We investigate induction from the viewpoint of nonmonotonic reasoning. Induction we consider in this paper is descriptive induction. Hypotheses from descriptive induction have the weak property that they only describe rules with respect to the observations and do not realize an inductive leap. In this paper, we define a new form of descriptive induction with circumscription and the idea of explanation and show two procedures for computing it. The new descriptive induction is called circumscriptive induction. By deciding the (...) roles of predicates in circumscription, we can intentionally minimize models of a given inductive problem. By adopting the idea of explanation, we can distinguish between background knowledge and observations. Additionally, we consider the relationship between the way of choosing the roles of predicates in computing circumscription and the property of hypotheses obtained by circumscriptive induction. It is shown that hypotheses from circumscriptive induction reflect a difference between background knowledge and observations and do not realize an inductive leap. We also investigate revision of hypotheses which is as important as generation of hypotheses. In a process of hypothesis revision, a difference between previous induction and circumscriptive induction is clearly characterised. (shrink)

This book by one of the world's foremost philosophers in the fields of epistemology and logic offers an account of suppositional reasoning relevant to practical deliberation, explanation, prediction and hypothesis testing. Suppositions made 'for the sake of argument' sometimes conflict with our beliefs, and when they do, some beliefs are rejected and others retained. Thanks to such belief contravention, adding content to a supposition can undermine conclusions reached without it. Subversion can also arise because suppositional reasoning is ampliative. These two (...) types of nonmonotonic logic are the focus of this book. A detailed comparison of nonmonotonicity appropriate to both belief contravening and ampliative suppositional reasoning reveals important differences that have been overlooked. (shrink)

The motivation of this study is that Reiter’s default theory as well as assumption-based argumentation frameworks corresponding to default theories have difficulties in handling disjunctive information, while a disjunctive default theory ( ddt) avoids them. This paper presents the semantic correspondence between generalized assumption-based argumentation (ABA) and extended disjunctive logic programming as well as the correspondence between ABA and nonmonotonic reasoning approaches such as disjunctive default logic and prioritized circumscription. To overcome the above-mentioned difficulties of ABA frameworks corresponding (...) to default theories, we propose an assumption-based framework (ABF) translated from an extended disjunctive logic program (EDLP) since an EDLP can be translated into a ddt. Our ABF incorporates explicit negation and the connective of disjunction “|” to Heyninck and Arieli’s ABF induced by a disjunctive logic program. In this paper, first, we show how arguments are constructed from disjunctive rules in our proposed ABF. Then, we show the correspondence between answer sets of an EDLP P and stable extensions of the ABF translated from P with trivialization rules. After defining rationality postulates, we show answer sets of a consistent EDLP are captured by consistent stable extensions of the translated ABF with no trivialization rules. Finally, we show the correspondence between ABA and disjunctive default logic (resp. prioritized circumscription). The relation between ABA and possible model semantics of EDLPs is also discussed. (shrink)

This proceedings volume contains a selection of revised and extended papers presented at the Second International Workshop on Nonmonotonic and InductiveLogic, NIL '91, which took place at Reinhardsbrunn Castle, December 2-6, 1991. The volume opens with an extended version of a tutorial on nonmonotonic logic by G. Brewka, J. Dix, and K. Konolige. Fifteen selected papers follow, on a variety of topics. The majority of papers belong either to the area of nonmonotonic reasoning or to the field (...) of inductive inference, but some papers integrate research from both areas. The first workshop in this series was held at the University of Karlsruhe in December 1990 and its proceedings were published as Lecture Notes in Artificial Intelligence Volume 543. The series of workshops was made possible by financial support from Volkswagen Stiftung, Hannover. This workshop was also supported by IBM Deutschland GmbH and Siemens AG. (shrink)

Graham Priest defends the use of a nonmonotonic logic, LPm, in his analysis of reasoning in the face of true contradictions, such as those arising from the paradoxes of self-reference. In the course of defending this choice of logic in the face of the criticism that this logic is not truth preserving, Priest argued that requirement is too much to ask: since LPm is a nonmonotonic logic, it necessarily fails to preserve truth. In this article, I show that (...) this assumption is incorrect, and I explain why nonmonotonic logics can nonetheless be truth preserving. Finally, I diagnose Priest's error, to explain when nonmonotonic logics do indeed fail to preserve truth. (shrink)

This paper is an effort to realize and explore the connections that exist between nonmonotonic logic and confirmation theory. We pick up one of the most wide-spread nonmonotonic formalisms – default logic – and analyze to what extent and under what adjustments it could work as a logic of induction in the philosophical sense. By making use of this analysis, we extend default logic so as to make it able to minimally perform the task of a logic of (...) induction, having as a result a system which we believe has interesting properties from the standpoint of theory of confirmation. It is for instance able to represent chains of inductive rules as well as to reason paraconsistently on the conclusions obtained from them. We then use this logic to represent some traditional ideas concerning confirmation theory, in particular the ones proposed by Carl Hempel in his classical paper "Studies in the Logic of Confirmation" of 1945 and the ones incorporated in the so-called abductive and hy-pothetico-deductive models. (shrink)

In this chapter we will deal with “mechanizing” induction, i.e. with ways in which theoretical computer science approaches inductive generalization. In the field of Machine Learning, algorithms for induction are developed. Depending on the form of the available data, the nature of these algorithms may be very different. Some of them combine geometric and statistical ideas, while others use classical reasoning based on logical formalism. However, we are not so much interested in the algorithms themselves, but more on the philosophical (...) and theoretical foundations they share. Thus in the first of two parts, we will examine different approaches and inductive assumptions in two particular learning settings. While many machine learning algorithms work well on a lot of tasks, the interpretation of the learned hypothesis is often difficult. Thus, while e.g. an algorithm surprisingly is able to determine the gender of the author of a given text with about 80 percent accuracy [Argamon and Shimoni, 2003], for a human it takes some extra effort to understand on the basis of which criteria the algorithm is able to do so. With that respect the advantage of approaches using logic are obvious: If the output hypothesis is a formula of predicate logic, it is easy to interpret. However, if decision trees or algorithms from the area of inductive logic programming are based purely on classical logic, they suffer from the fact that most universal statements do not hold for exceptional cases, and classical logic does not offer any convenient way of representing statements which are meant to hold in the “normal case”. Thus, in the second part we will focus on approaches for Nonmonotonic Reasoning that try to handle this problem. Both Machine Learning and Nonmonotonic Reasoning have been anticipated partially by work in philosophy of science and philosophical logic. At the same time, recent developments in theoretical computer science are expected to trig- ger further progress in philosophical theories of inference, confirmation, theory revision, learning, and the semantic and pragmatics of conditionals. We hope this survey will contribute to this kind of progress by building bridges between computational, logical, and philosophical accounts of induction. (shrink)

Parametric logic is a framework that generalises classical first-order logic. A generalised notion of logical consequence—a form of preferential entailment based on a closed world assumption—is defined as a function of some parameters. A concept of possible knowledge base—the counterpart to the consistent theories of first-order logic—is introduced. The notion of compactness is weakened. The degree of weakening is quantified by a nonnull ordinal—the larger the ordinal, the more significant the weakening. For every possible knowledge base T, a hierarchy of (...) sentences that are generalised logical consequences of T is built. The first layer of the hierarchies corresponds to sentences that can be obtained by a deductive inference, characterised by the compactness property. The second layer of the hierarchies corresponds to sentences that can be obtained by an inductive inference, characterised by the property of weak compactness quantified by 1. Weaker forms of compactness—quantified by nonnull ordinals—determine higher layers in the hierarchies, corresponding to more complex inferences. The naturalness of the hierarchies built over the possible knowledge bases is attested by fundamental connections with notions from Learning theory and from topology. The naturalness of the hierarchies built over the possible knowledge bases is attested by fundamental connections with notions from Learning theory—classification in the limit, with or without a bounded number of mind changes—and from topology—in reference to the Borel and the difference hierarchies. In this paper, we introduce the key model-theoretic aspects of Parametric logic, justify the concept of the knowledge base, define the hierarchies of generalised logical consequences and illustrate their relevance to Nonmonotonic reasoning. More specifically, we show that the degree of nonmonotonicity that is required to infer a sentence can be characterised by the least nonnull ordinal that quantifies the weakening of compactness used to locate the inferred sentence in the hierarchies. (shrink)

Nonmonotonic consequence is the subject of a vast literature, but the idea of a nonmonotonic counterpart of logical inconsistency—the idea of a defeasible property representing internal conflict of an inductive or evidential nature—has been entirely neglected. After considering and dismissing two possible analyses relating nonmonotonic consequence and a nonmonotonic counterpart of logical inconsistency, this paper offers a set of postulates for nonmonotonic inconsistency, an analysis of nonmonotonic inconsistency in terms of nonmonotonic consequence, and (...) a series of results showing that nonmonotonic inconsistency conforms to these postulates given the analysis of nonmonotonic inconsistency presented here and certain postulates for nonmonotonic consequence. The results presented here establish the interest of certain previously undiscussed postulates of nonmonotonic consequence. These results also show that nonmonotonicity, which has never seemed useful in the formulation of general principles governing nonmonotonic reasoning, is relevant to the positive characterization of nonmonotonic inference after all. (shrink)

Charles Morgan has argued that nonmonotonic logic is ``impossible''. We show here that those arguments are mistaken, and that Morgan's preferred alternative, the representation of nonmonotonic reasoning by ``presuppositions'' fails to provide a framework in which nonmonotonic reasoning can be constructively criticised. We argue that an inductive logic, based on probabilistic acceptance, offers more than Morgan's approach through presuppositions.

This thesis analyzes from a philosophical perspective different models for nonmonotonic inference, belief revision and the handling of inconsistencies. ;The first chapter serves as an introduction to the subject, giving examples and analyzing the main concepts. As a result of these discussions, this thesis tries to: produce a refined map of the main notions related to this subject, maintain that there can be a fault tolerant logic that stands in support of fault tolerant reasoning, and defend the use of (...) deductive databases as models for changes of belief. ;The second chapter explores monotonic proposals to deal with uncertain reasoning. These include logics based on a classical notion of consequence, interpretations of defeasible reasoning as containing implicit premises, and systems in which temporal change is an integral part of the representation of states of affairs, via temporal indices or more elaborate devices. ;The third chapter explores quantitative approaches to nonmonotonic reasoning like dispositional logic, and theories of probabilistic reasoning including Bayesian, certainty factors, and Dempster-Shafer. ;The fourth chapter explores qualitative approaches. Here we mention conditional, default, and nonmonotonic logics, and the circumscription and autoepistemic formalisms. ;The fifth chapter studies different proposals to deal with contradictions. It starts with a review of the types of belief inconsistencies, and then it presents mechanisms to prevent, control or correct them. I explore paraconsistent logics, specially relevance logics, to "bracket" the area of conflict and allow inferences about non-related topics to continue unaffected. Then I examine different methods to get rid of the inconsistencies, including the use of dependency-directed backtracking and of relevance logic. ;Finally, I present my conclusions, and mention some of the open problems. (shrink)

We introduce a family of preferential logics that are useful for handling information with different levels of uncertainty. The corresponding consequence relations are nonmonotonic, paraconsistent, adaptive, and rational. It is also shown that the formalisms in this family can be embedded in corresponding four-valued logics with at most three uncertainty levels, and that reasoning with these logics can be simulated by algorithms for processing circumscriptive theories, such as DLS and SCAN.

Probabilities are important in belief updating, but probabilistic reasoning does not subsume everything else (as the Bayesian would have it). On the contrary, Bayesian reasoning presupposes knowledge that cannot itself be obtained by Bayesian reasoning, making generic Bayesianism an incoherent theory of belief updating. Instead, it is indefinite probabilities that are of principal importance in belief updating. Knowledge of such indefinite probabilities is obtained by some form of statistical induction, and inferences to non-probabilistic conclusions are carried out in accordance with (...) the statistical syllogism. Such inferences have been the focus of much attention in the nonmonotonic reasoning literature, but the logical complexity of such inference has not been adequately appreciated. (shrink)

Coping with uncertainty is a necessary part of ordinary life and is crucial to an understanding of how the mind works. For example, it is a vital element in developing artificial intelligence that will not be undermined by its own rigidities. There have been many approaches to the problem of uncertain inference, ranging from probability to inductive logic to nonmonotonic logic. Thisbook seeks to provide a clear exposition of these approaches within a unified framework. The principal market for the (...) book will be students and professionals in philosophy, computer science, and AI. Among the special features of the book are a chapter on evidential probability, which has not received a basic exposition before; chapters on nonmonotonic reasoning and theory replacement, matters rarely addressed in standard philosophical texts; and chapters on Mill's methods and statistical inference that cover material sorely lacking in the usual treatments of AI and computer science. (shrink)

It is suggested that taking into account considerations that traditionally fall within the scope of computer science in general, and artificial intelligence in particular, sheds new light on the subject of causation. It is argued that adopting causal notions con be viewed as filling a computational need: They allow reasoning with incomplete information, facilitate economical representations, and afford relatively efficient methods for reasoning about those representations. Specifically, it is proposed that causal reasoning is intimately bound to nonmonotonic reasoning. An (...) account of causation is offered that relies upon this connection, and compares this proposal to previous accounts within philosophy and artificial intelligence. (shrink)

Reasoning almost always occurs in the face of incomplete information. Such reasoning is nonmonotonic in the sense that conclusions drawn may later be withdrawn when additional information is obtained. There is an active literature on the problem of modeling such nonmonotonic reasoning, yet no category of method-let alone a single method-has been broadly accepted as the right approach. This paper introduces a new method, called sweeping presumptions, for modeling nonmonotonic reasoning. The main goal of the paper is (...) to provide an example-driven, nontechnical introduction to the method of sweeping presumptions, and thereby to make it plausible that sweeping presumptions can usefully be applied to the problems of nonmonotonic reasoning. The paper discusses a representative sample of examples that have appeared in the literature on nonmonotonic reasoning, and discusses them from the point of view of sweeping presumptions. (shrink)

Nonmonotonic reasoning in its broadest sense is reasoning to conclusions on the basis of incomplete information. Given more information, previously drawn inferences may be retracted. Commonsense reasoning has a nonmonotonic component; it has been argued that almost all commonsense inferences are of this sort. From the end of the 1980s to the present there has been an explosion in research in nonmonotonic reasoning. It is now possible to understand more clearly the properties of the major formalisms from (...) a metatheoretical point of view, the relationships among the formalisms and their connection to independently developed proof methods. The goal of this monograph is to make this understanding more accessible. (shrink)

In this book the author gives a broad overview of different areas of research in nonmonotonic reasoning, and presents some new results and ideas based on his research. The guiding principles are: clarification of the different research activities in the area, which have sometimes been undertaken independently of each other; and appreciation of the fact that these research activities often represent different means to the same ends, namely sound theoretical foundations and efficient computation. The book begins with a discussion (...) of the various types of nonmonotonic reasoning, their applications and their logics. Theorem proving techniques for these logics are also described. The following chapters deal with formulations of nonmonotonic inheritance, and nonmonotonic reasoning based on nonmonotonic rules. The final chapter discusses the achievements in the field in the light of the Yale shooting example. The book will be welcomed by researchers in theoretical computer science and artificial intelligence. (shrink)

Three studies of human nonmonotonic reasoning are described. The results show that people find such reasoning quite difficult, although being given problems with known subclass-superclass relationships is helpful. The results also show that recognizing differences in the logical strengths of arguments is important for the nonmonotonic problems studied. For some of these problems, specificity – which is traditionally considered paramount in drawing appropriate conclusions – was irrelevant and so should have lead to a “can’t tell” response; however, people (...) could give rational conclusions based on differences in the logical consequences of arguments. The same strategy also works for problems where specificity is relevant, suggesting that in fact specificity is not paramount. Finally, results showed that subjects’ success at responding appropriately to nonmonotonic problems involving conflict relies heavily on the ability to appreciate differences in the logical strength of simple, non-conflicting, statements. (shrink)

Machine learning and nonmonotonic reasoning are closely related, both concerned with making plausible as well as certain inferences based on available data. In this document a brief overview of different approaches to nonmonotonic reasoning is presented, and it is shown how the concept of argumentation systems arises. The relationship with machine learning work is also discussed. The document aims to highlight the links between nonmonotonic reasoning, argumentation and machine learning and as a result propose some potentially useful (...) directions for new research. (shrink)

Nonmonotonic reasoning is a theory of the rational use of assumptions. We describe the relations between NMR and Logic, and two main paradigms of NMR, preferential and explanatory one.

In Gärdenfors and Makinson :197–245, 1994) and Gärdenfors it was shown that it is possible to model nonmonotonic inference using a classical consequence relation plus an expectation-based ordering of formulas. In this article, we argue that this framework can be significantly enriched by adopting a conceptual spaces-based analysis of the role of expectations in reasoning. In particular, we show that this can solve various epistemological issues that surround nonmonotonic and default logics. We propose some formal criteria for constructing (...) and updating expectation orderings based on conceptual spaces, and we explain how to apply them to nonmonotonic reasoning about objects and properties. (shrink)

This paper has two goals. First, we develop frameworks for logical systems which are able to reflect not only non-monotonic patterns of reasoning, but also paraconsistent reasoning. Our second goal is to have a better understanding of the conditions that a useful relation for nonmonotonic reasoning should satisfy. For this we consider a sequence of generalizations of the pioneering works of Gabbay, Kraus, Lehmann, Magidor and Makinson. These generalizations allow the use of monotonic nonclassical logics as the underlying logic (...) upon which nonmonotonic reasoning may be based. Our sequence of frameworks culminates in what we call plausible, nonmonotonic, multiple-conclusion consequences relations . Our study yields intuitive justifications for conditions that have been proposed in previous frameworks and also clarifies the connections among some of these systems. In addition, we present a general method for constructing plausible nonmonotonic relations. This method is based on a multiple-valued semantics, and on Shoham's idea of preferential models. (shrink)

This book covers lymphoproliferative disorders in patients with congenital or acquired immunodeficiencies. Acquired immunodeficiencies are caused by infections with the human immunodeficiency virus or arise following immunosuppressive therapy administered after organ transplantation or to treat connective tissue diseases such as rheumatoid arthritis. It was recently discovered that various diseases or therapeutic modalities that induce a state of immunosuppression may cause virally driven lymphoproliferations. This book summarizes for the first time this group of immunodeficiency-associated lymphoproliferations.

Humans learn new concepts extremely fast. One or two examples of a new concept are often sufficient for us to grasp its meaning. Traditional theories of concept formation, such as symbolic or connectionist representations, have problems explaining the quick learning exhibited by humans. In contrast to these representations, I advocate a third form of representing categories, which employs geometric structures. I argue that this form is appropriate for modeling concept learning. By using the geometric structures of what I call “conceptual (...) spaces,” I define properties and concepts. A learning model that shows how properties and concepts can be learned in a simple but naturalistic way is then presented. This model accounts well for the role of similarity judgments in concept learning. Finally, as an application, the concept representations are used to give an analysis of nonmonotonic reasoning. (shrink)

This book constitutes the refereed proceedings of the 7th International Conference on Logic Programming and Nonmonotonic Reasoning, LPNMR 2004, held in Fort Lauderdale, Florida, USA in January 2004. The 24 revised full papers presented together with 8 system descriptions were carefully reviewed and selected for presentation. Among the topics addressed are declarative logic programming, nonmonotonic reasoning, knowledge representation, combinatorial search, answer set programming, constraint programming, deduction in ontologies, and planning.

ABSTRACT What characterizes human reasoning is the ability of dealing with incomplete information. Incomplete logic is developed for modeling incomplete knowledge. The most distinctive feature of incomplete logic is its semantics. This is an alternative presentation of partial semantics. In this paper, we will introduce the general notion of incomplete logic (ICL), compare it with partial logic, and give the resolution method for it. We will also show how ICL can be applied to nonmonotonic reasoning. We define nonmonotonic (...) derivation as monotonic derivation in ICL from the database and some consistent assumptions. The mechanism of ICL makes it easy to assert the consistency of an assumption without asserting the assumption itself. (shrink)

This dissertation is intended to provide a formalism for those generics that trigger nonmonotonic inferences. The formalism is to reflect intentionality and exception-tolerating features of generics, and has an emphasis on the axiomatization of generic reasoning that encodes nonmonotonicity. ;A modal conditional approach is taken to formalize the nonmonotonic reasoning in general at the level of object language. A serial of logic systems---MN, NID, NCUM, N STCUM---are constructed in an increasing strength of the characterized nonmonotonic inference relation. (...) In these systems, two binary modal operators ⩾ and > are introduced in their syntax, and a ⊛ function lifted from the traditional * function is deployed in their semantics. These systems are shown to be sound and complete with respect to certain classes of frames defined in the semantics. They are decidable as well. The nonmonotonic inference is argued to be a ternary relation "[phi], Gamma |∼ alpha", and is defined in the system NSTCUM. Many widely discussed nonmonotonic inference patterns such as Defeasible Modus Ponens, Defeasible Transitivity, the Penguin Principle etc. are justified. The specificity rule is proved to be a theorem of the system N STCUM. The impact of negated defaults on an inference is also investigated and accounted for. ;A canonical form to read off generics is proposed: All generic sentences with subject-predicate structure can be re-written into their canonical form S . If S is a plural noun phrase, it can be further refined to be . Normal objects are selected based on the "meaning" of the subject and predicate terms. The second parameter provides an aspect with respect to which certain objects of a kind are considered normal. Due to such a way to select normal objects, the drowning problem is solved. ;The inference behaviors of generics are axiomatized in the system G, which is a quantificational extension of the system NSTCUM. It is proved to be sound and complete with respect to the class of L⩾,G -frames. Those benchmark examples of generic inferences are examined in the system G. (shrink)

Conclusions reached using common sense reasoning from a set of premises are often subsequently revised when additional premises are added. Because we do not always accept previous conclusions in light of subsequent information, common sense reasoning is said to be nonmonotonic. But in the standard formal systems usually studied by logicians, if a conclusion follows from a set of premises, that same conclusion still follows no matter how the premise set is augmented; that is, the consequence relations of standard (...) logics are monotonic. Much recent research in AI has been devoted to the attempt to develop nonmonotonic logics. After some motivational material, we give four formal proofs that there can be no nonmonotonic consequence relation that is characterized by universal constraints on rational belief structures. In other words, a nonmonotonic consequence relation that corresponds to universal principles of rational belief is impossible. We show that the nonmonotonicity of common sense reasoning is a function of the way we use logic, not a function of the logic we use. We give several examples of how nonmonotonic reasoning systems may be based on monotonic logics. (shrink)

Reasoning with conditionals is often thought to be non-monotonic, but there is no incompatibility with classical logic, and no need to formalise inference itself as probabilistic. When the addition of a new premise leads to abandonment of a previously compelling conclusion reached by modus ponens, for example, this is generally because it is hard to think of a model in which the conditional and the new premise are true.

A. Tarski [22] proposed the study of infinitary consequence operations as the central topic of mathematical logic. He considered monotonicity to be a property of all such operations. In this paper, we weaken the monotonicity requirement and consider more general operations, inference operations. These operations describe the nonmonotonic logics both humans and machines seem to be using when infering defeasible information from incomplete knowledge. We single out a number of interesting families of inference operations. This study of infinitary inference (...) operations is inspired by the results of [12] on nonmonotonic inference relations, and relies on some of the definitions found there. (shrink)

This monograph provides a new account of justified inference as a cognitive process. In contrast to the prevailing tradition in epistemology, the focus is on low-level inferences, i.e., those inferences that we are usually not consciously aware of and that we share with the cat nearby which infers that the bird which she sees picking grains from the dirt, is able to fly. Presumably, such inferences are not generated by explicit logical reasoning, but logical methods can be used to describe (...) and analyze such inferences. Part 1 gives a purely system-theoretic explication of belief and inference. Part 2 adds a reliabilist theory of justification for inference, with a qualitative notion of reliability being employed. Part 3 recalls and extends various systems of deductive and nonmonotonic logic and thereby explains the semantics of absolute and high reliability. In Part 4 it is proven that qualitative neural networks are able to draw justified deductive and nonmonotonic inferences on the basis of distributed representations. This is derived from a soundness/completeness theorem with regard to cognitive semantics of nonmonotonic reasoning. The appendix extends the theory both logically and ontologically, and relates it to A. Goldman's reliability account of justified belief. This text will be of interest to epistemologists and logicians, to all computer scientists who work on nonmonotonic reasoning and neural networks, and to cognitive scientists. (shrink)

An extended review of what is known about the formal behaviour of nonmonotonic inference operations, including those generated by the principal systems in the artificial intelligence literature. Directed towards computer scientists and others with some background in logic.

Nonmonotonic reasoning is often claimed to mimic human common sense reasoning. Only a few studies, though, investigated this claim empirically. In the present paper four psychological experiments are reported, that investigate three rules of system p, namely the and, the left logical equivalence, and the or rule. The actual inferences of the subjects are compared with the coherent normative upper and lower probability bounds derived from a non-infinitesimal probability semantics of system p. We found a relatively good agreement of (...) human reasoning and principles of nonmonotonic reasoning according to the coherence interpretation of system p. Contrary to the results reported in the “heuristics and biases” tradition, the subjects committed relatively few upper bound violations (conjunction fallacies). More lower than upper bound violations were observed. When the premises were presented in terms of intervals higher mean lower bounds were observed as when the premises were presented in terms of point percentages. (shrink)

Theoria, Volume 88, Issue 3, Page 494-528, June 2022.