We propose a combination of probabilistic reasoning from conditional constraints with approaches to default reasoning from conditional knowledge bases. In detail, we generalize the notions of Pearl's entailment in system Z, Lehmann's lexicographic entailment, and Geffner's conditional entailment to conditional constraints. We give some examples that show that the new notions of z-, lexicographic, and conditional entailment have similar properties like their classical counterparts. Moreover, we show that the new notions of z-, lexicographic, and conditional entailment are proper generalizations (...) of both their classical counterparts and the classical notion of logical entailment for conditional constraints. (shrink)

Based on a close study of benchmark examples in default reasoning, such as Nixon Diamond, Penguin Principle, etc., this paper provides an in depth analysis of the basic features of default reasoning. We formalize default inferences based on Modus Ponens for Default Implication, and mark the distinction between "local inferences"(to infer a conclusion from a subset of given premises) and "global inferences"(to infer a conclusion from the entire set of given premises). These conceptual analyses are captured (...) by a formal semantics that is built upon the set-selection function technique. A minimal logic system M of default reasoning that accommodates Modus Ponens for Default Implication and suitable for local inferences is proposed, and its soundness is proved. (shrink)

Look before you leap. - Proverb. He who hesitates is lost. - Another proverb.

Particularism takes an extremely ecumenical view of what considerations might count as reasons and thereby threatens to ‘flatten the moral landscape’ by making it seem that there is no deep difference between, for example, pain, and shoelace color. After all, particularists have claimed, either could provide a reason provided a suitable moral context. To avoid this result, some particularists draw a distinction between default and non-default reasons. The present paper argues that all but the most deflationary (...) ways of drawing this distinction are either implausible or else insufficient to help the particularist avoid flattening the moral landscape. The difficulty can be avoided, however, if we reject particularism's extremely ecumenical view of reasons. (shrink)

In this paper I will argue that (principled) attempts to ground a priori knowledge in default reasonable beliefs cannot capture certain common intuitions about what is required for a priori knowledge. I will describe hypothetical creatures who derive complex mathematical truths like Fermat’s last theorem via short and intuitively unconvincing arguments. Many philosophers with foundationalist inclinations will feel that these creatures must lack knowledge because they are unable to justify their mathematical assumptions in terms of the kind of basic (...) facts which can be known without further argument. Yet, I will argue that nothing in the current literature lets us draw a principled distinction between what these creatures are doing and paradigmatic cases of good a priori reasoning (assuming that the latter are to be grounded in default reasonable beliefs). I will consider, in turn, appeals to reliability, coherence, conceptual truth and indispensability and argue that none of these can do the job. (shrink)

Since its inception, situation theory has been concerned with the situated nature of meaning and cognition, a theme which has also recently gained some prominence in Artificial Intelligence. Channel theory is a recently developed framework which builds on concepts introduced in situation theory, in an attempt to provide a general theory of information flow. In particular, the channel theoretic framework offers an account of fallible regularities, regularities which provide enough structure to an agent's environment to support efficient cognitive processing but (...) which are limited in their reliability to specific circumstances. This paper describes how this framework can lead to a different perspective on defeasible reasoning: rather than being seen as reasoning with incomplete information, an agent makes use of a situated regularity, choosing to use the regularity that seems best suited (trading off reliability and simplicity) to the circumstances it happens to find itself in. We present a formal model for this task, based on the channel theoretic framework, and sketch how the model may be used as the basis for a methodology of defeasible situated reasoning, whereby agents reason with simple monotonic regularities but may revise their choice of regularity on learning more about their circumstances. (shrink)

Reasoning by default is a relevant aspect of everyday life that has traditionally attracted the attention of many fields of research, from psychology to the philosophy of logic, from economics to artificial intelligence. Also in the field of law, default reasoning is widely used by lawyers, judges and other legal decision-makers. In this paper, a philosopher of language (Carlo Penco) and a philosopher of law (Damiano Canale) attempt to explore some uses of default reasoning that are scarcely (...) considered by legal theory. In particular, the dialogue dwells on the notion of literal meaning, witness testimony, and the problem of disagreement among experts in legal proceedings. The paper is intended as a sort of brain storming useful to identify new lines of research straddling philosophy of law, cognitive psychology and philosophy of language. (shrink)

We present two approaches to investigate the validity of connexive principles and related formulas and properties within coherence-based probability logic. Connexive logic emerged from the intuition that conditionals of the formif not-A,thenA, should not hold, since the conditional’s antecedentnot-Acontradicts its consequentA. Our approaches cover this intuition by observing that the only coherent probability assessment on the conditional event$${A| \overline{A}}$$A|A¯is$${p(A| \overline{A})=0}$$p(A|A¯)=0. In the first approach we investigate connexive principles within coherence-based probabilistic default reasoning, by interpreting defaults and negated defaults in (...) terms of suitable probabilistic constraints on conditional events. In the second approach we study connexivity within the coherence framework of compound conditionals, by interpreting connexive principles in terms of suitable conditional random quantities. After developing notions of validity in each approach, we analyze the following connexive principles:Aristotle’s theses,Aristotle’s Second Thesis,Abelard’s First Principle, andBoethius’ theses. We also deepen and generalize some principles and investigate further properties related to connexive logic (likenon-symmetry). Both approaches satisfyminimalrequirements for a connexive logic. Finally, we compare both approaches conceptually. (shrink)

This paper addresses a recent suggestion that moral particularists can extend their view to countenance default reasons (at a first stab, reasons that are pro tanto unless undermined) by relying on certain background expectations of normality. I first argue that normality must be understood non-extensionally. Thus if default reasons rest on normality claims, those claims won't bestow upon default reasons any definite degree of extensional generality. Their generality depends rather on the contingent distributional (...) aspects of the world, which no theory of reasons should purport to settle. Appeals to default reasons cannot therefore uniquely support particularism. But this argument also implies that if moral generalism entailed that moral reasons by necessity have invariant valence (in the natural extensional sense), it would be a non-starter. Since generalism is not a non-starter, my argument forces us to rethink the parameters of the generalism-particularism debate. Here I propose to clarify the debate by focusing on its modal rather than extensional aspects. In closing, I outline the sort of generalism that I think is motivated by my discussion, and then articulate some worries this view raises about the theoretical usefulness of the label ‘default reason’. -/- [Note: The outline of moral generalism provided in this paper is superseded by those in "Moral Generalism: Enjoy in Moderation" and "A Theory of Hedged Moral Principles".]. (shrink)

This is a position paper concerning the role of empirical studies of human default reasoning in the formalization of AI theories of default reasoning. We note that AI motivates its theoretical enterprise by reference to human skill at default reasoning, but that the actual research does not make any use of this sort of information and instead relies on intuitions of individual investigators. We discuss two reasons theorists might not consider human performance relevant to formalizing (...) class='Hi'>default reasoning: (a) that intuitions are sufficient to describe a model, and (b) that human performance in this arena is irrelevant to a competence model of the phenomenon. We provide arguments against both these reasons. We then bring forward three further considerations against the use of intuitions in this arena: (a) it leads to an unawareness of predicate ambiguity, (b) it presumes an understanding of ordinary language statements of typicality, and (c) it is similar to discredited views in other fields. We advocate empirical investigation of the range of human phenomena that intuitively embody default reasoning. Gathering such information would provide data with which to generate formal default theories and against which to test the claims of proposed theories. Our position is that such data are the very phenomena that default theories are supposed to explain. (shrink)

. This paper first provides a brief survey of a possibilistic handling of default rules. A set of default rules of the form, “generally, from α deduce β”, is viewed as the family of possibility distributions satisfying constraints expressing that the situation where α and β is true has a greater plausibility than the one where a and - β is true. When considering only the subset of linear possibility distributions, the well-known System P of postulates proposed by (...) Kraus, Lehmann and Magidor, has been obtained. We also present two rational extensions: one based on the minimum specificity principle and the other is based on the lexicographic ordering. The second part of the paper presents an empirical study of three desirable properties for a consequence relation that capture default reasoning: Rationality, Property Inheritance and Ambiguity Preservation. An experiment is conducted to investigate 13 patterns of inference for the test of these properties. Our experimental apparatus confirms previous results on the relevance of System P, and enforces the psychological relevance of the studied properties. (shrink)

There has long been a history of studies investigating how people (“ordinary people”) perform on tasks that involve deductive reasoning. The upshot of these studies is that people characteristically perform some deductive tasks well but others badly. For instance, studies show that people will typically perform MP (“modus ponens”: from ‘If A then B’ and ‘A’, infer ‘B’) and bi-conditional MP (from: ‘A if and only if B’ and ‘A’, infer ‘B’) correctly when invited to make the inference and additionally (...) can discover of their own accord when such inferences are appropriate. On the other hand, the same studies show that people typically perform MT (“modus tollens”: from ‘If A then B’ and ‘not-B’, infer ‘not-A’) and biconditional MT badly. They not only do not recognize when it is appropriate to draw such inferences, but also they will balk at doing them even when they are told that they can make it. Related to these shortcomings seems to be the inability of people to understand that contrapositives are equivalent (that ‘If A then B’ is equivalent to ‘If not-B then not-A’). [Studies of people’s deductive inference-drawing abilities have a long history, involving many studies in the early 20th century concerning Aristotelian syllogisms. But the current spate of studies draws much of its impetus from Wason (Wason, 1968; see also Wason & Johnson-Laird, 1972). ] The general conclusion seems to be that there are specific areas where “ordinary people” do not perform very logically. This conclusion will not come as a surprise to teachers of elementary logic, who have long thought that the majority of “ordinary people” are inherently illogical and need deep and forceful schooling in order to overcome this flaw. (shrink)

This paper presents a formalism that combines useful properties of both logic and probabilities. Like logic, the formalism admits qualitative sentences and provides symbolic machinery for deriving deductively closed beliefs and, like probability, it permits us to express if-then rules with different levels of firmness and to retract beliefs in response to changing observations. Rules are interpreted as order-of-magnitude approximations of conditional probabilities which impose constraints over the rankings of worlds. Inferences are supported by a unique priority ordering on rules (...) which is syntactically derived from the knowledge base. This ordering accounts for rule interactions, respects specificity considerations and facilitates the construction of coherent states of beliefs. Practical algorithms are developed and analyzed for testing consistency, computing rule ordering, and answering queries. Imprecise observations are incorporated using qualitative versions of Jeffrey's rule and Bayesian updating, with the result that coherent belief revision is embodied naturally and tractably. Finally, causal rules are interpreted as imposing Markovian conditions that further constrain world rankings to reflect the modularity of causal organizations. These constraints are shown to facilitate reasoning about causal projections, explanations, actions and change. (shrink)

In their unifying theory to model uncertainty, Friedman and Halpern (1995–2003) applied plausibility measures to default reasoning satisfying certain sets of axioms. They proposed a distinctive condition for plausibility measures that characterizes “qualitative” reasoning (as contrasted with probabilistic reasoning). A similar and similarly fundamental, but more general and thus stronger condition was independently suggested in the context of “basic” entrenchment-based belief revision by Rott (1996–2003). The present paper analyzes the relation between the two approaches to formalizing basic notions of (...) plausibility as used in qualitative default reasoning. While neither approach is a special case of the other, translations can be found that elucidate their relationship. I argue that Rott’s notion of plausibility allows for a more modular set-up and has a better philosophical motivation than that of Friedman and Halpern. (shrink)

We study probabilistic logic under the viewpoint of the coherence principle of de Finetti. In detail, we explore how probabilistic reasoning under coherence is related to model- theoretic probabilistic reasoning and to default reasoning in System . In particular, we show that the notions of g-coherence and of g-coherent entailment can be expressed by combining notions in model-theoretic probabilistic logic with concepts from default reasoning. Moreover, we show that probabilistic reasoning under coherence is a generalization of default (...) reasoning in System . That is, we provide a new probabilistic semantics for System , which neither uses infinitesimal probabilities nor atomic bound (or big-stepped) probabilities. These results also provide new algorithms for probabilistic reasoning under coherence and for default reasoning in System , and they give new insight into default reasoning with conditional objects. (shrink)

This paper argues for the reasonableness of an inclusive conception of default reasoning. The inclusive conception allows untriggered default rules to influence beliefs: Since a default “from φ, infer ψ” is a defeasible inference rule, it by default warrants a belief in the material implication φ → ψ, even if φ is not believed. Such inferences are not allowed in standard default logic of the Reiter tradition, but are reasonable by analogy to the Deduction Theorem (...) for classical logic. Our main contribution is a formal framework for inclusive default reasoning. The framework has a solid philosophical foundation, it draws conclusions non-trivially different from non-inclusive frameworks, and it exhibits a host of benchmark properties deemed desirable in the literature—e.g., that extensions always exist and are consistent. (shrink)

Particularism is widely conceived to endorse the view that moral reason is context-dependent. This being so, it is often accused of flattening the moral landscape—treating the feature of promise-keeping as constituting no more of a (moral) reason for action than the feature of wearing a yellow shoelace in advance of the considerations of the contexts. In reply, Dancy maintains that his particularism allows some features such as promise-keeping to have a reason status by default, ontologically speaking; it is just (...) that their default reason status might get ‘switched off’ in some contexts. In this paper, I will argue that Dancy's ontological understanding of default reason wouldn't help the particularists address the flattening objection, due to a violation of what Tsu calls ‘the embedded thesis’, which is a general constraint on how moral reason behaves. However, once the nature of default reason is correctly understood as psychological, particularism will be enabled to deflate the flattening objection, or so I will argue. (shrink)

This paper first provides a brief survey of a possibilistic handling of default rules. A set of default rules of the form, "generally, from α deduce β", is viewed as the family of possibility distributions satisfying constraints expressing that the situation where α and β is true has a greater plausibility than the one where α and ⇁β is true. When considering only the subset of linear possibility distributions, the well-known System P of postulates proposed by Kraus, Lehmann (...) and Magidor, has been obtained. We also present two rational extensions: one based on the minimum specificity principle and the other is based on the lexicographic ordering. The second part of the paper presents an empirical study of three desirable properties for a consequence relation that capture default reasoning: Rationality, Property Inheritance and Ambiguity Preservation. An experiment is conducted to investigate 13 patterns of inference for the test of these properties. Our experimental apparatus confirms previous results on the relevance of System P, and enforces the psychological relevance of the studied properties. (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)

We study a probabilistic logic based on the coherence principle of de Finetti and a related notion of generalized coherence (g-coherence). We examine probabilistic conditional knowledge bases associated with imprecise probability assessments defined on arbitrary families of conditional events. We introduce a notion of conditional interpretation defined directly in terms of precise probability assessments. We also examine a property of strong satisfiability which is related to the notion of toleration well known in default reasoning. In our framework we give (...) more general definitions of the notions of probabilistic consistency and probabilistic entailment of Adams. We also recall a notion of strict p-consistency and some related results. Moreover, we give new proofs of some results obtained in probabilistic default reasoning. Finally, we examine the relationships between conditional probability rankings and the notions of g-coherence and g-coherent entailment. (shrink)

The goal of this paper is to frame a theory of reasons--what they are, how they support actions or conclusions--using the tools of default logic. After sketching the basic account of reasons as provided by defaults, I show how it can be elaborated to deal with two more complicated issues: first, situations in which the priority relation among defaults, and so reasons as well, is itself established through default reasoning; second, the treatment of undercutting defeat (...) and exclusionary reasons. Finally, and by way of application, I show how the resulting account can shed some light on Jonathan Dancy's argument from reason holism to a form of extreme particularism in moral theory. (shrink)

Language employs various coordinators to connect propositions, a subset of which are “logical” in nature and thus analogous to the truth operators of formal logic. We here focus on two linguistic connectives and their negations: conjunction _and_ and (inclusive) disjunction _or_. Linguistic connectives exhibit a truth-conditional component as part of their meaning (their semantics), but their use in context can give rise to various implicatures and presuppositions (the domain of pragmatics) as well as to inferences that go beyond semantic/pragmatic properties (...) (the result of reasoning processes). We provide a comprehensive review of the role of the logical connectives in language and argue that three sets of factors—semantic, pragmatic, and those related to reasoning—are separate and separable, though some details may differ cross-linguistically. As a way to showcase the argument, we present two experiments in language comprehension in Spanish wherein pragmatic content was minimised and reasoning processes neutered, thus potentially highlighting what might be the default meanings of the connectives under study. In Experiment 1 we show that the conjunctive reading of inclusive disjunction is available in positive contexts other than in syntactically intricate cases such as downward entailing and free choice contexts, contrary to what has been claimed in the literature. In Experiment 2 we show that negated conjunctions and disjunctions in Spanish can easily receive the same interpretation when contrasted against the same context and, moreover, that these interpretations match those available in English, despite claims from the literature that linguistic connectives and local negation interact differently in English and Romance languages. (shrink)

Epistemology of testimony’s map has been charted by identifying the basic controversy between reductionism and non-reductions. John McDowell’s article “Knowledge by Hearsay” (1993/1998) has been taken as a clear example of non-reductionism. This is, however, only partially right. It is correct that, as a non-reductionist, he defends the justifying role that the default position plays in testimonial knowledge. But, his insistence on situating the default position inside the space of reasons suggests that default position should be (...) understood as a kind of reasoning, and that only then evidential reasons can be applied in concrete justifying procedures. This is a very different understanding of the default position from that of classical non-reductionists such as Coady (1992) and Burge (1993, 1997). If McDowell’s epistemology of testimony can be understood in this way, as this paper aims to establish, it should be considered as an attempt tosupersede the reductionist and non-reductionist dichotomy, an attempt that brings a series of reconsiderations of a satisfactory epistemology of testimony. (shrink)

Default reasoning occurs whenever the truth of the evidence available to the reasoner does not guarantee the truth of the conclusion being drawn. Despite this, one is entitled to draw the conclusion “by default” on the grounds that we have no information which would make us doubt that the inference should be drawn. It is the type of conclusion we draw in the ordinary world and ordinary situations in which we find ourselves. Formally speaking, ‘nonmonotonic reasoning’ refers to (...) argumentation in which one uses certain information to reach a conclusion, but where it is possible that adding some further information to those very same premises could make one want to retract the original conclusion. It is easily seen that the informal notion of default reasoning manifests a type of nonmonotonic reasoning. Generally speaking, default statements are said to be true about the class of objects they describe, despite the acknowledged existence of “exceptional instances” of the class. In the absence of explicit information that an object is one of the exceptions we are enjoined to apply the default statement to the object. But further information may later tell us that the object is in fact one of the exceptions. So this is one of the points where nonmonotonicity resides in default reasoning. (shrink)