Various theories try to give accounts of how measures of this confidence do or ought to behave, both as far as the internal mental consistency of the agent as ...

Degrees of belief are familiar to all of us. Our confidence in the truth of some propositions is higher than our confidence in the truth of other propositions. We are pretty confident that our computers will boot when we push their power button, but we are much more confident that the sun will rise tomorrow. Degrees of belief formally represent the strength with which we believe the truth of various propositions. The higher an agent’s degree of belief for a particular (...) proposition, the higher her confidence in the truth of that proposition. For instance, Sophia’s degree of belief that it will be sunny in Vienna tomorrow might be .52, whereas her degree of belief that the train will leave on time might be .23. The precise meaning of these statements depends, of course, on the underlying theory of degrees of belief. These theories offer a formal tool to measure degrees of belief, to investigate the relations between various degrees of belief in different propositions, and to normatively evaluate degrees of belief. (shrink)

This paper argues that formal models of coherence are useful for constructing a legal epistemology. Two main formal approaches to coherence are examined: coherence-based models of belief revision and the theory of coherence as constraint satisfaction. It is shown that these approaches shed light on central aspects of a coherentist legal epistemology, such as the concept of coherence, the dynamics of coherentist justification in law, and the mechanisms whereby coherence may be built in the course of legal decision-making.

Conceptual limitations restrict our epistemic options. One cannot believe, disbelieve, or doubt what one cannot grasp. I show how, even granting an epistemic ought-implies-can principle, such restrictions might lead to epistemic dilemmas: situations where each of one’s options violates some epistemic requirement. An alternative reaction would be to take epistemic norms to be sensitive to one’s options in ways that ensure dilemmas never arise. I propose, on behalf of the dilemmist, that we treat puzzlement as a kind of epistemic residue, (...) roughly analogous with guilt, appropriate only when one has violated an epistemic requirement. Sometimes, in bumping up against the limits of one’s concepts, it is appropriate to be puzzled no matter what one believes. Puzzlement can thus play the same role in an epistemic dilemmist’s theory that guilt plays in the theories of many moral dilemmists. (shrink)

This thesis investigates a sort of non-prioritized multiple revision, the operation of making up one's mind, and its generalization, the operation of choice revision. Making up one's mind about a sentence is a belief change that takes the agent to a belief state in which either the sentence or its negation is believed. In choice revision, the input information is represented by a set of sentences, and the agent should make a choice on which sentences to be accepted. Apart from (...) being practically important, these operations are technically interesting since the standard approach of intersecting a set of optimal outcomes is not workable. Paper I provides a construction based on descriptor revision in which the operation of making up one's mind can be modelled in a ``select-direct'' way, which is different from the traditional ``select-and-intersect'' methodology employed in the AGM model. The article shows that this construction is axiomatically characterized with a set of plausible postulates, and investigates the additional postulates that correlate with properties of the construction. Paper II investigates a new modelling for sentential belief revision operations, which is based on a set of relations on sentences named believability relations. It demonstrates that two special kinds of such relations, i.e. H-believability relations and basic believability relations, are faithful alternative models of two typical sentential revision generated from descriptor revision. It also shows that traditional AGM revision operations can be reconstructed from a strengthened variant of the basic believability relation and there exists a close connection between this strengthened believability relation and the standard epistemic entrenchment relation. Paper III studies the constructions of choice revision based on descriptor revision and multiple believability relations, which extends the domain of believability relations from sentences to sets of sentences. It is shown that each of two variants of choice revision based on descriptor revision is axiomatically characterized with a set of plausible postulates, assuming that the object language is finite. Furthermore, without assuming a finite language, it is shown that choice revision constructed from multiple believability relations is axiomatically characterized with the same sets of postulates proposed for choice revision derived from descriptor revision, whenever these relations satisfy certain rationality conditions. Paper IV explores choice revision on belief bases. A generalized version of expansion operation called partial expansion is introduced for developing models of this kind of choice revision. Based on the partial expansion as well as two multiple contraction operations from the literature, two kinds of choice revision operators on belief bases are constructed. This paper proposes several postulates for such two operators and shows that they can be axiomatically characterized by such postulates. Furthermore, it investigates two kinds of making up one's mind operators generated from these two choice revision operators and presents the axiomatic characterizations of them. (shrink)

Nonindexical Context-Dependence and the Interpretation as Abduction Approach Inclusive nonindexical context-dependence occurs when the preferred interpretation of an utterance implies its lexically-derived meaning. It is argued that the corresponding processes of free or lexically mandated enrichment can be modeled as abductive inference. A form of abduction is implemented in Simple Type Theory on the basis of a notion of plausibility, which is in turn regarded a preference relation over possible worlds. Since a preordering of doxastic alternatives taken for itself only (...) amounts to a relatively vacuous ad hoc model, it needs to be combined with a rational way of learning from new evidence. Lexicographic upgrade is implemented as an example of how an agent might revise his plausibility ordering in light of new evidence. Various examples are given how this apparatus may be used to model the contextual resolution of context-dependent or semantically incomplete utterances. The described form of abduction is limited and merely serves as a proof of concept, but the idea in general has good potential as one among many ways to build a bridge between semantics and pragmatics since inclusive context-dependence is ubiquitous. (shrink)

We examine carefully the rationale underlying the approaches to belief change taken in the literature, and highlight what we view as methodological problems. We argue that to study belief change carefully, we must be quite explicit about the ontology or scenario underlying the belief change process. This is something that has been missing in previous work, with its focus on postulates. Our analysis shows that we must pay particular attention to two issues that have often been taken for granted: the (...) first is how we model the agent's epistemic state. (Do we use a set of beliefs, or a richer structure, such as an ordering on worlds? And if we use a set of beliefs, in what language are these beliefs are expressed?) We show that even postulates that have been called beyond controversy are unreasonable when the agent's beliefs include beliefs about her own epistemic state as well as the external world. The second is the status of observations. (Are observations known to be true, or just believed? In the latter case, how firm is the belief?) Issues regarding the status of observations arise particularly when we consider iterated belief revision, and we must confront the possibility of revising by and then by ¬. (shrink)

In an earlier paper [Rational choice and AGM belief revision, _Artificial Intelligence_, 2009] a correspondence was established between the set-theoretic structures of revealed-preference theory (developed in economics) and the syntactic belief revision functions of the AGM theory (developed in philosophy and computer science). In this paper we extend the re-interpretation of those structures in terms of one-shot belief revision by relating them to the trichotomous attitude towards information studied in Garapa (Rev Symb Logic, 1–21, 2020) where information may be either (...) (1) fully accepted or (2) rejected or (3) taken seriously but not fully accepted. We begin by introducing the syntactic notion of _filtered belief revision_ and providing a characterization of it in terms of a mixture of both AGM revision and contraction. We then establish a correspondence between the proposed notion of filtered belief revision and the above-mentioned set-theoretic structures, interpreted as semantic _partial_ belief revision structures. We also provide an interpretation of the trichotomous attitude towards information in terms of the degree of implausibility of the information. (shrink)

In The Uses of Argument, Stephen Toulmin proposed a model for the layout of arguments: claim, data, warrant, qualifier, rebuttal, backing. Since then, Toulmin’s model has been appropriated, adapted and extended by researchers in speech communications, philosophy and artificial intelligence. This book assembles the best contemporary reflection in these fields, extending or challenging Toulmin’s ideas in ways that make fresh contributions to the theory of analysing and evaluating arguments.

The main purpose of this paper is to propose and defend anew definition of synonymy. Roughly (and slightly misleadingly), theidea is that two expressions are synonymous iff intersubstitutions insentences preserve the degree of doxastic revisability. In Section 1 Iargue that Quine''s attacks on analyticity leave room for such adefinition. The definition is presented in Section 2, and Section 3elaborates on the concept of revisability. The definition is defendedin Sections 4 and 5. It is, inter alia, shown that the definition hasdesired (...) formal properties. In Sections 6 and 7 I briefly comment on,first, the relation of the definition to Quine''s later ideas about (stimulus)synonymy, and, second, its relation to a general, interlinguistic, conceptof meaning. (shrink)

This article investigates the properties of multistate top revision, a dichotomous model of belief revision that is based on an underlying model of probability revision. A proposition is included in the belief set if and only if its probability is either 1 or infinitesimally close to 1. Infinitesimal probabilities are used to keep track of propositions that are currently considered to have negligible probability, so that they are available if future information makes them more plausible. Multistate top revision satisfies a (...) slightly modified version of the set of basic and supplementary AGM postulates, except the inclusion and success postulates. This result shows that hyperreal probabilities can provide us with efficient tools for overcoming the well known difficulties in combining dichotomous and probabilistic models of belief change. (shrink)

In the literature of belief revision, it is widely accepted that: there is only one revision phase in belief revision which is well characterized by the Bayes’ Rule, Jeffrey’s Rule, etc.. However, as I argue in this article, there are at least four successive phases in belief revision, namely first/second order evaluation and first/second order revision. To characterize these phases, I propose mainly four rules of belief revision based on agent’s criteria, and make one composition rule to characterize belief revision (...) as a whole. (shrink)

A range of formal models of human reasoning have been proposed in a number of fields such as philosophy, logic, artificial intelligence, computer science, psychology, cognitive science, etc.: various logics, probabilistic systems, belief revision systems, neural networks, among others. Now, it seems reasonable to require that formal models of human reasoning be empirically adequate if they are to be viewed as models of the phenomena in question. How are formal models of human reasoning typically put to empirical test? One way (...) to do so is to isolate a number of key principles of the system, and design experiments to gauge the extent to which participants do or do not follow them in reasoning tasks. Another way is to take relevant existing results and check whether a particular formal model predicts these results. The present investigation provides an illustration of the second kind of empirical testing by comparing two formal models for reasoning – namely the non-monotonic logic known as preferential logic; and a particular version of belief revision theories, screened belief revision – against the reasoning phenomenon known as belief bias in the psychology of reasoning literature: human reasoners typically seek to maintain the beliefs they already hold, and conversely to reject contradicting incoming information. The conclusion of our analysis will be that screened belief revision is more empirically adequate with respect to belief bias than preferential logic and non-monotonic logics in general, as what participants seem to be doing is above all a form of belief management on the basis of background knowledge. The upshot is thus that, while it may offer valuable insights into the nature of human reasoning, preferential logic is ultimately inadequate as a formal model of the phenomena in question. (shrink)

Modern belief revision theory is based to a large extent on partial meet contraction that was introduced in the seminal article by Carlos Alchourrón, Peter Gärdenfors, and David Makinson that appeared in 1985. In the same year, Alchourrón and Makinson published a significantly different approach to the same problem, called safe contraction. Since then, safe contraction has received much less attention than partial meet contraction. The present paper summarizes the current state of knowledge on safe contraction, provides some new results (...) and offers a list of unsolved problems that are in need of investigation. (shrink)

A model of coherentist belief contraction is constructed. The outcome of belief contraction is required to be one of the coherent subsets of the original belief set, and a set of plausible properties is proposed for this set of coherent subsets. The contraction operators obtained in this way are shown to coincide with well-known belief base operations. This connection between coherentist and foundationalist approaches to belief change has important implications for the philosophical interpretation of models of belief change.

When an agent can not recognize, immediately, the implausible part of new information received, she will usually first expand her belief state by the new information, and then she may encounter some belief conflicts, and find the implausible information based on her criteria to consolidate her belief state. This process indicates a new kind of non-prioritized multiple revision, called metabolic revision. I give some axiomatic postulates for metabolic revision and propose two functional constructions for it, namely kernel metabolic revision and (...) partial meet metabolic revision, with respect to which the representation theorems are proved. I also compare metabolic revision with some related works in the literature, including semi-revision, merging with integrity constraints, evaluation, and evaluative multiple revision. (shrink)

We introduce a new operator, called rational evaluation, in belief change. The operator evaluates new information according to the agent’s core beliefs, and then exports the plausible part of the new information. It belongs to the decision module in belief change. We characterize rational evaluation by axiomatic postulates and propose two functional constructions for it, based on the well-known constructions of kernel sets and remainder sets, respectively. The main results of the paper are two representation theorems with respect to the (...) two functional constructions. We also compare and connect the evaluation operator with some related operators in belief revision, including contraction, set contraction, and prioritized multiple revision. (shrink)

This paper presents a Ramsey account of conditionals within the framework of an implemented reason maintenance system. The reason maintenance system is built on top of a deductive reasoning engine based on relevance logic. Thus, the account of conditionals provided is not susceptible to the fallacies of relevance. In addition, it is shown that independently motivated requirements on practical relevant reason maintenance allow us to gracefully circumvent Gärdenfors's triviality result.

The thesis that every truth is knowable is usually glossed by decomposing knowability into possibility and knowledge. Under elementary assumptions about possibility and knowledge, considered as modal operators, the thesis collapses the distinction between truth and knowledge (as shown by the so-called Fitch-argument). We show that there is a more plausible interpretation of knowability—one that does not decompose the notion in the usual way—to which the Fitch-argument does not apply. We call this the potential knowledge-interpretation of knowability. We compare our (...) interpretation with the rephrasal of knowability proposed by Edgington and Rabinowicz and Segerberg, inserting an actuality-operator. This proposal shares some key features with ours but suffers from requiring specific transworld-knowledge. We observe that potential knowledge involves no transworld-knowledge. We describe the logic of potential knowledge by providing models for interpreting the new operator. Finally we show that the knowability thesis can be added to elementary conditions on potential knowledge without collapsing modal distinctions. (shrink)

A new formal model of belief dynamics is proposed, in which the epistemic agent has both probabilistic beliefs and full beliefs. The agent has full belief in a proposition if and only if she considers the probability that it is false to be so close to zero that she chooses to disregard that probability. She treats such a proposition as having the probability 1, but, importantly, she is still willing and able to revise that probability assignment if she receives information (...) that gives her sufficient reasons to do so. Such a proposition is undoubted, but not undoubtable. In the formal model it is assigned a probability 1 − δ, where δ is an infinitesimal number. The proposed model employs probabilistic belief states that contain several underlying probability functions representing alternative probabilistic states of the world. Furthermore, a distinction is made between update and revision, in the same way as in the literature on belief change. The formal properties of the model are investigated, including properties relevant for learning from experience. The set of propositions whose probabilities are infinitesimally close to 1 forms a belief set. Operations that change the probabilistic belief state give rise to changes in this belief set, which have much in common with traditional operations of belief change. (shrink)

This book provides a critical examination of how the choice of what to believe is represented in the standard model of belief change. In particular the use of possible worlds and infinite remainders as objects of choice is critically examined. Descriptors are introduced as a versatile tool for expressing the success conditions of belief change, addressing both local and global descriptor revision. The book presents dynamic descriptors such as Ramsey descriptors that convey how an agent’s beliefs tend to be changed (...) in response to different inputs. It also explores sentential revision and demonstrates how local and global operations of revision by a sentence can be derived as a special case of descriptor revision. Lastly, the book examines revocation, a generalization of contraction in which a specified sentence is removed in a process that may possibly also involve the addition of some new information to the belief set. (shrink)

Most approaches to iterated belief revision are accompanied by some motivation for the use of the proposed revision operator (or family of operators), and typically encode enough information in the epistemic state of an agent for uniquely determining one-step revision. But in those approaches describing a family of operators there is usually little indication of how to proceed uniquely after the first revision step. In this paper we contribute towards addressing that deficiency by providing a formal framework which goes beyond (...) the first revision step in two ways. First, the framework is obtained by enriching the epistemic state of an agent starting from the following intuitive idea: we associate to each world x two abstract objects x⁺ and x⁻, and we assume that, in addition to preferences over the set of worlds, we are given preferences over this set of objects as well. The latter can be considered as meta-information encoded in the epistemic state which enables us to go beyond the first revision step of the revision operator being applied, and to obtain a unique set of preferences over worlds. We then extend this framework to consider, not only the revision of preferences over worlds, but also the revision of this extended structure itself. We look at some desirable properties for revising the structure and prove the consistency of these properties by giving a concrete operator satisfying all of them. Perhaps more importantly, we show that this framework has strong connections with two other types of constructions in related areas. Firstly, it can be seen as a special case of preference aggregation which opens up the possibility of extending the frame-work presented here into a full-fledged framework for preference aggregation and social choice theory. Secondly, it is related to existing work on the use of interval orderings in a number of different contexts. (shrink)

I argue that the analysis most capable of systematising our intuitions about coherence as a relation is one according to which a set of beliefs, A, coheres with another set, B, if and only if the set-theoretical union of A and B is a coherent set. The second problem I consider is the role of coherence in epistemic justification. I submit that there are severe problems pertaining to the idea, defended most prominently by Keith Lehrer, that justification amounts to coherence (...) with an acceptance system. Instead I advance a more dynamic approach according to which the problem of justification is the problem of how to merge new information with old coherently, a process which is seen to be closely connected with relational coherence. (shrink)

We investigate an approach for drawing logical inference from inconsistent premisses. The main idea in this approach is that the inconsistencies in the premisses should be interpreted as uncertainty of the information. We propose a mechanism, based on Kinght’s [14] study of inconsistency, for revising an inconsistent set of premisses to a minimally uncertain, probabilistically consistent one. We will then generalise the probabilistic entailment relation introduced in [15] for propositional languages to the first order case to draw logical inference from (...) a probabilistic set of premisses. We will show how this combination can allow us to limit the effect of uncertainty introduced by inconsistent premisses to only the reasoning on the part of the premise set that is relevant to the inconsistency. (shrink)

There is a deep tension between logical and probabilistic norms of belief. This article illustrates the normative force that is associated with these frameworks by showing how rather unrestricted belief bases can be improved by undergoing logical and probabilistic reflection. It is argued that probabilistic reasoning accounts for the reliability of the conclusions one can draw from the beliefs. Most importantly, reliability commands us to care for the increasing uncertainty of conjunctions of beliefs. Deductive logic captures the agent's commitment towards (...) all conclusions of her beliefs. In other words, it seems that commitment forces the agent to believe conclusions, which reliability tells her to view with scepticism. This conflict is resolved by arguing that commitment merely forces the agent to find the logical conclusions of her beliefs acceptable, not necessarily to believe them. This demands consistency but no deductive closure. Furthermore, it is shown that by restoring consistency, a straightforward connection between high subjective probability and full belief is undermined. Finally, the article delineates how this approach deals with the lottery paradox and the preface paradox. (shrink)

This paper focuses on the extension of AGM that allows change for a belief base by a set of sentences instead of a single sentence. In [FH94], Fuhrmann and Hansson presented an axiomatic for Multiple Contraction and a construction based on the AGM Partial Meet Contraction. We propose for their model another way to construct functions: Multiple Kernel Contraction, that is a modification of Kernel Contraction, proposed by Hansson [Han94] to construct classical AGM contractions and belief base contractions. This construction (...) works out the unsolved problem pointed out by Hansson in [Han99, pp. 369]. (shrink)

This paper aims at comparing and relating belief revision and argumentation as approaches to model reasoning processes. Referring to some prominent literature references in both fields, we will discuss their (implicit or explicit) assumptions on the modeled processes and hence commonalities and differences in the forms of reasoning they are suitable to deal with. The intended contribution is on one hand assessing the (not fully explored yet) relationships between two lively research fields in the broad area of defeasible reasoning and (...) on the other hand pointing out open issues and potential directions for future research. (shrink)

This survey is the first to review the combination of computational trust and argumentation. The combination of the two approaches seems like a natural match, with the two areas tackling different aspects of reasoning in an uncertain, social environment. We discuss the different areas of research and describe the approaches taken so far, analysing both how they address the problems and the challenges that are unaddressed.

The 1985 paper by Carlos Alchourrón, Peter Gärdenfors, and David Makinson, “On the Logic of Theory Change: Partial Meet Contraction and Revision Functions” was the starting-point of a large and rapidly growing literature that employs formal models in the investigation of changes in belief states and databases. In this review, the first twenty-five years of this development are summarized. The topics covered include equivalent characterizations of AGM operations, extended representations of the belief states, change operators not included in the original (...) framework, iterated change, applications of the model, its connections with other formal frameworks, computatibility of AGM operations, and criticism of the model. (shrink)

An agent can usually hold a very large number of beliefs. However, only a small part of these beliefs is used at a time. Efficient operations for belief change should affect the beliefs of the agent locally, that is, the changes should be performed only in the relevant part of the belief state. In this paper we define a local consequence operator that only considers the relevant part of a belief base. This operator is used to define local versions of (...) the operations for belief change. Representation theorems are given for the local operators. (shrink)

Belief revision is concerned with belief change fired by incoming information. Despite the variety of frameworks representing it, most revision policies share one crucial feature: incoming information outweighs current information and hence, in case of conflict, incoming information will prevail. However, if one is interested in representing the way actual humans revise their beliefs, one might not always want for the agent to blindly believe everything they are told. This manuscript presents a semantic approach to non-prioritized belief revision. It uses (...) plausibility models for depicting an agent’s beliefs, and model operations for displaying the way beliefs change. The first proposal, semantically-based screened revision, compares the current model with the one the revision would yield, accepting or rejecting the incoming information depending on whether the ‘differences’ between these models go beyond a given threshold. The second proposal, semantically-based gradual revision, turns the binary decision of acceptance or rejection into a more general setting in which a revision always occurs, with the threshold used rather to choose ‘the right revision’ for the given input and model. (shrink)

In the area known as model-based diagnosis, a system is described by-means of a set of formulas together with assumptions that all the components are functioning correctly. When we observe a behavior of the system which is inconsistent with the system description, we must relax some of the assumptions. In previous work, we have presented operations of belief change which only affect the relevant part of a belief base. In this paper, we propose the application of the same strategy to (...) the problem of model-based diagnosis. We Erst isolate the subset of the system description which is relevant for a given observation. By doing this, we reduce the size of the problem and then solve the diagnosis problem for the relevant subset. (shrink)

The axiom of recovery, while capturing a central intuition regarding belief change, has been the source of much controversy. We argue briefly against putative counterexamples to the axiom—while agreeing that some of their insight deserves to be preserved—and present additional recovery-like axioms in a framework that uses epistemic states, which encode preferences, as the object of revisions. This makes iterated revision possible and renders explicit the connection between iterated belief change and the axiom of recovery. We provide a representation theorem (...) that connects the semantic conditions we impose on iterated revision and our additional syntactical properties. We show interesting similarities between our framework and that of Darwiche–Pearl (Artificial Intelligence 89:1–29 1997). In particular, we show that intuitions underlying the controversial (C2) postulate are captured by the recovery axiom and our recovery-like postulates (the latter can be seen as weakenings of (C2)). We present postulates for contraction, in the same spirit as the Darwiche–Pearl postulates for revision, and provide a theorem that connects our syntactic postulates with a set of semantic conditions. Lastly, we show a connection between the contraction postulates and a generalisation of the recovery axiom. (shrink)