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.

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)

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)

Defeasibility, most generally speaking, means that given some set of conditions A, something else B will hold, unless or until defeating conditions C apply. While the term was introduced into philosophy by legal philosopher H.L.A. Hart in 1949, today, the concept of defeasibility is employed in many different areas of philosophy. This volume for the first time brings together contributions on defeasibility from epistemology , legal philosophy and ethics and the philosophy of action . The volume ends with an extensive (...) bibliography. (shrink)

This paper introduces a generalization of Reiter’s notion of “extension” for default logic. The main difference from the original version mainly lies in the way conflicts among defaults are handled: in particular, this notion of “general extension” allows defaults not explicitly triggered to pre-empt other defaults. A consequence of the adoption of such a notion of extension is that the collection of all the general extensions of a default theory turns out to have a nontrivial algebraic structure. This fact has (...) two major technical fall-outs: first, it turns out that every default theory has a general extension; second, general extensions allow one to define a well-behaved, skeptical relation of defeasible consequence for default theories, satisfying the principles of Reflexivity, Cut, and Cautious Monotonicity formulated by D. Gabbay. (shrink)

We contend that it is possible to argue reasonably for and against arguments from classifications and definitions, provided they are seen as defeasible (subject to exceptions and critical questioning). Arguments from classification of the most common sorts are shown to be based on defeasible reasoning of various kinds represented by patterns of logical reasoning called defeasible argumentation schemes. We show how such schemes can be identified with heuristics, or short-cut solutions to a problem. We examine a variety (...) of arguments of this sort, including argument from abductive classification, argument from causal classification, argument from analogy-based classification and arguments from classification based on generalizations. (shrink)

In concrete applications of probability, statistical investigation gives us knowledge of some probabilities, but we generally want to know many others that are not directly revealed by our data. For instance, we may know prob(P/Q) (the probability of P given Q) and prob(P/R), but what we really want is prob(P/Q& R), and we may not have the data required to assess that directly. The probability calculus is of no help here. Given prob(P/Q) and prob(P/R), it is consistent with the probability (...) calculus for prob(P/Q& R) to have any value between 0 and 1. Is there any way to make a reasonable estimate of the value of prob(P/Q& R) 1 A related problem occurs when probability practitioners adopt undefended assumptions of statistical independence simply on the basis of not seeing any connection between two propositions. This is common practice, but its justification has eluded probability theorists, and researchers are typically apologetic about making such assumptions. Is there any way to defend the practice? This paper shows that on a certain conception of probability—nomic probability—there are principles of "probable probabilities" that license inferences of the above sort. These are principles telling us that although certain inferences from probabilities to probabilities are not deductively valid, nevertheless the second-order probability of their yielding correct results is 1. This makes it defeasibly reasonable to make the inferences. Thus I argue that it is defeasibly reasonable to assume statistical independence when we have no information to the contrary. And I show that there is a function Y(r, s, a) such that if prob(P/Q) = r, prob(P/R) = s, andprob(P/U) = a (where U is our background knowledge) then it is defeasibly reasonable to expect that prob(P/Q&R) = Y(r, s, a). Numerous other defeasible inferences are licensed by similar principles of probable probabilities. This has the potential to greatly enhance the usefulness of probabilities in practical application. (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)

The impossibility results of Bovens and Hartmann (2003, Bayesian epistemology. Oxford: Clarendon Press) and Olsson (2005, Against coherence: Truth, probability and justification. Oxford: Oxford University Press.) show that the link between coherence and probability is not as strong as some have supposed. This paper is an attempt to bring out a way in which coherence reasoning nevertheless can be justified, based on the idea that, even if it does not provide an infallible guide to probability, it can give us an (...) indication thereof. It is further shown that this actually is the case, for several of the coherence measures discussed in the literature so far. We also discuss how this affects the possibility to use coherence as a means of epistemic justification. (shrink)

The paper discusses the notion of defeasibility and focuses specifically on defeasible norms. First, it delineates a robust notion of the phenomenon of defeasibility, which poses a serious problem for both moral and legal theory. It does this by laying out the conditions and desiderata that a model of defeasibility should be able to meet. It further focuses on a specific model of defeasibility that utilises the notion of normal conditions to expound the robust notion of defeasibility. It argues (...) that this model fails in its attempt to do this, particularly since it presupposes further pertinent norms and we have reasons to doubt if these are defeasible. It thus does not allow defeasibility to go “all the way down” in the normative domain and limits it merely to a feature of some sort of mid-level norm. In conclusion, it draws lessons from this and positions defeasibility models within a more general pluralistic approach to norms. (shrink)

The problem of induction and the problem of Cartesian/brain-in-the-vat skepticism have much in common. Both are instances of a general problem of defeasible justification . I use the term "defeasible justification" to refer to a relation between a piece of evidence.

Inheritance diagrams are directed acyclic graphs with two types of connections between nodes: x → y and x ↛ y . Given a diagram D, one can ask the formal question of “is there a valid path between node x and node y?” Depending on the existence of a valid path we can answer the question “x is a y” or “x is not a y”. The answer to the above question is determined through a complex inductive algorithm on paths (...) between arbitrary pairs of points in the graph. This paper aims to simplify and interpret such diagrams and their algorithms. We approach the area on two fronts. Suggest reactive arrows to simplify the algorithms for the winning paths. We give a conceptual analysis of inheritance diagrams, and compare our analysis to the “small” and “big sets” of preferential and related reasoning. In our analysis, we consider nodes as information sources and truth values, direct links as information, and valid paths as information channels and comparisons of truth values. This results in an upward chaining, split validity, off-path preclusion inheritance formalism of a particularly simple type. We show that the small and big sets of preferential reasoning have to be relativized if we want them to conform to inheritance theory, resulting in a more cautious approach, perhaps closer to actual human reasoning. We will also interpret inheritance diagrams as theories of prototypical reasoning, based on two distances: set difference, and information difference. We will see that some of the major distinctions between inheritance formalisms are consequences of deeper and more general problems of treating conflicting information. It is easily seen that inheritance diagrams can also be analysed in terms of reactive diagrams - as can all argumentation systems. AMS Classification: 68T27, 68T30. (shrink)

My aim is to show that supervenience claims follow from instances of a principle I call the principle of defeasibly sufficient reason. This principle construes the completeness of physics quite differently from strong or reductive physicalism and encodes both scientific and common sense patterns of explanation and justification. Rather than thoroughly defending the principle in the short space of this paper, I will sketch how one might defend it and a resulting fainthearted physicalism.

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)

In a recent and interesting paper “Experientially Defeasible A Priori Justification,” Joshua Thurow argues that many a priori justified beliefs are defeasible by experience. The argument takes the form of an objection against Albert Casullo’s recent book, A Priori Justification, where Casullo, according to Thurow, denies that if a justified belief is non-experientially defeasible, then that belief is also experientially defeasible. This paper critically examines Thurow’s two arguments in the first two sections I–II. In the last (...) section, III, an alternative line of argument for Thurow’s thesis is suggested that employs other parts of the framework that Casullo provides—especially the thesis of overdetermination of justification. It will be argued that the prospects for this suggestion are brighter than for bothof Thurow’s arguments. (shrink)

In jurisprudential literature, the adjective 'defeasible' appears as a predicate of many terms: concepts, laws, rules, reasoning, justification, proof, and so on. In this paper, we analyze the effects of some versions of the thesis of the defeasibility of legal norms on the reconstruction of the notion of legal validity. We analyze some possible justifications of this thesis considered as a claim concerning validity, and enquire into two possible sets of problems related to the defeasibility of the criteria of (...) identification of a legal system. We also provide a formalization of some options regarding defeasible criteria of identification, which can be used as a tool for meta-jurisprudential analysis. Finally, the thesis according to which defeasibility is better conceived of as a feature of legal application is examined and questioned. (shrink)

For many women experiencing motherhood for the first time, the message they receive is clear: mothers who do not breastfeed ought to have good reasons not to; bottle feeding by choice is a failure of maternal duty. We argue that this pressure to breastfeed arises in part from two misconceptions about maternal duty: confusion about the scope of the duty to benefit and conflation between moral reasons and duties. While mothers have a general duty to benefit, we argue that this (...) does not imply a duty to carry out any particular beneficent act. Therefore, the expectation that mothers should breastfeed unless they have sufficient countervailing reasons not to is morally unwarranted. Recognising the difference between reasons and duties can allow us to discuss the benefits of breastfeeding and the importance of supporting mothers who wish to breastfeed without subjecting mothers who bottle feed to guilt, blame and failure. (shrink)

In this paper we will analyse the issue of defeasibility in the law, taking into account research carried out in philosophy, artificial intelligence and legal theory. We will adopt a very general idea of legal defeasibility, in which we will include all different ways in which certain legal conclusions may need to be abandoned, though no mistake was made in deriving them. We will argue that defeasibility in the law involves three different aspects, which we will call inference‐based defeasibility, process‐based (...) defeasibility, and theory‐based defeasibility. Only the integration of these three perspectives allows us to provide a satisfactory account of the role of defeasibility in legal reasoning. (shrink)

In jurisprudential literature, the adjective ‘defeasible’ appears as a predicate of many terms: concepts, laws, rules, reasoning, justification, proof, and so on. In this paper, we analyze the effects of some versions of the thesis of the defeasibility of legal norms on the reconstruction of the notion of legal validity. We analyze some possible justifications of this thesis considered as a claim concerning validity, and enquire into two possible sets of problems related to the defeasibility of the criteria of (...) identification of a legal system. We also provide a formalization of some options regarding defeasible criteria of identification, which can be used as a tool for meta-jurisprudential analysis. Finally, the thesis according to which defeasibility is better conceived of as a feature of legal application is examined and questioned. (shrink)

Naturalism rejects a sui generis and fundamental realm of the evaluative or normative. Thought and talk about the good and the right must hence be understood without appeal to any such evaluative or normative concepts or properties. In Sections I and II, we see noncognitivism step forward with its account of evaluative and normative language as fundamentally optative or prescriptive. Prescriptivism falls afoul of several problems. Prominent among them below is the “problem of prima facie reasons”: the problem, namely that (...) prescriptions do not properly capture the character of defeasibility of the prima facie, featured by nearly all our moral convictions. We find in Section II that, ironically, emotivism, with its emphasis on optative rather than prescriptive language, though historically more primitive, is yet better attuned to that crucial prima facie aspect of the normative and the evaluative. But even emotivism still faces serious difficulties that beset noncognitivism generally, such as the problem of embedding in subordinate clauses, and the problem of normative fallibility. That takes us up to Section III. (shrink)

The purpose of this paper is to analyze the structure and the defeasibility conditions of argument from analogy, addressing the issues of determining the nature of the comparison underlying the analogy and the types of inferences justifying the conclusion. In the dialectical tradition, different forms of similarity were distinguished and related to the possible inferences that can be drawn from them. The kinds of similarity can be divided into four categories, depending on whether they represent fundamental semantic features of the (...) terms of the comparison or non-semantic ones, indicating possible characteristics of the referents. Such distinct types of similarity characterize different kinds of analogical arguments, all based on a similar general structure, in which a common genus is abstracted. Depending on the nature of the abstracted common feature, different rules of inference will apply, guaranteeing the attribution of the analogical predicate to the genus and to the primary subject. This analysis of similarity and the relationship thereof with the rules of inference allows a deeper investigation of the defeasibility conditions. (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.

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 article investigates to what extent protocols for dynamicdisputes, i.e., disputes in which the information base can vary at differentstages, can be justified in terms of logics for defeasible argumentation. Firsta general framework is formulated for dialectical proof theories for suchlogics. Then this framework is adapted to serve as a framework for protocols fordynamic disputes, after which soundness and fairness properties are formulated for such protocols relative to dialectical proof theories. It then turns out that certaintypes of protocols that (...) are perfectly fine with a static information base, arenot sound or fair in a dynamic setting. Finally, a natural dynamic protocolis defined for which soundness and fairness can be established. (shrink)

This article investigates to what extent protocols for dynamicdisputes, i.e., disputes in which the information base can vary at differentstages, can be justified in terms of logics for defeasible argumentation. Firsta general framework is formulated for dialectical proof theories for suchlogics. Then this framework is adapted to serve as a framework for protocols fordynamic disputes, after which soundness and fairness properties are formulated for such protocols relative to dialectical proof theories. It then turns out that certaintypes of protocols that (...) are perfectly fine with a static information base, arenot sound or fair in a dynamic setting. Finally, a natural dynamic protocolis defined for which soundness and fairness can be established. (shrink)

This paper is concerned with formal solutions to the lottery paradox on which high probability defeasibly warrants acceptance. It considers some recently proposed solutions of this type and presents an argument showing that these solutions are trivial in that they boil down to the claim that perfect probability is sufficient for rational acceptability. The argument is then generalized, showing that a broad class of similar solutions faces the same problem. An argument against some formal solutions to the lottery paradox The (...) argument generalized Some variations Adding modalities Anticipated objections. (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)

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. (shrink)

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. (shrink)

Proceedings of the 2008 AAAI Spring Symposium on Architectures for Intelligent Theory-Based Agents. “OSCAR is a fully implemented architecture for a cognitive agent, based largely on the author’s work in philosophy concerning epistemology and practical cognition. The seminal idea is that a generally intelligent agent must be able to function in an environment in which it is ignorant of most matters of fact. The architecture incorporates a general-purpose defeasible reasoner, built on top of an efficient natural deduction reasoner for (...) first-order logic. It is based upon a detailed theory about how the various aspects of epistemic and practical cognition should interact, and many of the details are driven by theoretical results concerning 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.

This paper reports on an approach to model generalized implicatures using nonmonotonic logics. The approach, called compositional, is based on the idea of compositional semantics, where the implicatures carried by a sentence are constructed from the implicatures carried by its constituents, but it also includes some aspects nonmonotonic logics in order to model the defeasibility of generalized implicatures.

Here’s a false generalization with manifestly false consequences: all people who differ by one millimeter in height from a short person are themselves short. Why are we inclined to believe it? Boundary-shifters, usually lumped together under the heading “contextualists”, say that we believe the false generalization because when we consider any instance, that instance is true at the time of our consideration. Critics complain that the explanation is no good, for (i) if it were, then fallacious inferences would be rampant; (...) (ii) if it were, then we would always generalize from instances that we knew to be true at the time we considered them. But, they say, fallacious inferences are not rampant and we do not always generalize from the instances. Responses: (i) boundary-shifters require only that weakly fallacious inferences are rampant, and indeed they are; (ii) generalizing from the instances is both natural and explanatory, albeit defeasible. (shrink)

In this paper we introduce hypersequent-based frameworks for the modelling of defeasible reasoning by means of logic-based argumentation and the induced entailment relations. These structures are an extension of sequent-based argumentation frameworks, in which arguments and the attack relations among them are expressed not only by Gentzen-style sequents, but by more general expressions, called hypersequents. This generalization allows us to overcome some of the known weaknesses of logical argumentation frameworks and to prove several desirable properties of the entailments that (...) are induced by the extended frameworks. It also allows us to incorporate as the deductive base of our formalism some well-known logics, which lack cut-free sequent calculi, and so are not adequate for standard sequent-based argumentation. We show that hypersequent-based argumentation yields robust defeasible variants of these logics, with many desirable properties. (shrink)

ABSTRACT: If an event of one kind does not always lead to an event of a second given kind, it does not follow (of course) that the occurrence of an event of the first kind can never explain the occurrence of an event of the second kind. I’m concerned here with cases of belief. In the service of defending a plausible “boundary-shifting” solution to the sorites paradox, I argue that a certain paradoxical belief(in the universally-generalized premise of the sorites paradox) (...) can be explained by our having reasonable beliefs that entail it (beliefs in the instances of that generalization). Some have argued against boundary-shifting solutions on the grounds that beliefs in instances do not always lead to beliefs in generalizations over those instances. I argue that the objection flounders. An event of one kind can explain an event of another kind even if events of the first kind do not always lead to events of the second kind. One does not impugn an explanation merely by pointing to its defeasibility. (shrink)

The paper contains a survey of (mainly unpublished) adaptive logics of inductive generalization. These defeasible logics are precise formulations of certain methods. Some attention is also paid to ways of handling background knowledge, introducing mere conjectures, and the research guiding capabilities of the logics.

There are several areas in logic where the monotonicity of the consequence relation fails to hold. Roughly these are the traditional non-monotonic systems arising in Artificial Intelligence (such as defeasible logics, circumscription, defaults, ete), numerical non-monotonic systems (probabilistic systems, fuzzy logics, belief functions), resource logics (also called substructural logics such as relevance logic, linear logic, Lambek calculus), and the logic of theory change (also called belief revision, see Alchourron, Gärdenfors, Makinson [2224]). We are seeking a common axiomatic and semantical (...) approach to the notion of consequence whieh can be specialised to any of the above areas. This paper introduces the notions of structured consequence relation, shift operators and structural connectives, and shows an intrinsic connection between the above areas. (shrink)

In a priori analogies, the analogue is constructed in imagination, sharing certain properties with the primary subject. The analogue has some further property clearly consequent on those shared properties. Ceteris paribus the primary subject has that property also. The warrant involves non-empirical, e.g., moral intuition but is also defeasible. The argument is thus neither deductive nor inductive, but an additional type. In an inductive analogy, the analogues back the warrant from below. Distinguishing these two types of arguments by analogy (...) gives epistemic evaluative factors primacy over resemblance factors in classifying arguments—a prescient insight on Govier’s part. (shrink)

The problems that arise from the presence of self-attacking ar- guments and odd-length cycles of attack within argumentation frameworks are widely recognized in the literature on defeasible argumentation. This paper introduces two simple semantics to capture different intuitions about what kinds of arguments should become justified in such scenarios. These semantics are modeled upon two extensions of argumentation frameworks, which we call sustainable and tolerant. Each one is constructed on the common ground of the powerful concept of admissibility introduced (...) by Dung in [10]. The novelty of this approach consists in viewing the admissibility of a subset of arguments as relative to potentially challenging subsets of arguments. Both sustainable and tolerant semantics are more credulous than preferred semantics (i.e. they justify at least the same arguments, and possibly more). Given certain sufficient conditions they coincide among them as well as with other semantics introduced by Dung. (shrink)