Defeasible Conditionals Research Articles

Legal positions reexamined

This commentary originated from discussions held within the blind peer review process of David Duarte's paper ‘Rights as formal combinations of normative variables’, recently published in Revus (2023) 51. The author challenges Duarte's norm-based analysis of fundamental legal positions on eight counts. It argues that Duarte's analysis fails to fully respect the distinction between genuine norms and normative propositions; raises insubstantial questions about norm individuation; does not clarify whether conditional norms rely on material conditionals, stronger generalized conditionals, or defeasible conditionals; misplaces the opportunity conditions for norm application in the antecedent of a conditional norm; wrongly assumes the universality of bilateral permissions for claim-right holders to accept the results of obligatory actions and that all exercises of legal power are necessarily permitted; and, finally, improperly reduces legal provisions of strong incompetence and immunity to merely declarative statements.

Revision, defeasible conditionals and non-monotonic inference for abstract dialectical frameworks

For propositional beliefs, there are well-established connections between belief revision, defeasible conditionals, and nonmonotonic inference. In argumentative contexts, such connections have not yet been investigated. On the one hand, the exact relationship between formal argumentation and nonmonotonic inference relations is a research topic that keeps on eluding researchers despite recently intensified efforts, whereas argumentative revision has been studied in numerous works during recent years. In this paper, we show that relationships between belief revision, defeasible conditionals, and nonmonotonic inference similar to those in propositional logic hold in argumentative contexts as well. We first define revision operators for abstract dialectical frameworks, and use such revision operators to define dynamic conditionals by means of the Ramsey test. We show that such conditionals can be equivalently defined using a total preorder over three-valued interpretations, and study the inferential behaviour of the resulting conditional inference relations.

Principles of KLM-style Defeasible Description Logics

The past 25 years have seen many attempts to introduce defeasible-reasoning capabilities into a description logic setting. Many, if not most, of these attempts are based on preferential extensions of description logics, with a significant number of these, in turn, following the so-called KLM approach to defeasible reasoning initially advocated for propositional logic by Kraus, Lehmann, and Magidor. Each of these attempts has its own aim of investigating particular constructions and variants of the (KLM-style) preferential approach. Here our aim is to provide a comprehensive study of the formal foundations of preferential defeasible reasoning for description logics in the KLM tradition. We start by investigating a notion of defeasible subsumption in the spirit of defeasible conditionals as studied by Kraus, Lehmann, and Magidor in the propositional case. In particular, we consider a natural and intuitive semantics for defeasible subsumption, and we investigate KLM-style syntactic properties for both preferential and rational subsumption. Our contribution includes two representation results linking our semantic constructions to the set of preferential and rational properties considered. Besides showing that our semantics is appropriate, these results pave the way for more effective decision procedures for defeasible reasoning in description logics. Indeed, we also analyse the problem of non-monotonic reasoning in description logics at the level of entailment and present an algorithm for the computation of rational closure of a defeasible knowledge base. Importantly, our algorithm relies completely on classical entailment and shows that the computational complexity of reasoning over defeasible knowledge bases is no worse than that of reasoning in the underlying classical DL ALC .

A Cut-Free Sequent Calculus for Defeasible Erotetic Inferences

In recent years, the effort to formalize erotetic inferences---i.e., inferences to and from questions---has become a central concern for those working in erotetic logic. However, few have sought to formulate a proof theory for these inferences. To fill this lacuna, we construct a calculus for (classes of) sequents that are sound and complete for two species of erotetic inferences studied by Inferential Erotetic Logic (IEL): erotetic evocation and erotetic implication. While an effort has been made to axiomatize the former in a sequent system, there is currently no proof theory for the latter. Moreover, the extant axiomatization of erotetic evocation fails to capture its defeasible character and provides no rules for introducing or eliminating question-forming operators. In contrast, our calculus encodes defeasibility conditions on sequents and provides rules governing the introduction and elimination of erotetic formulas. We demonstrate that an elimination theorem holds for a version of the cut rule that applies to both declarative and erotetic formulas and that the rules for the axiomatic account of question evocation in IEL are admissible in our system.

Preferential Accessibility and Preferred Worlds

Modal accounts of normality in non-monotonic reasoning traditionally have an underlying semantics based on a notion of preference amongst worlds. In this paper, we motivate and investigate an alternative semantics, based on ordered accessibility relations in Kripke frames. The underlying intuition is that some world tuples may be seen as more normal, while others may be seen as more exceptional. We show that this delivers an elegant and intuitive semantic construction, which gives a new perspective on defeasible necessity. Technically, the revisited logic does not change the expressive power of our previously defined preferential modalities. This conclusion follows from an analysis of both semantic constructions via a generalisation of bisimulations to the preferential case. Reasoners based on the previous semantics therefore also suffice for reasoning over the new semantics. We complete the picture by investigating different notions of defeasible conditionals in modal logic that can also be captured within our framework.

The Defeasibility of Knowledge‐How

Reductive intellectualists (e.g., Stanley & Williamson 2001; Stanley 2011a; 2011b; Brogaard 2008; 2009; 2011) hold that knowledge‐how is a kind of knowledge‐that. If this thesis is correct, then we should expect the defeasibility conditions for knowledge‐how and knowledge‐that to be uniform—viz., that the mechanisms of epistemic defeat which undermine propositional knowledge will be equally capable of imperilling knowledge‐how. The goal of this paper is twofold: first, against intellectualism, we will show that knowledge‐how is in fact resilient to being undermined by the very kinds of traditional (propositional) epistemic defeaters which clearly defeat the items of propositional knowledge which intellectualists identify with knowledge‐how. Second, we aim to fill an important lacuna in the contemporary debate, which is to develop an alternative way in which epistemic defeat for knowledge‐how could be modelled within an anti‐intellectualist framework.

Pragmatic Maxims and Presumptions in Legal Interpretation

The fields of linguistic pragmatics and legal interpretation are deeply interrelated. The purpose of this paper is to show how pragmatics and the developments in argumentation theory can contribute to the debate on legal interpretation. The relation between the pragmatic maxims and the presumptions underlying the legal canons are brought to light, unveiling the principles that underlie the types of argument usually used to justify a construction. The Gricean maxims and the arguments of legal interpretation are regarded as presumptions subject to default used to justify an interpretation. This approach can allow one to trace the different legal interpretive arguments back to their basic underlying presumptions, so that they can be compared, ordered, and assessed according to their defeasibility conditions. This approach allows one to understand the difference between various types of interpretive canons, and their strength in justifying an interpretation.

In All But Finitely Many Possible Worlds: Model-Theoretic Investigations on ‘Overwhelming Majority’ Default Conditionals

Defeasible conditionals are statements of the form `ifAthen normallyB'. One plausible interpretation introduced in nonmonotonic reasoning dictates that ($$A\Rightarrow B$$AźB) is true iff B is true in `most' A-worlds. In this paper, we investigate defeasible conditionals constructed upon a notion of `overwhelming majority', defined as `truth in a cofinite subset of$$\omega $$ź', the first infinite ordinal. One approach employs the modal logic of the frame $$(\omega , <)$$(ź,<), used in the temporal logic of discrete linear time. We introduce and investigate conditionals, defined modally over $$(\omega , <)$$(ź,<); several modal definitions of the conditional connective are examined, with an emphasis on the nonmonotonic ones. An alternative interpretation of `majority' as sets cofinal (in $$\omega $$ź) rather than cofinite (subsets of $$\omega $$ź) is examined. For these modal approaches over $$(\omega , <)$$(ź,<), a decision procedure readily emerges, as the modal logic $${\mathbf {K4DLZ}}$$K4DLZ of this frame is well-known and a translation of the conditional sentences can be mechanically checked for validity; this allows also for a quick proof of $$\mathsf {NP}$$NP-completeness of the satisfiability problem for these logics. A second approach employs the conditional version of Scott-Montague semantics, in the form of $$\omega $$ź-many possible worlds, endowed with neighborhoods populated by collections of cofinite subsets of $$\omega $$ź. This approach gives rise to weak conditional logics, as expected. The relative strength of the conditionals introduced is compared to (the conditional logic `equivalent' of) KLM logics and other conditional logics in the literature.

Analogical Arguments: Inferential Structures and Defeasibility Conditions

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 (essential similarities) or non-semantic ones, indicating possible characteristics of the referents (accidental similarities). Such distinct types of similarity characterize different kinds of analogical arguments, all based on a similar general structure, in which a common genus (or rather a generic feature) 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.

The bad habit of bearing children

Procreation—the act of having and raising biological children—is generally not a life choice that is subject to moral scrutiny. In this article, we argue that decisions to procreate are morally evaluable, and that such evaluation reveals that prospective parents have a defeasible obligation to prioritize adoption over procreation. The obligation is defeated by the lack of desire to become a parent, and also in certain cases where legal hurdles are logistically onerous. We conclude that those prospective parents who are unaffected by the defeasibility conditions have a duty to prioritize adoption, regardless of the strength, power, or depth of the desire for biological offspring.

Legal Reasons: Between Universalism and Particularism

AbstractThe first part of this work analyses the universalist and the particularist conceptions of reasons. The second part projects this analysis to the legal domain. The author stresses that universalism and particularism regarding reasons are mutually exclusive theories linked to incompatible conceptions of norms, i.e. norms as strict universal conditionals and norms as defeasible conditionals. In giving an account of this tenet, different meanings of universality and defeasibility are explored. A parallel debate regarding reasons can be found in the legal domain, where two contrasting categories of norms are usually distinguished: rules and principles. On this issue the author argues that the conception of legal reasons depends on the way in which this contrast between different kinds of legal norms is shaped.

Contrary-to-duty obligations

We investigate under what conditions contrary-to-duty (CTD) structures lacking temporal and action elements can be given a coherent reading. We argue, contrary to some recent proposals, that CTD is not an instance of defeasible reasoning, and that methods of nonmonotonic logics are inadequate since they are unable to distinguish between defeasibility and violation of primary obligations. We propose a semantic framework based on the idea that primary and CTD obligations are obligations of different kinds: a CTD obligation pertains to, or pre-supposes, a certain context in which a primary obligation is already violated. This framework is presented initially as an extension of Standard Deontic Logic (SDL), a normal modal logic of type KD, and is illustrated by application to a series of examples. The concluding section is concerned with some resemblances between CTD and defeasible reasoning. We show first that the SDL-based framework contains a flaw and must be adjusted. A discussion of possible adjustments, including an alternative treatment in terms of a preference-based semantics, reveals difficulties that are reminiscent of problems in defeasible reasoning and intensional accounts of defeasible conditionals.

Carlos E. Alchourrón. Breve biografía intelectual

This paper is a short intellectual biography of Professor Carlos E. Alchourrón. I analyze his main contributions in three fields: 1) the logic of normative systems, 2) the logic of theory change, and 3) the logic of defeasible conditionals. I review the historical development of his thought on these three subjects. Furthermore, I show how the problems that arise in the field of normative logic stimulated him to find solutions in the AGM theory and in defeasible logic. Lastly, I show how in his last papers these three fields converge in a general englobing approach.

Towards a formal theory of defeasible deontic conditionals

The paper outlines the approach to the analysis of deontic conditionals taken in earlier work of Jones and Porn, comparing it briefly with two main trends within dyadic deontic logic, and discussing problems associated with the augmentation principle and the factual detachment principle. A modification of the Jones and Porn system is then presented, using a classical but not normal (in the sense of Chellas) deontic modality, to provide the basis for an alternative analysis of deontic conditionals. This new analysis validates neither the factual detachment nor the augmentation principles. However, influenced by the approach of Delgrande to default reasoning, it is shown how a restricted form of factual detachment might be accommodated within the revised system.