We investigate the discrete (finite) case of the Popper–Renyi theory of conditional probability, introducing discrete conditional probabilistic models for knowledge and conditional belief, and comparing them with the more standard plausibility models. We also consider a related notion, that of safe belief, which is a weak (non-negatively introspective) type of “knowledge”. We develop a probabilistic version of this concept (“degree of safety”) and we analyze its role in games. We completely axiomatize the logic of conditional belief, (...) knowledge and safe belief over conditional probabilistic models. We develop a theory of probabilistic dynamic belief revision, introducing probabilistic “action models” and proposing a notion of probabilistic update product, that comes together with appropriate reduction laws. (shrink)

In this paper we present a new modeling for belief revision that is what we term irrevocable. This modeling is of philosophical interest since it captures some features of suppositional reasoning, and of formal interest since it is closely connected with AGM, yet provides for iterated belief revision. The analysis is couched in terms of dynamic doxastic logic.

We show how belief revision can be treated systematically in the format of dynamicepistemic logic, when operators of conditional belief are added. The core engine consists of definable update rules for changing plausibility relations between worlds, which have been proposed independently in the dynamic-epistemic literature on preference change. Our analysis yields two new types of modal result. First, we obtain complete logics for concrete mechanisms of belief revision, based on compositional reduction axioms. Next, (...) we show how various abstract postulates for belief revision can be analyzed by standard modal frame correspondences for model-changing operations. (shrink)

We propose a dynamic hyperintensional logic of belief revision for non-omniscient agents, reducing the logical omniscience phenomena affecting standard doxastic/epistemic logic as well as AGM belief revision theory. Our agents don’t know all a priori truths; their belief states are not closed under classical logical consequence; and their belief update policies are such that logically or necessarily equivalent contents can lead to different revisions. We model both plain and conditional belief, (...) then focus on dynamic belief revision. The key idea we exploit to achieve non-omniscience focuses on topic- or subject matter-sensitivity: a feature of belief states which is gaining growing attention in the recent literature. (shrink)

I want to look at recent developments of representing AGM-style belief revision in dynamic epistemic logics and the options for doing something similar for ranking theory. Formally, my aim will be modest: I will define a version of basic dynamic doxastic logic using ranking functions as the semantics. I will show why formalizing ranking theory this way is useful for the ranking theorist first by showing how it enables one to compare ranking theory more easily (...) with other approaches to belief revision. I will then use the logic to state an argument for defining ranking functions on larger sets of ordinals than is customary. Secondly, I will argue that the only way to extend the account of belief revision given by ranking theory to higher-order beliefs and revisions is by continuing the approach taken by me and defining ranking theoretical equivalents of dynamic epistemic logics. For proponents of dynamic epistemic logic, such logics will naturally be of interest provided they are convinced of the revision operator defined by ranking theory. (shrink)

We consider the connections between belief revision, conditional logic and nonmonotonic reasoning, using as a foundation the approach to theory change developed by Alchourrón, Gärdenfors and Makinson (the AGM approach). This is first generalized to allow the iteration of theory change operations to capture the dynamics of epistemic states according to a principle of minimal change of entrenchment. The iterative operations of expansion, contraction and revision are characterized both by a set of postulates and by Grove's (...) construction based on total pre-orders on the set of complete theories of the belief logic. We present a sound and complete conditional logic whose semantics is based on our iterative revision operation, but which avoids Gärdenfors's triviality result because of a severely restricted language of beliefs and hence the weakened scope of our extended postulates. In the second part of the paper, we develop a computational approach to theory dynamics using Rott's E-bases as a representation for epistemic states. Under this approach, a ranked E-base is interpreted as standing for the most conservative entrenchment compatible with the base, reflecting a kind of foundationalism in the acceptance of evidence for a belief. Algorithms for the computation of our iterative versions of expansion, contraction and revision are presented. Finally, we consider the relationship between nonmonotonic reasoning and both conditional logic and belief revision. Adapting the approach of Delgrande, we show that the unique extension of a default theory expressed in our conditional logic of belief revision corresponds to the most conservative belief state which respects the theory: however, this correspondence is limited to propositional default theories. Considering first order default theories, we present a belief revision algorithm which incorporates the assumption of independence of default instances and propose the use of a base logic for default reasoning which incorporates uniqueness of names. We conclude with an examination of the behavior of an implemented system on some of Lifschitz's benchmark problems in nonmonotonic reasoning. (shrink)

Krister Segerberg proposed irrevocable belief revision, to be contrasted with standard belief revision, in a setting wherein belief of propositional formulas is modelled explicitly. This suggests that in standard belief revision is revocable: one should be able to unmake (‘revoke’) the fresh belief in the revision formula, given yet further information that contradicts it. In a dynamic epistemic logical setting for belief revision, for multiple agents, we investigate what (...) the requirements are for revocable belief revision. By this we not merely mean recovering belief in non-modal propositions, as in the recovery principle for belief contraction, but recovering belief in modal propositions: beliefs about beliefs. These requirements are almost never met, a surprising result. (shrink)

This talk shows how propositional dynamic logic (PDL) can be interpreted as a logic for multi-agent knowledge update and belief revision, or as a logic of preference change, if the basic relations are read as preferences instead of plausibilities. Our point of departure is the logic of communication and change (LCC) of [9]. Like LCC, our logic uses PDL as a base epistemic language. Unlike LCC, we start out from agent plausibilities, add (...) their converses, and build knowledge and belief operators from these with the PDL constructs. We extend the update mechanism of LCC to an update mechanism that handles belief change as relation substitution, and we show that the update part of this logic is more expressive than either that of LCC or that of epistemic/doxastic PDL with a belief change modality. Next, we show that the properties of knowledge and belief are preserved under any update, unlike in LCC. We prove completeness of the logic and give examples of its use. If there is time, we will also look at the preference interpretation of the system, and at preference change scenarios that can be modelled with it. (shrink)

In ‘belief revision’ a theory is revised with a formula φ resulting in a revised theory . Typically, is in , one has to give up belief in by a process of retraction, and φ is in . We propose to model belief revision in a dynamic epistemic logic. In this setting, we typically have an information state (pointed Kripke model) for the theory wherein the agent believes the negation of the revision (...) formula, i.e., wherein is true. The revision with φ is a program *φ that transforms this information state into a new information state. The transformation is described by a dynamic modal operator [*φ], that is interpreted as a binary relation [ [*φ] ] between information states. The next information state is computed from the current information state and the belief revision formula. If the revision is successful, the agent believes φ in the resulting state, i.e., Bφ is then true. To make this work, as information states we propose ‘doxastic epistemic models’ that represent both knowledge and degrees of belief. These are multi-modal and multi-agent Kripke models. They are constructed from preference relations for agents, and they satisfy various characterizable multi-agent frame properties. Iterated, revocable, and higher-order belief revision are all quite natural in this setting. We present, for an example, five different ways of such dynamic belief revision. One can also see that as a non-deterministic epistemic action with two alternatives, where one is preferred over the other, and there is a natural generalization to general epistemic actions with preferences. (shrink)

This paper shows how propositional dynamic logic can be interpreted as a logic for multi-agent belief revision. For that we revise and extend the logic of communication and change of [9]. Like LCC, our logic uses PDL as a base epistemic language. Unlike LCC, we start out from agent plausibilities, add their converses, and build knowledge and belief operators from these with the PDL constructs. We extend the update mechanism of LCC to (...) an update mechanism that handles belief change as relation substitution, and we show that the update part of this logic is more expressive than either that of LCC or that of doxastic/epistemic PDL with a belief change modality. It is shown that the properties of knowledge and belief are preserved under any update, and that the logic is complete. © 2008 Springer-Verlag Berlin Heidelberg. (shrink)

We use the normality framework of Goodman and Salow (2018, 2021, 2023b) to investigate of dynamics of rational belief. The guiding idea is that people are entitled to believe that their circumstances aren’t especially abnormal. More precisely, a rational agent’s beliefs rule out all and only those possibilities that are either (i) ruled out by their evidence or (ii) sufficiently less normal than some other possibility not ruled out by their evidence. Working within this framework, we argue that the (...) logic of rational belief revision is much weaker than is usually supposed. We do so by isolating a natural family of orthodox principles about belief revision, describing realistic cases in which these principles seem to fail, and showing how these counterexamples are predicted by independently motivated models of the cases in question. In these models, whether one evidential possibility counts as sufficiently less normal than another is determined by underlying probabilities (together with a contextually determined question). We argue that the resulting probabilistic account of belief compares favorably with other such accounts, including Lockeanism (Foley, 1993), a ‘stability’ account inspired by Leitgeb (2017), the ‘tracking theory’ of Lin and Kelly (2012), and the influential precursor of Levi (1967). We show that all of these accounts yield subtly different but similarly heterodox logics of belief revision. (shrink)

This book aims to lay bare the logical foundations of tractable reasoning. It draws on Marvin Minsky's seminal work on frames, which has been highly influential in computer science and, to a lesser extent, in cognitive science. Only very few people have explored ideas about frames in logic, which is why the investigation in this book breaks new ground. The apparent intractability of dynamic, inferential reasoning is an unsolved problem in both cognitive science and logic-oriented artificial intelligence. (...) By means of a logical investigation of frames and frame concepts, Andreas devises a novel logic of tractable reasoning, called frame logic. Moreover, he devises a novel belief revision scheme, which is tractable for frame logic. These tractability results shed new light on our logical and cognitive means to carry out dynamic, inferential reasoning. Modularity remains central for tractability, and so the author sets forth a logical variant of the massive modularity hypothesis in cognitive science. (shrink)

I develop a dynamic logic for reasoning about "interrogative belief revision", a new branch of belief revision theory that has been developed in a small number of papers, beginning with E. J. Olsson and D. Westlund's paper "On the role of the research agenda in epistemic change" [12]. In interrogative belief revision, epistemic states are taken to include a research agenda, consisting of questions the agent seeks to answer. I present a (...) class='Hi'>logic for revision of such epistemic states based on the notion of an epistemic strategy, a stable plan of action that determines changes in the agent's research agenda. This idea is a further development of an idea put forward in [6], that changes in the research agenda of an agent should be determined by stable, "long term" research interests. I provide complete axioms and a decidability result for the logic. (shrink)

This thesis deals with the theory of interrogative belief revision, a recent development in the subfield of philosophical logic known as belief revision theory. While classical belief revision theory deals with the dynamics of an agent’s beliefs, interrogative belief revision aims to describe the dynamics of the agent’s questions about the world, or research agenda, as well. Great emphasis is put on the interaction between belief change and changes in the (...) research agenda. I develop both the technical framework for this theory by constructing and investigating modal logics for reasoning about the dynamics of research interests, as well as pursuing further the philosophical foundations and applications of the theory. Among the contributions of the thesis are: - a novel interpretation of the theory founded on a notion of epistemic strategies - a solution to the previously open problem of contraction and revision in this context - several systems of modal logic that can be used to reason about interrogative belief revision - completeness results and decidability results for these logics - a characterization of a class of relevant conditionals based on a notion of agenda relevance. (shrink)

In the companion paper (Towards a “sophisticated” model of belief dynamics. Part I), a general framework for realistic modelling of instantaneous states of belief and of the operations involving them was presented and motivated. In this paper, the framework is applied to the case of belief revision. A model of belief revision shall be obtained which, firstly, recovers the Gärdenfors postulates in a well-specified, natural yet simple class of particular circumstances; secondly, can accommodate iterated (...) revisions, recovering several proposed revision operators for iterated revision as special cases; and finally, offers an analysis of Rott’s recent counterexample to several Gärdenfors postulates [32], elucidating in what sense it fails to be one of the special cases to which these postulates apply. (shrink)

This paper presents eight (previously unpublished) adaptive logics for belief revision, each of which define a belief revision operation in the sense of the AGM framework. All these revision operations are shown to satisfy the six basic AGM postulates for belief revision, and Parikh's axiom of Relevance. Using one of these logics as an example, we show how their proof theory gives a more dynamic flavor to belief revision than existing (...) approaches. It is argued that this turns belief revision (that obeys Relevance) into a more natural undertaking, where analytic steps are performed only as soon as they turn out to be necessary in order to uphold certain beliefs. (shrink)

I propose a novel hyperintensional semantics for belief revision and a corresponding system of dynamic doxastic logic. The main goal of the framework is to reduce some of the idealisations that are common in the belief revision literature and in dynamic epistemic logic. The models of the new framework are primarily based on potentially incomplete or inconsistent collections of information, represented by situations in a situation space. I propose that by shifting the (...) representational focus of doxastic models from belief sets to collections of information, and by defining changes of beliefs as artifacts of changes of information, we can achieve a more realistic account of belief representation and belief change. The proposed dynamic operation suggests a non-classical way of changing beliefs: belief revision occurs in non-explosive environments which allow for a non-monotonic and hyperintensional belief dynamics. A logic that is sound with respect to the semantics is also provided. (shrink)

This work contrasts conservative or minimally mutilating revisions of empirical theories as they are identified in the presently dominant AGM model of formal belief revision and the structuralist program for the reconstruction of empirical theories. The aim is to make understandable why both approaches only partly succeed in substantially informing and formally restraining the issue. With respect to the rationality of minimal change, the overall result is negative. Readers with an interest in formal epistemology are provided with application (...) cases (mercury anomaly, revision of early thermo-dynamics, introduction of the neutrino), the historically inclined reader is offered a systematic perspective. The discussion can largely be followed without a background in formal logic. (shrink)

This paper adds evidence structure to standard models of belief, in the form of families of sets of worlds. We show how these more fine-grained models support natural actions of “evidence management”, ranging from update with external new information to internal rearrangement. We show how this perspective leads to new richer languages for existing neighborhood semantics for modal logic. Our main results are relative completeness theorems for the resulting dynamic logic of evidence.

Scientists collect evidence in order to confirm or falsify scientific theories. Unfortunately, scientific evidence may sometimes be false or deceiving and as a consequence lead individuals to believe in a false theory. By interaction between scientists, such false beliefs may spread through the entire community. There is currently a debate about the effect of various network configurations on the epistemic reliability of scientific communities. To contribute to this debate from a logical perspective, this paper introduces an epistemic logical framework of (...) observation, interaction and belief revision in scientific communities. The presented sound and complete system provides the formal tools for qualitative analysis of the social dynamics of scientific inquiry. Furthermore, this paper includes detailed suggestions for future applications of the framework. (shrink)

The present paper aims at a synthesis of belief revision theory with the Sneed formalism known as the structuralist theory of science. This synthesis is brought about by a dynamisation of classical structuralism, with an abductive inference rule and base generated revisions in the style of Rott (2001). The formalism of prioritised default logic (PDL) serves as the medium of the synthesis. Why seek to integrate the Sneed formalism into belief revision theory? With the hybrid (...) system of the present investigation, a substantial simplification of the ranking information that is necessary to define revisions and contractions uniquely is achieved. This system is, furthermore, expressive enough to capture complex and non-trivial scientific examples. It is thus closely related to a novel research area within belief revision theory which addresses the dynamics of scientific knowledge. (shrink)

Belief revision theories aim to model the dynamics of epistemic states. Besides beliefs, epistemic states comprise most importantly justificational structures. Typically, belief revision theories, however, model the dynamics of beliefs while neglecting justificational structures over and above logical relations. Despite some awareness that this approach is problematic, how devastating the consequences of this neglect are has not yet been fully grasped. In this paper, I argue that taking justificational structures into account could solve four well-known problems (...) of belief revision. (shrink)

Postulational approaches attempt to understand the dynamics of belief revision by appealing to no more than the set of beliefs held by an agent and the logical relations between them. It is argued there that such an approach cannot work. A proper account of belief revision must also appeal to the arguments supporting beliefs, and recognize that those arguments can be defeasible. If we begin with a mature epistemological theory that accommodates this, it can be seen (...) that the belief revision operators on which the postulational theories are based are ill-defined. It is further argued that there is no way to repair the definitions so as to retain the spirit of those theory. Belief revision is better studied from within an independently motivated epistemological theory. (shrink)

The success of the AGM paradigmn, Gis remarkable, as even a quick look at the literature it has generated will testify. But it is also remarkable, at least in hindsight, how limited was the original effort. For example, the theory concerns the beliefs of just one agent; all incoming information is accepted; belief change is uniquely determined by the new information; there is no provision for nested beliefs. And perhaps most surprising: there is no analysis of iterated change.

Epistemic logic with its possible worlds semantic model is a powerful framework that allows us to represent an agent’s information not only about propositional facts, but also about her own information. Nevertheless, agents represented in this framework are logically omniscient: their information is closed under logical consequence. This property, useful in some applications, is an unrealistic idealisation in some others. Many proposals to solve this problem focus on weakening the properties of the agent’s information, but some authors have argued (...) that solutions of this kind are not completely adequate because they do not look at the heart of the matter: the actions that allow the agent to reach such omniscient state. Recent works have explored how acts of observation, inference, consideration and forgetting affect an agent’s implicit and explicit knowledge; the present work focuses on acts that affect an agent’s implicit and explicit beliefs. It starts by proposing a framework in which these two notions can be represented, and then it looks into their dynamics, first by reviewing the existing notion of belief revision, and then by introducing a rich framework for representing diverse forms of inference that involve both knowledge and beliefs. (shrink)

We contrast Bonanno’s ‘Belief Revision in a Temporal Framework’ [15] with preference change and belief revision from the perspective of dynamic epistemic logic (DEL). For that, we extend the logic of communication and change of [11] with relational substitutions [8] for preference change, and show that this does not alter its properties. Next we move to a more constrained context where belief and knowledge can be defined from preferences [29; 14; 5; 7], (...) prove completeness of a very expressive logic of belief revision, and define a mechanism for updating belief revision models using a combination of action priority update [7] and preference substitution [8]. (shrink)

In this paper we explore the relationship between norms of belief revision that may be adopted by members of a community and the resulting dynamic properties of the distribution of beliefs across that community. We show that at a qualitative level many aspects of social belief change can be obtained from a very simple model, which we call ‘threshold influence’. In particular, we focus on the question of what makes the beliefs of a community stable under (...) various dynamical situations. We also consider refinements and alternatives to the ‘threshold’ model, the most significant of which is to consider changes to plausibility judgements rather than mere beliefs. We show first that some such change is mandated by difficult problems with belief-based dynamics related to the need to decide on an order in which different beliefs are considered. Secondly, we show that the resulting plausibility-based account results in a deterministic dynamical system that is non-deterministic at the level of beliefs. (shrink)

We present a theory of truth in fiction that improves on Lewis's [1978] ‘Analysis 2’ in two ways. First, we expand Lewis's possible worlds apparatus by adding non-normal or impossible worlds. Second, we model truth in fiction as belief revision via ideas from dynamic epistemic logic. We explain the major objections raised against Lewis's original view and show that our theory overcomes them.

Scientific inquiry is represented as a process of rational hypothesis revision in the face of data. For the concept of rationality, we rely on the theory of belief dynamics as developed in [5, 9]. Among other things, it is shown that if belief states are left unclosed under deductive logic then scientific theories can be expanded in a uniform, consistent fashion that allows inquiry to proceed by any method of hypothesis revision based on "kernel" contraction. (...) In contrast, if belief states are closed under logic, then no such expansion is possible. (shrink)

Vlastos’ famous characterization of the Socratic elenchus focuses on two main aspects of this method: its epistemic roots and its dialogical nature. Our aim is to lay the groundwork to formally capture this characterization. To do so, first, we outline an epistemic framework in which the elenchus can be inscribed. More precisely, we focus our analysis on the passage from unconscious ignorance to conscious (or Socratic) ignorance and provide new insights about the epistemic outcome of an elenctic argument. Secondly, from (...) a logical perspective, we consider the elenchus as a dynamic exchange allowing Socrates’ respondents to revise their beliefs, on pain of inconsistency. By stressing this point, we represent this method as a process of belief revision in dynamic epistemic logic and provide a new logical solution to what Vlastos called the problem of the elenchus. (shrink)

In [11] it is shown how propositional dynamic logic (PDL) can be interpreted as a logic of belief revision that extends the logic of communication and change (LCC) given in [7]. This new version of epistemic/doxastic PDL does not impose any constraints on the basic relations and because of this it does not suffer from the drawback of LCC that these constraints may get lost under updates that are admitted by the system. Here, we (...) will impose one constraint, namely that the agent’s plausibility relations are linked. Linkedness is a natural extension of local connectedness to the multi-agent case and it assures that we know the agent’s preferences between all relevant alternatives. Since the belief updates that are used in [11] may not preserve linkedness, we limit ourselves to a particular kind of belief change that does preserve it. Our framework has obvious connections to coalition logic [17] and social choice theory [19]. We show how we can use it to model consensus seeking in plenary Dutch meetings. In Dutch meetings, a belief update is done for all agents in the meeting if a majority beliefs the proposition that is under discussion. A special case of these meetings is judgement aggregation, and we apply our framework to the discursive dilemma in this field [15]. (shrink)

This paper continues the recent tradition of investigating iterated AGM revision by reasoning directly about the dynamics for total pre-order (“implausibility ordering”) representations of AGM revision functions. We reorient discussion, however, by proving that symmetry considerations, almost by themselves, suffice to determine a particular, AGM-friendly implausibility ordering dynamics due to Spohn 1988, which we call “J-revision”. After exploring the connections between implausibility ordering dynamics and the social choice theory of Arrow 1963, we provide symmetry arguments in the (...) social choice-theoretic framework for an interesting generalization of J-revision due to Nayak 1994. We conclude by arguing that the symmetry principles that uniquely favor J-revision and its generalizations are importantly expressive of the purely qualitative framework for representing beliefs that distinguishes the AGM program. Our results therefore comprehensively vindicate Spohn's 1988 conjecture that essentially J-revision is the best that can be done by way of a purely qualitative model of belief revision. (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)

In this paper we forge a connection between dynamic epistemic logics of belief revision on one hand and studies of collective judgement and multi-agent preference change on the other. Belief revision in the spirit of dynamic epistemic logic uses updating with relational substitutions to change the beliefs of individual agents. Collective judgement in social choice theory studies the collective outcomes of individual belief changes. We start out from the logic of communication (...) and change (LCC), which is basically epistemic propositional dynamic logic (PDL) extended with update action modalities. We show how epistemic PDL can be made to handle belief operators. Our new version of epistemic/doxastic PDL does not impose any constraints on the basic relations. Because of this it does not suffer from the drawback of LCC that constraints on epistemic relations, such as transitivity and reflexivity, may get lost under updates that are admitted by the system. After introducing the base system without constraints, we study the effects of imposing a single constraint, namely the constraint that the agent’s preference relations are linked. Linkedness is a natural extension of local connectedness to the multi-agent case. It assures that if Alice prefers y to x and Bob prefers z to x, then both Alice and Bob can make up their minds when given a choice between y and z. Since general belief changes may not preserve linkedness, we propose a recipe for belief change that does preserve it. Finally, we show that the resulting framework can be used to model consensus seeking procedures. We focus on the case of plenary Dutch meetings. In Dutch meetings, a belief change (or rather: preference change) is performed for all agents in the meeting if a majority believes (or: is in favour of) the proposition that is under discussion. A special case of these meetings is judgement aggregation, and we apply our framework to the discursive dilemma in.. (shrink)

In researching presuppositions dealing with logic and dynamic of belief we distinguish two related parts. The first part refers to presuppositions and logic, which is not necessarily involved with intentional operators. We are primarily concerned with classical, free and presuppositonal logic. Here, we practice a well known Strawson’s approach to the problem of presupposition in relation to classical logic. Further on in this work, free logic is used, especially Van Fraassen’s research of the (...) role of presupposition in supervaluations logical systems. At the end of the first part, presuppositional logic, advocated by S.K. Thomason, is taken into consideration. The second part refers to the presuppositions in relation to the logic of the dynamics of belief. Here the logic of belief change is taken into consideration and other epistemic notions with immanent mechanism for the presentation of the dynamics. Three representative and dominant approaches are evaluated. First, we deal with new, less classical, situation semantics. Besides Strawson’s theory, the second theory is the theory of the belief change, developed by Alchourron, Gärdenfors, and Makinson (AGM theory). At the end, the oldest, universal, and dominant approach is used, recognized as Hintikka’s approach to the analysis of epistemic notions. (shrink)

In this paper we show how recent concepts from Dynamic Logic, and in particular from Dynamic Epistemic logic, can be used to model and interpret quantum behavior. Our main thesis is that all the non-classical properties of quantum systems are explainable in terms of the non-classical flow of quantum information. We give a logical analysis of quantum measurements (formalized using modal operators) as triggers for quantum information flow, and we compare them with other logical operators previously (...) used to model various forms of classical information flow: the “test” operator from Dynamic Logic, the “announcement” operator from Dynamic Epistemic Logic and the “revision” operator from Belief Revision theory. The main points stressed in our investigation are the following: (1) The perspective and the techniques of “logical dynamics” are useful for understanding quantum information flow. (2) Quantum mechanics does not require any modification of the classical laws of “static” propositional logic, but only a non-classical dynamics of information. (3) The main such non-classical feature is that, in a quantum world, all information-gathering actions have some ontic side-effects. (4) This ontic impact can affect in its turn the flow of information, leading to non-classical epistemic side-effects (e.g. a type of non-monotonicity) and to states of “objectively imperfect information”. (5) Moreover, the ontic impact is non-local: an information-gathering action on one part of a quantum system can have ontic side-effects on other, far-away parts of the system. (shrink)

in UndeterminedInterrogative belief revision is a relatively recent framework for belief revision theory, in which the epistemic state of an agent includes a representation of that agent's research agenda, i.e. the set of questions the agent wants to have answers to. This added structure opens new possibilites for various types of epistemic change that cannot be distinguished in traditional belief revision. In this article I use the so-called 'action model' approach known from the literature (...) on dynamic epistemic logic to provide a unified framework in which we can reason about these various types of epistemic changes. I show how to model some natural examples of epistemic changes involving change of the research agenda in this framework. The action models give rise to a dynamic logic which is proven to be decidable. (shrink)

Dynamic doxastic logic (DDL) is used in connexion with theories of belief revision. Here we try to show that languages of DDL are suitable also for discussing aspects of default logic. One ingredient of our analysis is a concept of coherence-as-ratifiability.

Several tasks in artificial intelligence require the ability to find models about knowledge dynamics. They include belief revision, fusion and belief merging, and abduction. In this paper, we exploit the algebraic framework of mathematical morphology in the context of propositional logic and define operations such as dilation or erosion of a set of formulas. We derive concrete operators, based on a semantic approach, that have an intuitive interpretation and that are formally well behaved, to perform (...) class='Hi'>revision, fusion and abduction. Computation and tractability are addressed, and simple examples illustrate the main results. (shrink)

We model three examples of beliefs that agents may have about other agents’ beliefs, and provide motivation for this conceptualization from the theory of mind literature. We assume a modal logical framework for modelling degrees of belief by partially ordered preference relations. In this setting, we describe that agents believe that other agents do not distinguish among their beliefs (‘no preferences’), that agents believe that the beliefs of other agents are in part as their own (‘my preferences’), and the (...) special case that agents believe that the beliefs of other agents are exactly as their own (‘preference refinement’). This multi-agent belief interaction is frame characterizable. We provide examples for introspective agents. We investigate which of these forms of belief interaction are preserved under three common forms of belief revision. (shrink)

In this paper we distinguish between various kinds of doxastic theories. One distinction is between informal and formal doxastic theories. AGM-type theories of belief change are of the former kind, while Hintikka’s logic of knowledge and belief is of the latter. Then we distinguish between static theories that study the unchanging beliefs of a certain agent and dynamic theories that investigate not only the constraints that can reasonably be imposed on the doxastic states of a rational (...) agent but also rationality constraints on the changes of doxastic state that may occur in such agents. An additional distinction is that between non-introspective theories and introspective ones. Non-introspective theories investigate agents that have opinions about the external world but no higher-order opinions about their own doxasticnstates. Standard AGM-type theories as well as the currently existing versions of Segerberg’s dynamic doxastic logic (DDL) are non-introspective. Hintikka-style doxastic logic is of course introspective but it is a static theory. Thus, the challenge remains to devise doxastic theories that are both dynamic and introspective. We outline the semantics for truly introspective dynamic doxastic logic, i.e., a dynamic doxastic logic that allows us to describe agents who have both the ability to form higher-order beliefs and to reflect upon and change their minds about their own (higher-order) beliefs. This extension of DDL demands that we give up the Preservation condition on revision. We make some suggestions as to how such a non-preservative revision operation can be constructed. We also consider extending DDL with conditionals satisfying the Ramsey test and show that Gärdenfors’ well-known impossibility result applies to such a framework. Also in this case, Preservation has to be given up. (shrink)

This paper introduces Agreement Theorems to dynamic-epistemic logic. We show first that common belief of posteriors is sufficient for agreement in epistemic-plausibility models, under common and well-founded priors. We do not restrict ourselves to the finite case, showing that in countable structures the results hold if and only if the underlying plausibility ordering is well-founded. We then show that neither well-foundedness nor common priors are expressible in the language commonly used to describe and reason about epistemic-plausibility models. (...) The static agreement result is, however, finitely derivable in an extended modal logic. We provide the full derivation. We finally consider dynamic agreement results. We show they have a counterpart in epistemic-plausibility models, and provide a new form of agreements via public announcements. (shrink)

This paper studies the idea of conservatism with respect to belief change strategies in the setting of unary, iterated belief revision functions (based on the conclusions of Rott, ‘Coherence and Conservatism in the Dynamics of Belief, Part I: Finding the Right Framework’, Erkenntnis 50, 1999, 387–412). Special attention is paid to the case of ‘basic belief change’ where neither the (weak) AGM postulates concerning conservatism with respect to beliefs nor the (stong) supplementary AGM postulates concerning (...) dispositional coherence need to be satisfied. One‐step belief change generated by ‘basic entrenchment’ is combined with a natural conservative method of revising entrenchment relations. A logical characterization of this method is presented, and it is compared with three other methods known from the literature which I call ‘external’, ‘radical’ and ‘moderate’ belief revision. While conservative belief change turns out to be incoherent in its treatment of the recency of information, moderate belief change is more satisfactory in this respect. (shrink)

This paper discusses the possibility of modelling inductive inference (Gold 1967) in dynamic epistemic logic (see e.g. van Ditmarsch et al. 2007). The general purpose is to propose a semantic basis for designing a modal logic for learning in the limit. First, we analyze a variety of epistemological notions involved in identification in the limit and match it with traditional epistemic and doxastic logic approaches. Then, we provide a comparison of learning by erasing (Lange et al. (...) 1996) and iterated epistemic update (Baltag and Moss 2004) as analyzed in dynamic epistemic logic. We show that finite identification can be modelled in dynamic epistemic logic, and that the elimination process of learning by erasing can be seen as iterated belief-revision modelled in dynamic doxastic logic. Finally, we propose viewing hypothesis spaces as temporal frames and discuss possible advantages of that perspective. (shrink)

It has been an open question whether or not we can define a belief revision operation that is distinct from simple belief expansion using paraconsistent logic. In this paper, we investigate the possibility of meeting the challenge of defining a belief revision operation using the resources made available by the study of dynamic epistemic logic in the presence of paraconsistent logic. We will show that it is possible to define dynamic (...) operations of belief revision in a paraconsistent setting. (shrink)

This paper develops a logical theory that unifies all three standard types of argumentative attack in AI, namely rebutting, undercutting and undermining attacks. We build on default justification logic that already represents undercutting and rebutting attacks, and we add undermining attacks. Intuitively, undermining does not target default inference, as undercutting, or default conclusion, as rebutting, but rather attacks an argument’s premise as a starting point for default reasoning. In default justification logic, reasoning starts from a set of premises, (...) which is then extended by conclusions that hold by default. We argue that modeling undermining defeaters in the view of default theories requires changing the set of premises upon receiving new information. To model changes to premises, we give a dynamic aspect to default justification logic by using the techniques from the logic of belief revision. More specifically, undermining is modeled with belief revision operations that include contracting a set of premises, that is, removing some information from it. The novel combination of default reasoning and belief revision in justification logic enriches both approaches to reasoning under uncertainty. By the end of the paper, we show some important aspects of defeasible argumentation in which our logic compares favorably to structured argumentation frameworks. (shrink)

In recent decades, the logical study of rational belief dynamics has played an increasingly important role in philosophy. However, the dynamics of concepts such as conceptual learning received comparatively little attention within this debate. This is problematic insofar as the occurrence of conceptual change (especially in the sciences) has been an influential argument against a merely logical analysis of beliefs. Especially Kuhn’s ideas about the incommensurability, i.e., untranslatability, of succeeding theories seem to stand in the way of logical reconstruction. (...) This paper investigates conceptual change as model-changing operations similar to belief revision and relates it to the notion of incommensurability. I consider several versions of conceptual change and discuss their influences on the expressive power, translatability and the potential arising of incommensurability. The paper concludes with a discussion of animal taxonomy in Aristotle’s and Linnaeus’s work. (shrink)

It is well-known that classical models of belief are not realistic representations of human doxastic capacity; equally, models of actions involving beliefs, such as decisions based on beliefs, or changes of beliefs, suffer from a similar inaccuracies. In this paper, a general framework is presented which permits a more realistic modelling both of instantaneous states of belief, and of the operations involving them. This framework is motivated by some of the inadequacies of existing models, which it overcomes, whilst (...) retaining technical rigour in so far as it relies on known, natural logical and mathematical notions. The companion paper (Towards a “sophisticated” model of belief dynamics. Part II) contains an application of this framework to the particular case of belief revision. (shrink)