One goal of normative multi-agent system theory is to formulate principles for normative system change that maintain the rule-like structure of norms and preserve links between norms and individual agent obligations. A central question raised by this problem is whether there is a framework for norm change that is at once specific enough to capture this rule-like behavior of norms, yet general enough to support a full battery of norm and obligation change operators. In this paper we propose an answer (...) to this question by developing a bimodal logic for norms and obligations called NO. A key to our approach is that norms are treated as propositional formulas, and we provide some independent reasons for adopting this stance. Then we define norm change operations for a wide class of modal systems, including the class of NO systems, by constructing a class of modal revision operators that satisfy all the AGM postulates for revision, and constructing a class of modal contraction operators that satisfy all the AGM postulates for contraction. More generally, our approach yields an easily extendable framework within which to work out principles for a theory of normative system change. (shrink)

This paper aims to make explicit the methodological conditions that should be satisfied for the Bayesian model to be used as a normative model of human probability judgment. After noticing the lack of a clear definition of Bayesianism in the psychological literature and the lack of justification for using it, a classic definition of subjective Bayesianism is recalled, based on the following three criteria: an epistemic criterion, a static coherence criterion and a dynamic coherence criterion. Then it is shown that (...) the adoption of this framework has two kinds of implications. The first one regards the methodology of the experimental study of probability judgment. The Bayesian framework creates pragmatic constraints on the methodology that are linked to the interpretation of, and the belief in, the information presented, or referred to, by an experimenter in order for it to be the basis of a probability judgment by individual participants. It is shown that these constraints have not been satisfied in the past, and the question of whether they can be satisfied in principle is raised and answered negatively. The second kind of implications consists of two limitations in the scope of the Bayesian model. They regard (1) the background of revision (the Bayesian model considers only revising situations but not updating situations), and (2) the notorious case of the null priors. In both cases Lewis’ rule is an appropriate alternative to Bayes’ rule, but its use faces the same operational difficulties. (shrink)

Various representation results have been established for logics of belief revision, in terms of remainder sets, epistemic entrenchment, systems of spheres and so on. In this paper I present another representation for logics of belief revision, as an algebra of theories. I show that an algebra of theories, enriched with a set of rejection operations, provides a suitable algebraic framework to characterize the theory change operations of systems of belief revision. The theory change operations arise as power operations of the (...) conjunction and disjunction connectives of the underlying logic. (shrink)

In this paper I discuss the foundations of a formal theory of coherent and conservative belief change that is (a) suitable to be used as a method for constructing iterated changes of belief, (b) sensitive to the history of earlier belief changes, and (c) independent of any form of dispositional coherence. I review various ways to conceive the relationship between the beliefs actually held by an agent and her belief change strategies (that also deal with potential belief sets), show the (...) problems they suffer from, and suggest that belief states should be represented by unary revision functions that take sequences of inputs. Three concepts of coherence implicit in current theories of belief change are distinguished: synchronic, diachronic and dispositional coherence. Diachronic coherence is essentially identified with what is known as conservatism in epistemology. The present paper elaborates on the philosophical motivation of the general framework; formal details and results are provided in a companion paper. (shrink)

The AGM theory of belief revision provides a formal framework to represent the dynamics of epistemic states. In this framework, the beliefs of the agent are usually represented as logical formulas while the change operations are constrained by rationality postulates. In the original proposal, the logic underlying the reasoning was supposed to be supraclassical, among other properties. In this paper, we present some of the existing work in adapting the AGM theory for non-classical logics and discuss their interconnections and what (...) is still missing for each approach. (shrink)

In studies of multi-agent interaction, especially in game theory, the notion of equilibrium often plays a prominent role. A typical scenario for the belief merging problem is one in which several agents pool their beliefs together to form a consistent "group" picture of the world. The aim of this paper is to define and study new notions of equilibria in belief merging. To do so, we assume the agents arrive at consistency via the use of a social belief removal function, (...) in which each agent, using his own individual removal function, removes some belief from his stock of beliefs. We examine several notions of equilibria in this setting, assuming a general framework for individual belief removal due to Booth et al. We look at their inter-relations as well as prove their existence or otherwise. We also show how our equilibria can be seen as a generalisation of the idea of taking maximal consistent subsets of agents. (shrink)

This paper addresses the question whether the past couple of decades of formal research in belief revision offers evidence of a new psychologism in logic. In the first part I examine five potential arguments in favour of this thesis and find them all wanting. In the second part of the paper I argue that belief revision research has climbed up a hierarchy of models for the change of doxastic states that appear to be clearly normative at the bottom, but are (...) more amenable to an empirical-descriptive interpretation on higher levels. I conclude that this observation might offer a foothold for the thesis that there is a new psychologism in logic. (shrink)

In many logics dealing with information one needs to make statements not only about cognitive states, but also about transitions between them. In this paper we analyze a dynamic modal logic that has been designed with this purpose in mind. On top of an abstract information ordering on states it has instructions to move forward or backward along this ordering, to states where a certain assertion holds or fails, while it also allows combinations of such instructions by means of operations (...) from relation algebra. In addition, the logic has devices for expressing whether in a given state a certain instruction can be carried out, and whether that state can be arrived at by carrying out a certain instruction. This paper deals mainly with technical aspects of our dynamic modal logic. It gives an exact description of the expressive power of this language; it also contains results on decidability for the language with 'arbitrary' structures and for the special case with a restricted class of admissible structures. In addition, a complete axiomatization is given. The paper concludes with a remark about the modal algebras appropriate for our dynamic modal logic, and some questions for further work. The paper only contains some sketchy examples showing how the logic can be used to capture situations of dynamic interest, far more detailed applications are given in a companion to this paper (De Rijke [33]). (shrink)

ABSTRACT Although much effort has been expended by researchers in trying to maintain a consistent belief base in formalizing commonsense reasoning, there is some evidence that the nature of commonsense reasoning itself brings inconsistencies with it. I will outline a number of sources of such inconsistencies, and discuss why they appear unavoidable. I will also suggest that, far from being a roadblock to effective commonsense, (detected) inconsistencies are often a reasoner's best guide to what to do next.

The Bayesian model has been used in psychology as the standard reference for the study of probability revision. In the first part of this paper we show that this traditional choice restricts the scope of the experimental investigation of revision to a stable universe. This is the case of a situation that, technically, is known as focusing. We argue that it is essential for a better understanding of human probability revision to consider another situation called updating (Katsuno & Mendelzon, 1992), (...) in which the universe is evolving. In that case the structure of the universe has definitely been transformed and the revision message conveys information on the resulting universe. The second part of the paper presents four experiments based on the Monty Hall puzzle that aim to show that updating is a natural frame for individuals to revise their beliefs. (shrink)

We show how to construct partial nontrivial base revision operators that satisfy the analogues of the AGM postulates and depends on no extra‐logical consideration. These operators, closely related to the full meet revision process, are defined on stratified bases, in which the information can be ranked in logical sequences. Stratified bases, which can be viewed as sets of graded sheaves, are exactly the knowledge bases for which the full meet revision operator satisfies the rationality postulate K*8. As the revision of (...) a stratified base is again a stratified base, it is possible to perform iterated revisions, and the resulting output is particularly easy to determine. (shrink)

We discuss similarities and residual differences, within the general semantic framework of minimality, between defeasible inference, belief revision, counterfactual conditionals, updating — and also conditional obligation in deontic logic. Our purpose is not to establish new results, but to bring together existing material to form a clear overall picture.

We introduce a constructive model of selective belief revision in which it is possible to accept only a part of the input information. A selective revision operator ο is defined by the equality K ο α = K * f(α), where * is an AGM revision operator and f a function, typically with the property ⊢ α → f(α). Axiomatic characterizations are provided for three variants of selective revision.

A semantics is presented for belief revision in the face of common announcements to a group of agents that have beliefs about each other’s beliefs. The semantics is based on the idea that possible worlds can be viewed as having an internal-structure, representing the belief independent features of the world, and the respective belief states of the agents in a modular fashion. Modularity guarantees that changing one aspect of the world (a belief independent feature or a belief state) has no (...) effect on any other aspect of the world. This allows us to employ an AGM-style selection function to represent revision. The semantics is given a complete axiomatisation (identical to the axiomatisation found by Gerbrandy and Groeneveld for a semantics based on non-wellfounded set theory) for the special case of expansion. (shrink)

It is well known that aggregating the degree-of-belief functions of different subjects by linear pooling or averaging is subject to a commutativity dilemma: other than in trivial cases, conditionalizing the individual degree-of-belief functions on a piece of evidence E followed by linearly aggregating them does not yield the same result as rst aggregating them linearly and then conditionalizing the resulting social degree- of-belief function on E. In the present paper we suggest a novel way out of this dilemma: adapting the (...) method of update or learning such that linear pooling com- mutes with it. As it turns out, the resulting update scheme – imaging on the evidence – is well-known from areas such as the study of conditionals and cau- sal decision theory, and a formal result from which the required commutativity property is derivable was supplied already by Gärdenfors in a different con- text. We end up determining under which conditions imaging would seem to be right method of update, and under which conditions, therefore, group update would not be affected by the commutativity dilemma. (shrink)

Although the change of beliefs in the face of new information has been widely studied with some success, the revision of other mental states has received little attention from the theoretical perspective. In particular, intentions are widely recognised as being a key attitude for rational agents, and while several formal theories of intention have been proposed in the literature, the logic of intention revision has been hardly considered. There are several reasons for this: perhaps most importantly, intentions are very closely (...) connected with other mental states—in particular, beliefs about the future and the abilities of the agent. So, we cannot study them in isolation. We must consider the interplay between intention revision and the revision of other mental states, which complicates the picture considerably. In this paper, we present some first steps towards a theory of intention revision. We develop a simple model of an agent’s mental states, and define intention revision operators. Using this model, we develop a logic of intention dynamics, and then investigate some of its properties. (shrink)

This paper works within a model of ungraded belief that characterizes epistemic states as logically closed and consistent sets of sentences. The aim of this paper is to discuss three diachronic coherence conditions for such beliefs. These coherence conditions are formulated in terms of the reasoner's present beliefs about how his present beliefs will evolve in the future, for instance, in response to different pieces of future evidence.

In this paper we investigate a logic for modelling individual and collective acceptances that is called acceptance logic. The logic has formulae of the form $A_{Gx} \phi $ reading 'if the agents in the set of agents G identify themselves with institution x then they together accept that φ'. We extend acceptance logic by two kinds of dynamic modal operators. The first kind are public announcements of the form x!ψ, meaning that the agents learn that ψ is the case in (...) context x. Formulae of the form [x!ψ]φ mean that φ is the case after every possible occurrence of the event x!ψ. Semantically, public announcements diminish the space of possible worlds accepted by agents and sets of agents. The announcement of ψ in context x makes all ¬ψ-Worlds inaccessible to the agents in such context. In this logic, if the set of accessible worlds of G in context x is empty, then the agents in G are not functioning as members of x, they do not identify themselves with x. In such a situation the agents in G may have the possibility to join x. To model this we introduce here a second kind of dynamic modal operator of acceptance shifting of the form G:x↑ψ. The latter means that the agents in G shift (change) their acceptances in order to accept ψ in context x. Semantically, they make ψ-worlds accessible to G in the context x, which means that, after such operation, G is functioning as member of x (unless there are no ψ-worlds). We show that the resulting logic has a complete axiomatization in terms of reduction axioms for both dynamic operators. In the paper we also show how the logic of acceptance and its dynamic extension can be used to model some interesting aspects of judgement aggregation. In particular, we apply our logic of acceptance to a classical scenario in judgment aggregation, the so-called 'doctrinal paradox' or 'discursive dilemma' (Pettit, Philosophical Issues 11: 268-299, 2001; Kornhauser and Sager, Yale Law Journal 96: 82-117, 1986). (shrink)

In this paper we investigate a logic for modelling individual and collective acceptances that is called acceptance logic. The logic has formulae of the form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rm A}_{G:x} \varphi$$\end{document} reading ‘if the agents in the set of agents G identify themselves with institution x then they together accept that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varphi}$$\end{document} ’. We extend acceptance logic by two kinds of dynamic modal operators. The first (...) kind are public announcements of the form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${x!\psi}$$\end{document}, meaning that the agents learn that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\psi}$$\end{document} is the case in context x. Formulae of the form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${[x!\psi]\varphi}$$\end{document} mean that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varphi}$$\end{document} is the case after every possible occurrence of the event x!ψ. Semantically, public announcements diminish the space of possible worlds accepted by agents and sets of agents. The announcement of ψ in context x makes all \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\lnot\psi}$$\end{document} -worlds inaccessible to the agents in such context. In this logic, if the set of accessible worlds of G in context x is empty, then the agents in G are not functioning as members of x, they do not identify themselves with x. In such a situation the agents in G may have the possibility to join x. To model this we introduce here a second kind of dynamic modal operator of acceptance shifting of the form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${G:x\uparrow\psi}$$\end{document}. The latter means that the agents in G shift (change) their acceptances in order to accept ψ in context x. Semantically, they make ψ-worlds accessible to G in the context x, which means that, after such operation, G is functioning as member of x (unless there are no ψ-worlds). We show that the resulting logic has a complete axiomatization in terms of reduction axioms for both dynamic operators. In the paper we also show how the logic of acceptance and its dynamic extension can be used to model some interesting aspects of judgement aggregation. In particular, we apply our logic of acceptance to a classical scenario in judgment aggregation, the so-called ‘doctrinal paradox’ or ‘discursive dilemma’ (Pettit, Philosophical Issues 11:268–299, 2001; Kornhauser and Sager, Yale Law Journal 96:82–117, 1986). (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.

While the theory of belief change has attracted a lot of interest from researchers, work on implementing belief change and actually putting it to use in real-world problems is still scarce. In this paper, we present an implementation of propositional belief change using Binary Decision Diagrams. Upper complexity bounds for the algorithm are presented and discussed. The approach is presented both in the general case, as well as on specific belief change operators from the literature. In an effort to gain (...) a better understanding of the empirical efficiency of the algorithms involved, a fault diagnosis problem on combinational circuits is presented, implemented and evaluated. (shrink)

‘Incongruity is never superfluous’Thea Arbee (2016) Is the superfluous a (new) modality?11. Even if much has been written about ingredients that trigger laughter, researchers are still far from hav...

The temporal updating of an agent’s beliefs in response to a flow of information is modeled in a simple modal logic that, for every date t, contains a normal belief operator B t and a non-normal information operator I t which is analogous to the ‘only knowing’ operator discussed in the computer science literature. Soundness and completeness of the logic are proved and the relationship between the proposed logic, the AGM theory of belief revision and the notion of plausibility is (...) discussed. (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)

It is now well known that, on pain of triviality, the probability of a conditional cannot be identified with the corresponding conditional probability [25]. This surprising impossibility result has a qualitative counterpart. In fact, Peter Gärdenfors showed in [13] that believing ‘If A then B’ cannot be equated with the act of believing B on the supposition that A — as long as supposing obeys minimal Bayesian constraints. Recent work has shown that in spite of these negative results, the question (...) ‘how to accept a conditional?’ has a clear answer. Even if conditionals are not truth-carriers, they do have precise acceptability conditions. Nevertheless most epistemic models of conditionals do not provide acceptance conditions for iterated conditionals. One of the main goals of this essay is to provide a comprehensive account of the notion of epistemic conditionality covering all forms of iteration. First we propose an account of the basic idea of epistemic conditionality, by studying the conditionals validated by epistemic models where iteration is permitted but not constrained by special axioms. Our modeling does not presuppose that epistemic states should be represented by belief sets (we only assume that to each epistemic state corresponds an associated belief state). A full encoding of the basic epistemic conditionals (encompassing all forms of iteration) is presented and a representation result is proved. In the second part of the essay we argue that the notion of change involved in the evaluation of conditionals is suppositional, and that such notion should be distinguished from the notion of updating (modelled by AGM and other methods). We conclude by considering how some of the recent modellings of iterated change fare as methods for iterated supposing. (shrink)

The purpose of this paper is to introduce a form of update based on the minimization of the geodesic distance on a graph. We provide a characterization of this class using set- theoretic operators and show that such operators bijectively correspond to geodesic metrics. As distance is generated by distinguishability, our framework is appropriate in contexts where distance is generated by threshold, and therefore, when measurement is erroneous.