Ranking theory is one of the salient formal representations of doxastic states. It differs from others in being able to represent belief in a proposition (= taking it to be true), to also represent degrees of belief (i.e. beliefs as more or less firm), and thus to generally account for the dynamics of these beliefs. It does so on the basis of fundamental and compelling rationality postulates and is hence one way of explicating the rational structure of doxastic states. Thereby (...) it provides foundations for accounts of defeasible or nonmonotonic reasoning. It has widespread applications in philosophy, it proves to be most useful in Artificial Intelligence, and it has started to find applications as a model of reasoning in psychology. (shrink)

In this article we explore multiple change operators, i.e., operators in which the epistemic input is a set of sentences instead of a single sentence. We propose two types of change: prioritized change, in which the input set is fully accepted, and symmetric change, where both the epistemic state and the epistemic input are equally treated. In both kinds of operators we propose a set of postulates and we present different constructions: kernel changes and partial meet changes.

There are several approaches implementing reasoning based on conditional knowledge bases, one of the most popular being System Z (Pearl, Proceedings of the 3rd conference on theoretical aspects of reasoning about knowledge, TARK ’90, Morgan Kaufmann Publishers Inc., San Francisco, CA, USA, pp. 121–135, 1990). We look at ranking functions (Spohn, The Laws of Belief: Ranking Theory and Its Philosophical Applications, Oxford University Press, Oxford, 2012) in general, conditional structures and c-representations (Kern-Isberner, Conditionals in Nonmonotonic Reasoning and Belief Revision: Considering (...) Conditionals as Agents, vol. 2087 of LNCS, Springer, Berlin, 2001) in order to examine the reasoning strength of the different approaches by learning which of the known calculi of nonmonotonic reasoning (System P and R) and Direct Inference are applicable to these inference relations. Furthermore we use the recently proposed Enforcement-postulate (Kern-Isberner and Krümpelmann, Proceedings of the 22nd international joint conference on artificial intelligence, vol. 2, IJCAI’11, AAAI Press, pp. 937–942, 2011) to show dependencies between these approaches. (shrink)

Conditionals are omnipresent, in everyday life as well as in scientific environments; they represent generic knowledge acquired inductively or learned from books. They tie a flexible and highly interrelated network of connections along which reasoning is possible and which can be applied to different situations. Therefore, conditionals are important, but also quite problematic objects in knowledge representation. This book presents a new approach to conditionals which captures their dynamic, non-proportional nature particularly well by considering conditionals as agents shifting possible worlds (...) in order to establish relationships and beliefs. This understanding of conditionals yields a rich theory which makes complex interactions between conditionals transparent and operational. Moreover,it provides a unifying and enhanced framework for knowledge representation, nonmonotonic reasoning, belief revision,and even for knowledge discovery. (shrink)

We propose a revision operator on a stratified belief base, i.e., a belief base that stores beliefs in different strata corresponding to the value an agent assigns to these beliefs. Furthermore, the operator will be defined as to perform the revision in such a way that information is never lost upon revision but stored in a stratum or layer containing information perceived as having a lower value. In this manner, if the revision of one layer leads to the rejection of (...) some information to maintain consistency, instead of being withdrawn it will be kept and introduced in a different layer with lower value. Throughout this development we will follow the principle of minimal change, being one of the important principles proposed in belief change theory, particularly emphasized in the AGM model. Regarding the reasoning part from the stratified belief base, the agent will obtain the inferences using an argumentative formalism. Thus, the argumentation framework will decide which information prevails when sentences of different layers are used for entailing conflicting beliefs. We will also illustrate how inferences are changed and how the status of arguments can be modified after a revision process. (shrink)

There are numerous formal systems that allow inference of new conditionals based on a conditional knowledge base. Many of these systems have been analysed theoretically and some have been tested against human reasoning in psychological studies, but experiments evaluating the performance of such systems are rare. In this article, we extend the experiments in [19] in order to evaluate the inferential properties of c-representations in comparison to the well-known Systems P and Z. Since it is known that System Z and (...) c-representations mainly differ in the sorts of inheritance inferences they allow, we discuss subclass inheritance and present experimental data for this type of inference in particular. (shrink)

The knowledge representation and reasoning of both humans and artificial systems often involves conditionals. A conditional connects a consequence which holds given a precondition. It can be easily recognized in natural languages with certain key words, like “if” in English. A vast amount of literature in both fields, both artificial intelligence and psychology, deals with the questions of how such conditionals can be best represented and how these conditionals can model human reasoning. On the other hand, findings in the psychology (...) of reasoning, such as those in the Suppression Task, have led to a paradigm shift from the monotonicity assumptions in human inferences towards nonmonotonic reasoning. Nonmonotonic reasoning is sensitive for information change, that is, inferences are drawn cautiously such that retraction of previous information is not required with the addition of new information. While many formalisms of nonmonotonic reasoning have been proposed in the field of Artificial Intelligence, their capability to model properties of human reasoning has not yet been extensively investigated. In this paper, we analyzed systematically from both a formal and an empirical perspective the power of formal nonmonotonic systems to model possible explicit defeaters, as in the Suppression Task, and more implicit conditional rules that trigger nonmonotonic reasoning by the keywords in such rules. The results indicated that the classical evaluation for the correctness of inferences has to be extended in the three major aspects regarding the inference system, the knowledge base, and possible assumed exceptions for the rule. (shrink)

Conditionals are most important objects in knowledge representation, commonsense reasoning and belief revision. Due to their non-classical nature, however, they are not easily dealt with. This paper presents a new approach to conditionals, which is apt to capture their dynamic power particularly well. We show how this approach can be applied to represent conditional knowledge inductively, and to guide revisions of epistemic states by sets of beliefs. In particular, we generalize system-Z* as an appropriate counterpart to maximum entropy-representations in a (...) semi-quantitative setting, and provide a theoretical justification to make its basic ideas usable also for belief revision. (shrink)

The idea of preserving conditional beliefs emerged recently as a new paradigm apt to guide the revision of epistemic states. Conditionals are substantially different from propositional beliefs and need specific treatment. In this paper, we present a new approach to conditionals, capturing particularly well their dynamic part as revision policies. We thoroughly axiomatize a principle of conditional preservation as an indifference property with respect to conditional structures of worlds. This principle is developed in a semi-quantitative setting, so as to reveal (...) its fundamental meaning for belief revision in quantitative as well as in qualitative frameworks. In fact, it is shown to cover other proposed approaches to conditional preservation. (shrink)

The idea of preserving conditional beliefs emerged recently as a new paradigm apt to guide the revision of epistemic states. Conditionals are substantially different from propositional beliefs and need specific treatment. In this paper, we present a new approach to conditionals, capturing particularly well their dynamic part as revision policies. We thoroughly axiomatize a principle of conditional preservation as an indifference property with respect to conditional structures of worlds. This principle is developed in a semi-quantitative setting, so as to reveal (...) its fundamental meaning for belief revision in quantitative as well as in qualitative frameworks. In fact, it is shown to cover other proposed approaches to conditional preservation. (shrink)

This article aims to achieve two goals: to show that probability is not the only way of dealing with uncertainty ; and to provide evidence that logic-based methods can well support reasoning with uncertainty. For the latter claim, two paradigmatic examples are presented: logic programming with Kleene semantics for modelling reasoning from information in a discourse, to an interpretation of the state of affairs of the intended model, and a neural-symbolic implementation of input/output logic for dealing with uncertainty in dynamic (...) normative contexts. (shrink)

This special issue “Inferences and Information Processing in a Conditional Framework“ is dedicated to conditionals as central objects for inferencing and information processing. It presents selected revised papers of the Workshop on Conditionals, Information, and Inference, CII'04, held in Ulm, Germany, co-located with the German national conference on AI, KI'2004.Conditional statements If A then B carry a very special kind of information that can not be captured by interpreting them as material implications. Roughly speaking, the premise, A, provides a context (...) in which it seems plausible to conclude B. So, each conditional can be seen as establishing a tight but flexible link between premise and conclusion, making up a unique piece of information. This link can and has been used successfully for knowledge representation, in particular, for nonclassical inferences and revising beliefs.It is just this generic, dynamic nature of conditionals that makes them most fascinating objects which are, however, difficult to control. But it seems that the problems one typically encounters when using conditionals for reasoning, mostly occur due to the narrowness of thinking strictly along classical lines that we have been getting used to. Classical logic has imposed a rigidity on human thinking that helped a lot making reasoning formal, precise, and clear. Conditionals, on the other hand, open up dimensions beyond classical theories, leaving room for plausibility, uncertainty, intuition, and commonsense reasoning. Philosophers and logicians have been discussing their logical nature since the …. (shrink)