Prima facie obligation

This paper presents a nonmonotonic deontic logic based on commonsense entailment. It establishes criteria a successful account of obligation should satisfy, and develops a theory that satisfies them. The theory includes two conditional notions of prima facie obligation. One is constitutive; the other is epistemic, and follows nonmonotonically from the constitutive notion. The paper defines unconditional notions of prima facie obligation in terms of the conditional notions.     

Embedding Modal Nonmonotonic Logics into Default Logic

We present a straightforward embedding of modal nonmonotonic logics into default logic.     

Some Syntactic Approaches to the Handling of Inconsistent Knowledge Bases: A Comparative Study Part 1: The Flat Case

This paper presents and discusses several methods for reasoning from inconsistent knowledge bases. A so-called argued consequence relation, taking into account the existence of consistent arguments in favour of a conclusion and the absence of consistent arguments in favour of its contrary, is particularly investigated. Flat knowledge bases, i.e., without any priority between their elements, are studied under different inconsistency-tolerant consequence relations, namely the so-called argumentative, free, universal, existential, cardinality-based, and paraconsistent consequence relations. The syntax-sensitivity of these consequence relations is studied. A companion paper is devoted to the case where priorities exist between the pieces of information in the knowledge base.     

Representing Meta-Knowledge in Poole-Systems

We show how Poole-systems, a simple approach to nonmonotonic reasoning, can be extended to take meta-information into account adequately. The meta-information is used to guide the choice of formulas accepted by the reasoner as premises. Existence of a consistent set of conclusions is guaranteed by a least fixpoint construction. The proposed formalism has useful applications in defeasible reasoning, knowledge base fusion and belief revision.     

A Nonmonotonic Modal Formalization of the Logic of Acceptance and Rejection

The problems we deal with concern reasoning about incomplete knowledge. Knowledge is understood as ability of an ideal rational agent to make decisions about pieces of information. The formalisms we are particularly interested in are Moore's autoepistemic logic (AEL) and its variant, the logic of acceptance and rejection (AEL2). It is well-known that AEL may be seen as the nonmonotonic KD45 modal logic. The aim is to give an appropriate modal formalization for AEL2.     

Entailment with Near Surety of Scaled Assertions of High Conditional Probability

An assertion of high conditional probability or, more briefly, an HCP assertion is a statement of the type: The conditional probability of B given A is close to one. The goal of this paper is to construct logics of HCP assertions whose conclusions are highly likely to be correct rather than certain to be correct. Such logics would allow useful conclusions to be drawn when the premises are not strong enough to allow conclusions to be reached with certainty. This goal is achieved by taking Adams" (1966) logic, changing its intended application from conditionals to HCP assertions, and then weakening its criterion for entailment. According to the weakened entailment criterion, called the Criterion of Near Surety and which may be loosely interpreted as a Bayesian criterion, a conclusion is entailed if and only if nearly every model of the premises is a model of the conclusion. The resulting logic, called NSL, is nonmonotonic. Entailment in this logic, although not as strict as entailment in Adams" logic, is more strict than entailment in the propositional logic of material conditionals. Next, NSL was modified by requiring that each HCP assertion be scaled; this means that to each HCP assertion was associated a bound on the deviation from 1 of the conditional probability that is the subject of the assertion. Scaling of HCP assertions is useful for breaking entailment deadlocks. For example, it it is known that the conditional probabilities of C given A and of ¬ C given B are both close to one but the bound on the former"s deviation from 1 is much smaller than the latter"s, then it may be concluded that in all likelihood the conditional probability of C given A B is close to one. The resulting logic, called NSL-S, is also nonmonotonic. Despite great differences in their definitions of entailment, entailment in NSL is equivalent to Lehmann and Magidor"s rational closure and, disregarding minor differences concerning which premise sets are considered consistent, entailment in NSL-S is equivalent to entailment in Goldszmidt and Pearl"s System-Z ⁺. Bacchus, Grove, Halpern, and Koller proposed two methods of developing a predicate calculus based on the Criterion of Near Surety. In their random-structures method, which assumed a prior distribution similar to that of NSL, it appears possible to define an entailment relation equivalent to that of NSL. In their random-worlds method, which assumed a prior distribution dramatically different from that of NSL, it is known that the entailment relation is different from that of NSL.     

Defeasibility and Inferential Particularism

In this paper I argue that defeasible (nonmonotonic) inferences are occasion-sensitive: the inferential connections of a given claim (plus collateral premises) depend on features of the circumstances surrounding the occasion of inference (including typical environmental conditions, and also pragmatic and contextual factors, such as the information available to agents and how high stakes are). More specifically, it is an occasion-sensitive matter which possible defeaters have to be considered explicitly by the premises of an inference and which possible defeaters may remain unconsidered, without making the inference enthymematic. As a result, a largely unexplored form of occasion-sensitivity arises in inferentialist theories of content that appeal to defeasible inferences.     

A Sound and Complete Tableau Calculus for Reasoning about only Knowing and Knowing at Most

We define a tableau calculus for the logic of only knowing and knowing at most ON, which is an extension of Levesque's logic of only knowing O. The method is based on the possible-world semantics of the logic ON, and can be considered as an extension of known tableau calculi for modal logic K45. From the technical viewpoint, the main features of such an extension are the explicit representation of "unreachable" worlds in the tableau, and an additional branch closure condition implementing the property that each world must be either reachable or unreachable. The calculus allows for establishing the computational complexity of reasoning about only knowing and knowing at most. Moreover, we prove that the method matches the worst-case complexity lower bound of the satisfiability problem for both ON and O. With respect to [22], in which the tableau calculus was originally presented, in this paper we both provide a formal proof of soundness and completeness of the calculus, and prove the complexity results for the logic ON.     

Consistency Defaults

A consistency default is a propositional inference rule that asserts the consistency of a formula in its consequence. Consistency defaults allow for a straightforward encoding of domains in which it is explicitely known when something is possible. The logic of consistency defaults can be seen as a variant of cumulative default logic or as a generalization of justified default logic; it is also able to simulate Reiter default logic in the seminormal case. A semantical characterization of consistency defaults in terms of processes and in terms of a fixpoint equation is given, as well as a normal form. Presented by Melvin Fitting     

AI &; Law,Logic and Argument Schemes

This paper reviews the history of AI & Law research from the perspective of argument schemes. It starts with the observation that logic, although very well applicable to legal reasoning when there is uncertainty, vagueness and disagreement, is too abstract to give a fully satisfactory classification of legal argument types. It therefore needs to be supplemented with an argument-scheme approach, which classifies arguments not according to their logical form but according to their content, in particular, according to the roles that the various elements of an argument can play. This approach is then applied to legal reasoning, to identify some of the main legal argument schemes. It is also argued that much AI & Law research in fact employs the argument-scheme approach, although it usually is not presented as such. Finally, it is argued that the argument-scheme approach and the way it has been employed in AI & Law respects some of the main lessons to be learnt from Toulmin’s The Uses of Argument.     

The Quantitative/Qualitative Watershed for Rules of Uncertain Inference

We chart the ways in which closure properties of consequence relations for uncertain inference take on different forms according to whether the relations are generated in a quantitative or a qualitative manner. Among the main themes are: the identification of watershed conditions between probabilistically and qualitatively sound rules; failsafe and classicality transforms of qualitatively sound rules; non-Horn conditions satisfied by probabilistic consequence; representation and completeness problems; and threshold-sensitive conditions such as ‘preface’ and ‘lottery’ rules. Special Issue Formal Epistemology I. Edited by Branden Fitelson     

Resource-origins of Nonmonotonicity

Formal nonmonotonic systems try to model the phenomenon that common sense reasoners are able to “jump” in their reasoning from assumptions Δ to conclusions C without their being any deductive chain from Δ to C. Such jumps are done by various mechanisms which are strongly dependent on context and knowledge of how the actual world functions. Our aim is to motivate these jump rules as inference rules designed to optimise survival in an environment with scant resources of effort and time. We begin with a general discussion and quickly move to Section 3 where we introduce five resource principles. We show that these principles lead to some well known nonmonotonic systems such as Nute’s defeasible logic. We also give several examples of practical reasoning situations to illustrate our principles. Edited by Hannes Leitgeb     

Normische Gesetzeshypothesen und die wissenschaftsphilosophische Bedeutung des nichtmonotonen Schliessens

Normic Laws and the Significance of Nonmonotonic Reasoning for Philosophy of Science. Normic laws have the form ‘if A then normally B’. They have been discovered in the explanation debate, but were considered as empirically vacuous (§1). I argue that the prototypical (or ideal) normality of normic laws implies statistical normality (§2), whence normic laws have empirical content. In §3–4 I explain why reasoning from normic laws is nonmonotonic, and why the understanding of the individual case is so important here. After sketching some foundations of nonmonotonic reasoning as developed by AI-researchers (§5), Iargue that normic laws are also the best way to understand ceteris paribus laws (§6). §7 deals with the difference between physical and non-physical disciplines and §9 with the difference between normicity and approximation. In §8 it is shown how nonmonotonic reasoning provides a new understanding of the protection of theories against falsification by auxiliary hypotheses. §10, finally, gives a system- and evolution-theoretical explanation of the deeper reason for the omnipresence of normic laws in practice and science, and forthe connection between ideal and statistical normality. This revised version was published online in August 2006 with corrections to the Cover Date.     

Together – apart: in touch in a time of separation

This paper explores the experience of working as a Jungian analyst through the various phases of the global COVID-19 pandemic, examining the importance of the physical containing space alongside the analyst’s internal mind and how technology can both help and hinder understanding. A number of clinical vignettes illustrate the challenge of communicating over a distance, paying particular attention to the way countertransference phenomena can become re-attuned. Reference is made to mythology and symbols of hope, and consideration given to the meaning and purpose of the pandemic.     

The Possibility of Meaning in Human Evolution

Science undermines the certitude of non-naturalistic answers to the question of whether human life has meaning. I explore whether evolution can provide a naturalistic basis for existential meaning. Using the work of philosopher Daniel Dennett and scientist Ursula Goodenough, I argue that evolution is the locus of the possibility of meaning because it has produced intentionality, the matrix of consciousness. I conclude that the question of the meaning of human life is an existentialist one: existential meaning is a product of the individual and collective tasks human beings undertake.     

Phenotypic plasticity and archetype: a response to common objections to the biological theory of archetype and instinct

Since Jung’s death in 1961, scholars have attempted to integrate growing biological science data into Jungian concepts such as the collective unconscious, instincts and the archetypes. This enterprise has been challenging due to persistent false dichotomies of gene and environment occasionally arising. Recent works by Roesler (2022a, 2022b) for example, have raised objections to the biological theory of archetypes, but the objections are plagued by such dichotomies. The concept of phenotypic plasticity, however, helps to both avoid this problem as well as bridge the gap between competing theories into a more integrated model with solid biological foundations.