoning works, or ought to work. In particular we need rules governing what a cognizer ought to believe given a set of interacting arguments some of which defeat others. That is what is called a “semantics” for defeasible reasoning, and this chapter will propose a new semantics that avoids certain clear counter-examples to all existing semantics. (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)

Non-monotonicity in logic is a symptom that may have many causes. In the formalisation of defeasible reasoning, an epistemic diagnosis has largely prevailed according to which some inferences are non-monotonic because they are provisionally drawn in the absence of relevant or complete information. The Gabbay-Makinson rules for cumulative consequence relations are a paradigmatic example of this epistemic approach. In this paper a different approach to defeasible reasoning is introduced, based on the idea of inferential perspectives. According (...) to this approach, some inferences are non-monotonic because they are drawn as from another reasoner’s perspective. Rules are introduced and discussed for a Perspectival Calculus, which show both similarities and interesting differences with respect to cumulative systems. (shrink)

In this paper I attempt to cast the current program verification debate within a more general perspective on the methodologies and goals of computer science. I show, first, how any method involved in demonstrating the correctness of a physically executing computer program, whether by testing or formal verification, involves reasoning that is defeasible in nature. Then, through a delineation of the senses in which programs can be run as tests, I show that the activities of testing and formal (...) verification do not necessarily share the same goals and thus do not always constitute alternatives. The testing of a program is not always intended to demonstrate a program's correctness. Testing may seek to accept or reject nonprograms including algorithms, specifications, and hypotheses regarding phenomena. The relationship between these kinds of testing and formal verification is couched in a more fundamental relationship between two views of computer science, one properly containing the other. (shrink)

An introduction to the motivations and mechanics of John Pollock's theory of defeasible reasoning, from a lecture at the Northern Institute of Philosophy in 2010.

We present different constructions for nonprioritized belief revision, that is, belief changes in which the input sentences are not always accepted. First, we present the concept of explanation in a deductive way. Second, we define multiple revision operators with respect to sets of sentences (representing explanations), giving representation theorems. Finally, we relate the formulated operators with argumentative systems and default reasoning frameworks.

HANDBOOK OF DEFEASIBLE REASONING AND UNCERTAINTY MANAGEMENT SYSTEMS EDITORS: DOV M. ... and A. Hunter Volume 3: Belief Change Edited by D. Dubois and H. Prade HANDBOOK OF DEFEASIBLE REASONING AND ...

Defeasible reasoning is concerned with the logics of non-deductive argument. As is described in the literature, the study of this type of reasoning is considerably more involved than the study of deductive argument, even so that, in realistic applications, there is often a lack of resources to perform an exhaustive analysis. It follows that, in a theory of defeasible reasoning, the order and direction in which arguments are developed, i.e. theprocedure, is important. The aim of (...) this article is to show that debate is the most efficient procedure to argue in the presence of limited resources. To do so, there is first some general theory on defeasible argumentation, which is followed by an introduction to the problem of dialectical search. The problem of dialectical search is (or at least, should be) the essential issue in every theory on argumentation, and emerges at every occasion that involves adjudication on competing arguments. Starting with an example, it is explained that dialectical search can be best scheduled according to classical debating techniques, that work along well-tried methods. These methods (which include various forms of curtailment, interruption, and interpretation) have proven their value in keeping debating efforts within reasonable bounds. How they apply in a theory of formal argument, will be shown in this article. (shrink)

This volume deals with approaches to handling contradictory information. These include approaches for actual contradiction - both A and not-A can be proven from the information - and approaches for potential contradiction - where the information may contain arguments for A and arguments for not-A, but the system suppresses the contradiction by, for example, preferring some arguments over others. Approaches covered include paraconsistent logics, modal logics, default logics, conditional logics, defeasible logics and paraconsistent semantics for logic programming. The volume (...) is of interest to students, researchers and practitioners in artificial intelligence, software engineering, logic, language and philosophy. This volume is the first handbook to give a comprehensive coverage of handling contradictory information. (shrink)

In this work, we propose a meaningful extension of description logics for non-monotonic reasoning. We introduce \, a logic allowing for the representation of and reasoning about both typical class-membership and typical instances of a relation. We propose a preferential semantics for \ in terms of partially-ordered DL interpretations which intuitively captures the notions of typicality we are interested in. We define a tableau-based algorithm for checking \ knowledge-base consistency that always terminates and we show that it is (...) sound and complete w.r.t. our preferential semantics. The general framework we here propose can serve as the foundation for further exploration of non-monotonic reasoning in description logics and similarly structured logics. (shrink)

In this paper two theories of defeasible reasoning, Pollock's account and my theory of ranking functions, are compared, on a strategic level, since a strictly formal comparison would have been unfeasible. A brief summary of the accounts shows their basic difference: Pollock's is a strictly computational one, whereas ranking functions provide a regulative theory. Consequently, I argue that Pollock's theory is normatively defective, unable to provide a theoretical justification for its basic inference rules and thus an independent notion (...) of admissible rules. Conversely, I explain how quite a number of achievements of Pollock's account can be adequately duplicated within ranking theory. The main purpose of the paper, though, is not to settle a dispute with formal epistemology, but rather to emphasize the importance of formal methods to the whole of epistemology. (shrink)

According to the Reasoning View about normative reasons, facts about normative reasons for action can be understood in terms of facts about the norms of practical reasoning. I argue that this view is subject to an overlooked class of counterexamples, familiar from debates about Subjectivist theories of normative reasons. Strikingly, the standard strategy Subjectivists have used to respond to this problem cannot be adapted to the Reasoning View. I think there is a solution to this problem, however. (...) I argue that the norms of practical reasoning, like the norms of theoretical reasoning, are characteristically defeasible, in a sense I make precise. Recognizing this property of those norms makes space for a solution to the problem. The resulting view is in a way analogous to the familiar defeasibility theory of knowledge, but it avoids a standard objection to that theory. (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.

The paper is motivated by the need of accounting for the practical syllogism as a piece of defeasible reasoning. To meet the need, the paper first refers to ranking theory as an account of defeasible descriptive reasoning. It then argues that two kinds of ought need to be distinguished, purely normative and fact-regarding obligations. It continues arguing that both kinds of ought can be iteratively revised and should hence be represented by ranking functions, too, just as (...) iteratively revisable beliefs. Its central proposal will then be that the fact-regarding normative ranking function must be conceived as the sum of a purely normative ranking function and an epistemic ranking function. The distinctions defends this proposal with a comparative discussion of some critical examples and some other distinctions made in the literature. It gives a more rigorous justification of this proposal. Finally, it starts developing the logic of purely normative and of fact-regarding normative defeasible reasoning, points to the difficulties of completing the logic of the fact-regarding side, but reaches the initial aim of accounting for the defeasible nature of the practical syllogism. (shrink)

The knowledge representation and reasoning of both humans and artificial systems often involves conditionals. A conditional connects a consequence which holds given a precondition. It can be easily recognized in natural languages with certain key words, like “if” in English. A vast amount of literature in both fields, both artificial intelligence and psychology, deals with the questions of how such conditionals can be best represented and how these conditionals can model human reasoning. On the other hand, findings in (...) the psychology of reasoning, such as those in the Suppression Task, have led to a paradigm shift from the monotonicity assumptions in human inferences towards nonmonotonic reasoning. Nonmonotonic reasoning is sensitive for information change, that is, inferences are drawn cautiously such that retraction of previous information is not required with the addition of new information. While many formalisms of nonmonotonic reasoning have been proposed in the field of Artificial Intelligence, their capability to model properties of human reasoning has not yet been extensively investigated. In this paper, we analyzed systematically from both a formal and an empirical perspective the power of formal nonmonotonic systems to model possible explicit defeaters, as in the Suppression Task, and more implicit conditional rules that trigger nonmonotonic reasoning by the keywords in such rules. The results indicated that the classical evaluation for the correctness of inferences has to be extended in the three major aspects regarding the inference system, the knowledge base, and possible assumed exceptions for the rule. (shrink)

Edited by J. Anthony Blair and Ralph H. Johnson King’s College London, UK: College Publications, 2011. Pp. vii, 1-299. Softcover. ISBN: 978-1-84890-030-1. US$ ~20.

This technical report describes the construction of an experimental planner that finds plans by reasoning about them defeasibly rather than by running a search algorithm. The need for such a planner is defended in the paper “The Logical Foundations of Goal-Regression Planning”.