In this paper we describe two approaches to the revision of probability functions. We assume that a probabilistic state of belief is captured by a counterfactual probability or Popper function, the revision of which determines a new Popper function. We describe methods whereby the original function determines the nature of the revised function. The first is based on a probabilistic extension of Spohn's OCFs, whereas the second exploits the structure implicit in the Popper function itself. This stands in contrast with (...) previous approaches that associate a unique Popper function with each absolute (classical) probability function. We also describe iterated revision using these models. Finally, we consider the point of view that Popper functions may be abstract representations of certain types of absolute probability functions, but we show that our revision methods cannot be naturally interpreted as conditionalization on these functions. (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)

Although AGM theory contraction (Alchourrón et al., 1985; Alchourrón and Makinson, 1985) occupies a central position in the literature on belief change, there is one aspect about it that has created a fair amount of controversy. It involves the inclusion of the postulate known as Recovery. As a result, a number of alternatives to AGM theory contraction have been proposed that do not always satisfy the Recovery postulate (Levi, 1991, 1998; Hansson and Olsson, 1995; Fermé, 1998; Fermé and Rodriguez, 1998; (...) Rott and Pagnucco, 1999). In this paper we present a new addition, systematic withdrawal, to the family of withdrawal operations, as they have become known. We define systematic withdrawal semantically, in terms of a set of preorders, and show that it can be characterised by a set of postulates. In a comparison of withdrawal operations we show that AGM contraction, systematic withdrawal and the severe withdrawal of Rott and Pagnucco (1999) are intimately connected by virtue of their definition in terms of sets of preorders. In a future paper it will be shown that this connection can be extended to include the epistemic entrenchment orderings of Gärdenfors (1988) and Gärdenfors and Makinson (1988) and the refined entrenchment orderings of Meyer et al. (2000). (shrink)

Generalisations of theory change involving operations on arbitrary sets ofwffs instead of on belief sets (i.e., sets closed under a consequencerelation), have become known as base change. In one view, a base should bethought of as providing more structure to its generated belief set, whichmeans that it can be employed to determine the theory contraction operationassociated with a base contraction operation. In this paper we follow suchan approach as the first step in defining infobase change. We think of an infobase (...) as a finite set of wffs consisting of independently obtainedbits of information. Taking AGM theory change (Alchourrón et al. 1985) as the general framework, we present a method that uses the structure of aninfobase B to obtain an AGM theory contraction operation for contractingthe belief set Cn(B). Both the infobase and the obtained theory contraction operation then play a role in constructing a unique infobasecontraction operation. Infobase revision is defined in terms of an analogueof the Levi Identity, and it is shown that the associated theory revisionoperation satisfies the AGM postulates for revision. Because every infobaseis associated with a unique infobase contraction and revision operation, the method also allows for iterated base change. (shrink)

We propose a logic of imagination, based on simulated belief revision, that intends to uncover the logical patterns governing the development of imagination in pretense. Our system complements the currently prominent logics of imagination in that ours in particular formalises (1) the algorithm that specifies what goes on in between receiving a certain input for an imaginative episode and what is imagined in the resulting imagination, as well as (2) the goal-orientedness of imagination, by allowing the context to determine, what (...) we call, the overall topic of the imaginative episode. To achieve this, we employ well-developed tools and techniques from dynamic epistemic logic and belief revision theory, enriched with a topicality component which has been exploited in the recent literature. As a result, our logic models a great number of cognitive theories of pretense and imagination [cf. Currie and Ravenscroft (Recreative minds, Oxford University Press, Oxford, 2002); Nichols and Stich (Mindreading: an integrated account of pretence, self-awareness, and understanding other minds, Oxford University Press, Oxford, 2003); Byrne (The rational imagination, The MIT Press, London, 2005); Williamson (The philosophy of philosophy, Blackwell Publishing, Oxford, 2007); Langland-Hassan (Philos Stud 159:155–179, 2012, in: Kind and Kung (eds) Knowledge through imaginaion, Oxford University Press, Oxford, 2016]. (shrink)

Weak filters were introduced by K. Schlechta in the ’90s with the aim of interpreting defaults via a generalized ‘most’ quantifier in first-order logic. They arguably represent the largest class of structures that qualify as a ‘collection of large subsets’ of a given index set |$I$|⁠, in the sense that it is difficult to think of a weaker, but still plausible, definition of the concept. The notion of weak ultrafilter naturally emerges and has been used in epistemic logic and other (...) knowledge representation (KR) applications. We provide a comprehensive exposition of weak filters and ultrafilters, comparing them with their classical counterparts that have found very important applications in logic, set theory and topology. Weak (ultra)filters capture the ‘majorities’ of social choice theory (which coincide with the commonsense understanding of a ‘large subset’) and in that respect, they outperform classical (ultra)filters in their role as ‘collections of large subsets’. Yet, they lack some of the elegant properties of classical (ultra)filters that make them an almost perfect match for logical theories. We investigate the extent to which some important classical results carry through in this new setting, and we focus on genuinely weak filters and genuinely weak ultrafilters. For weak ultrafilters, we proceed to provide concrete examples, answer questions of existence and characterize their construction. The class of weak (ultra)filters represents a genuine contribution of KR to set theory that might be of some interest to set theorists too and we initiate this study by providing a glimpse on natural set-theoretic questions. (shrink)

We propose a logic of imagination, based on simulated belief revision, that intends to uncover the logical patterns governing the development of imagination in pretense. Our system complements the currently prominent logics of imagination in that ours in particular formalises (1) the algorithm that specifies what goes on in between receiving a certain input for an imaginative episode and what is imagined in the resulting imagination, as well as (2) the goal-orientedness of imagination, by allowing the context to determine, what (...) we call, the overall topic of the imaginative episode. To achieve this, we employ well-developed tools and techniques from dynamic epistemic logic and belief revision theory, enriched with a topicality component which has been exploited in the recent literature. As a result, our logic models a great number of cognitive theories of pretense and imagination [cf. Currie and Ravenscroft (Recreative minds, Oxford University Press, Oxford, 2002); Nichols and Stich (Mindreading: an integrated account of pretence, self-awareness, and understanding other minds, Oxford University Press, Oxford, 2003); Byrne (The rational imagination, The MIT Press, London, 2005); Williamson (The philosophy of philosophy, Blackwell Publishing, Oxford, 2007); Langland-Hassan (Philos Stud 159:155–179, 2012, in: Kind and Kung (eds) Knowledge through imaginaion, Oxford University Press, Oxford, 2016]. (shrink)

According to the KK-principle, knowledge iterates freely. It has been argued, notably in Greco, that accounts of knowledge which involve essential appeal to normality are particularly conducive to defence of the KK-principle. The present article evaluates the prospects for employing normality in this role. First, it is argued that the defence of the KK-principle depends upon an implausible assumption about the logical principles governing iterated normality claims. Once this assumption is dropped, counter-instances to the principle can be expected to arise. (...) Second, it is argued that even if the assumption is maintained, there are other logical properties of normality which can be expected to lead to failures of KK. Such failures are noteworthy, since they do not depend on either a margins-for-error principle or safety condition of the kinds Williamson appeals to in motivating rejection KK. “Introduction: KK and Being in a Position to Know” Section formulates two versions of the KK-Principle; “Inexact Knowledge and Margins for Error” Section presents a version of Williamson’s margins-for-error argument against it; “Knowledge and Normality” and “Iterated Normality” Sections discuss the defence of the KK-Principle due to Greco and show that it is dependent upon the implausible assumption that the logic of normality ascriptions is at least as strong as K4; finally, “Knowledge in Abnormal Conditions” and “Higher-Order Ignorance Inside the Margins” Sections argue that a weakened version of Greco’s constraint on knowledge is plausible and demonstrate that this weakened constraint will, given uncontentious assumptions, systematically generate counter-instances to the KK-principle of a novel kind. (shrink)

Our understanding of subjunctive conditionals has been greatly enhanced through the use of possible world semantics and, more precisely, by the idea that they involve variably strict quantification over possible worlds. I propose to extend this treatment to ceteris paribus conditionals – that is, conditionals that incorporate a ceteris paribus or ‘other things being equal’ clause. Although such conditionals are commonly invoked in scientific theorising, they traditionally arouse suspicion and apprehensiveness amongst philosophers. By treating ceteris paribus conditionals as a species (...) of variably strict conditional I hope to shed new light upon their content and their logic. (shrink)

This paper presents an adaptive logic enhancement of conditional logics of normality that allows for defeasible applications of Modus Ponens to conditionals. In addition to the possibilities these logics already offer in terms of reasoning about conditionals, this way they are enriched by the ability to perform default inferencing. The idea is to apply Modus Ponens defeasibly to a conditional and a fact on the condition that it is ‘safe' to do so concerning the factual and conditional knowledge at hand. (...) It is for instance not safe if the given information describes exceptional circumstances: although birds usually fly, penguins are exceptional to this rule. The two adaptive standard strategies are shown to correspond to different intuitions, a skeptical and a credulous reasoning type, which manifest themselves in the handling of so-called floating conclusions. (shrink)

We describe a model of iterated belief revision that extends the AGM theory of revision to account for the effect of a revision on the conditional beliefs of an agent. In particular, this model ensures that an agent makes as few changes as possible to the conditional component of its belief set. Adopting the Ramsey test, minimal conditional revision provides acceptance conditions for arbitrary right-nested conditionals. We show that problem of determining acceptance of any such nested conditional can be reduced (...) to acceptance tests for unnested conditionals. Thus, iterated revision can be accomplished in a "virtual" manner, using uniterated revision. (shrink)

This paper concerns the apparent fact — discussed by Sinan Dogramaci and Brian Weatherson — that inductive reasoning often interacts in disastrous ways with patterns of reasoning that seem perfectly fine in the deductive case. In contrast to Dogramaci's and Weatherson's own suggestions, I argue that these cases show that we cannot reason inductively about arbitrary objects. Moreover, as I argue, this prohibition is neatly explained by a certain hypothesis about the rational basis of inductive reasoning — namely, the hypothesis (...) that inductive reasoning is fundamentally reasoning about what normally happens. (shrink)

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)

Epistemic entrenchment, as presented by Gärdenfors and Makinson (1988) and Gärdenfors (1988), is a formalisation of the intuition that, when forced to choose between two beliefs, an agent will giveup the less entrenched one. While their formalisation satisfactorilycaptures the intuitive notion of the entrenchment of beliefs in a number ofaspects, the requirement that all wffs be comparable has drawn criticismfrom various quarters. We define a set of refined versions of theirentrenchment orderings that are not subject to the same criticism, andinvestigate (...) the relationship between the refined entrenched orderings,the entrenchment orderings of Gärdenfors and Makinson, and AGM theorycontraction (Alchourrón et al., 1985). To conclude, we compare refinedentrenchment with two related approaches to epistemic entrenchment. (shrink)

This article proposes a systematic application of recent developments in the logic of preference to a number of topics in deontic logic. The key junction is the well‐known Hansson conditional for dyadic obligations. These conditionals are generalized by pairing them with reasoning about syntactic priority structures. The resulting two‐level approach to obligations is tested first against standard scenarios of contrary‐to‐duty obligations, leading also to a generalization for the Kanger‐Anderson reduction of deontic logic. Next, the priority framework is applied to model (...) two intuitively different sorts of deontic dynamics of obligations, based on information changes and on genuine normative events. In this two‐level setting, we also offer novel takes on vexed issues such as the Chisholm paradox and modelling strong permission. Finally, the priority framework is shown to provide a unifying setting for the study of operations on norms as such, in particular, adding or deleting individual norms, and even merging whole norm systems in different manners. (shrink)

This book illustrates the program of Logical-Informational Dynamics. Rational agents exploit the information available in the world in delicate ways, adopt a wide range of epistemic attitudes, and in that process, constantly change the world itself. Logical-Informational Dynamics is about logical systems putting such activities at center stage, focusing on the events by which we acquire information and change attitudes. Its contributions show many current logics of information and change at work, often in multi-agent settings where social behavior is essential, (...) and often stressing Johan van Benthem's pioneering work in establishing this program. However, this is not a Festschrift, but a rich tapestry for a field with a wealth of strands of its own. The reader will see the state of the art in such topics as information update, belief change, preference, learning over time, and strategic interaction in games. Moreover, no tight boundary has been enforced, and some chapters add more general mathematical or philosophical foundations or links to current trends in computer science. The theme of this book lies at the interface of many disciplines. Logic is the main methodology, but the various chapters cross easily between mathematics, computer science, philosophy, linguistics, cognitive and social sciences, while also ranging from pure theory to empirical work. Accordingly, the authors of this book represent a wide variety of original thinkers from different research communities. And their interconnected themes challenge at the same time how we think of logic, philosophy and computation. Thus, very much in line with van Benthem's work over many decades, the volume shows how all these disciplines form a natural unity in the perspective of dynamic logicians (broadly conceived) exploring their new themes today. And at the same time, in doing so, it offers a broader conception of logic with a certain grandeur, moving its horizons beyond the traditional study of consequence relations. (shrink)

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

Modal accounts of normality in non-monotonic reasoning traditionally have an underlying semantics based on a notion of preference amongst worlds. In this paper, we motivate and investigate an alternative semantics, based on ordered accessibility relations in Kripke frames. The underlying intuition is that some world tuples may be seen as more normal, while others may be seen as more exceptional. We show that this delivers an elegant and intuitive semantic construction, which gives a new perspective on defeasible necessity. Technically, the (...) revisited logic does not change the expressive power of our previously defined preferential modalities. This conclusion follows from an analysis of both semantic constructions via a generalisation of bisimulations to the preferential case. Reasoners based on the previous semantics therefore also suffice for reasoning over the new semantics. We complete the picture by investigating different notions of defeasible conditionals in modal logic that can also be captured within our framework. (shrink)

This paper concerns the apparent fact — discussed by Sinan Dogramaci and Brian Weatherson — that inductive reasoning often interacts in disastrous ways with patterns of reasoning that seem perfectly fine in the deductive case. In contrast to Dogramaci's and Weatherson's own suggestions, I argue that these cases show that we cannot reason inductively about arbitrary objects. Moreover, as I argue, this prohibition is neatly explained by a certain hypothesis about the rational basis of inductive reasoning — namely, the hypothesis (...) that inductive reasoning is fundamentally reasoning about what normally happens. (shrink)

This work proposes an understanding of deductive, default and abductive reasoning as different instances of the same phenomenon: epistemic dynamics. It discusses the main intuitions behind each one of these reasoning processes, and suggest how they can be understood as different epistemic actions that modify an agent’s knowledge and/or beliefs in a different way, making formal the discussion with the use of the dynamic epistemic logic framework. The ideas in this paper put the studied processes under the same umbrella, thus (...) highlighting their relationship and allowing a better understanding of how they interact together. (shrink)

Japanese has a large number of evidential and modal expressions. Many of the inferential evidentials – mitai, yoo, rashii – also have an adjectival use. On this use, they make a claim about the prototypicality of some object or individual with respect to another class of object, in the case of rashii, or about the similarity of these two objects, for yoo and mitai. This paper provides a compositional semantics for these adjectives, claiming that they are evaluated in terms of (...) the degree to which they instantiate a set of properties (conventionally) associated with a class of object. (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)

Preference is a key area where analytic philosophy meets philosophical logic. I start with two related issues: reasons for preference, and changes in preference, first mentioned in von Wright’s book The Logic of Preference but not thoroughly explored there. I show how these two issues can be handled together in one dynamic logical framework, working with structured two-level models, and I investigate the resulting dynamics of reason-based preference in some detail. Next, I study the foundational issue of entanglement between preference (...) and beliefs, and relate the resulting richer logics to belief revision theory and decision theory. (shrink)

We introduce and explore the notion of duality for entailment relations induced by preference orderings on states. We discuss the relationship between these preferential entailment relations from the perspectives of Boolean algebra, inference rules, and modal axiomatisation. Interpreting the preference relations as accessibility relations establishes modular Gödel-Löb logic as a suitable modal framework for rational preferential reasoning.

This work proposes an understanding of deductive, default and abductive reasoning as different instances of the same phenomenon: epistemic dynamics. It discusses the main intuitions behind each one of these reasoning processes, and suggest how they can be understood as different epistemic actions that modify an agent’s knowledge and/or beliefs in a different way, making formal the discussion with the use of the dynamic epistemic logic framework. The ideas in this paper put the studied processes under the same umbrella, thus (...) highlighting their relationship and allowing a better understanding of how they interact together. (shrink)

Proponents of the projection strategy take an epistemic rule for the evaluation of English conditionals, the Ramsey test, as clue to the truth-conditional semantics of conditionals. They also construe English conditionals as stronger than the material conditional. Given plausible assumptions, however, the Ramsey test induces the semantics of the material conditional. The alleged link between Ramsey test and truth conditions stronger than those of the material conditional can be saved by construing conditionals as ternary, rather than binary, propositional functions with (...) a hidden contextual parameter. But such a ternary construal raises problems of its own. (shrink)

Normality judgements are frequently used in everyday communication as well as in biological and social science. Moreover they became increasingly relevant to formal logic as part of defeasible reasoning. This paper distinguishes different kinds of normality statements. It is argued that normality laws like “Birds can normally fly” should be understood essentially in a statistical way. The argument has basically two parts: firstly, a statistical semantic core is mandatory for a descriptive reading of normality in order to explain the logical (...) features of normality laws. Secondly, a statistical justification of normality statements can be derived by game theoretic considerations if the normality law is understood as communication convention. (shrink)

This article proposes a systematic application of recent developments in the logic of preference to a number of topics in deontic logic. The key junction is the well-known Hansson conditional for dyadic obligations. These conditionals are generalized by pairing them with reasoning about syntactic priority structures. The resulting two-level approach to obligations is tested first against standard scenarios of contrary-to-duty obligations, leading also to a generalization for the Kanger-Anderson reduction of deontic logic. Next, the priority framework is applied to model (...) two intuitively different sorts of deontic dynamics of obligations, based on information changes and on genuine normative events. In this two-level setting, we also offer novel takes on vexed issues such as the Chisholm paradox and modelling strong permission. Finally, the priority framework is shown to provide a unifying setting for the study of operations on norms as such, in particular, adding or deleting individual norms, and even merging whole norm systems in different manners. (shrink)

This paper proposes a two-level modeling perspective which combines intrinsic 'betterness' and reason-based extrinsic preference, and develops its static and dynamic logic in tandem. Our technical results extend, integrate, and re-interpret earlier theorems on preference representation and update in the literature on preference change.