The received view says that possibility is the dual of necessity: a proposition is (metaphysically, logically, epistemically etc.) possible iff it is not the case that its negation is (metaphysically, logically, epistemically etc., respectively) necessary. This reading is usually taken for granted by modal logicians and indeed seems plausible when dealing with logical or metaphysical possibility. But what about epistemic possibility? We argue that the dual definition of epistemic possibility in terms of epistemic necessity generates tension when reasoning about non-idealized (...) agents and is a problem of concern for most hyperintensional epistemic logics that alleviate the problem of logical omniscience. The tension is particularly evident when knowledge is taken as a primitive to define other epistemic concepts, such as justification and belief, as done in the knowledge-first tradition. We propose a non-dual interpretation of epistemic possibility, employing a hyperintensionality filter similar to the one that makes the corresponding epistemic necessity operator hyperintensional. We employ the proposed semantics to model Stalnaker's belief as epistemic possibility of knowledge and provide a sound and complete axiomatization for a hyperintensional version of his bimodal logic of knowledge and belief. (shrink)

Counterfactual skepticism says that most ordinary counterfactuals are false. While few endorse counterfactual skepticism, the precise costs of the view are disputed and not generally well-understood. I have two aims in this paper. My first and primary aim is to establish, on grounds acceptable to all parties, that counterfactual skepticism is not benign. I argue it leads to significant skepticism about the future: if counterfactual skepticism is true, then we can have only very limited knowledge about the future. I give (...) three arguments to this conclusion, taking as premises principles connecting knowledge of indicative conditionals to knowledge of disjunctions; and principles linking knowledge of indicative conditionals to knowledge of counterfactual conditionals.My second aim is to examine the consequences for non-skeptical theories. My arguments indicate that not only are many ordinary counterfactuals true, but that we also know them. How can this be reconciled with the very real tension between counterfactuals and chance? I consider two solutions, one purely epistemic and one contextualist. Together they suggest something like contextualism about knowledge is required to fully resolve the skeptical threat. (shrink)

Metaphilosophy, Volume 53, Issue 2-3, Page 267-283, April 2022.

This paper expounds a simple and non-trivial Ramsey Test. Drawing on the work of Peter Gärdenfors, it aims to help establish an epistemic alternative to the semantics of variably strict conditionals by Robert Stalnaker (in: Rescher (ed), Studies in logical theory, Blackwell, Oxford, 1968) and David Lewis (Counterfactuals, Blackwell, Oxford, 1973). The novelty of the present contribution lies in considering the framework of Preferred Subtheories as model of belief change upon which conditionals are defined. The resulting semantics avoids triviality in (...) the sense that a major premise of the proof of Gärdenfors’ triviality theorem is violated. (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)

Games, Norms, and Reasons: Logic at the Crossroads provides an overview of modern logic focusing on its relationships with other disciplines, including new interfaces with rational choice theory, epistemology, game theory and informatics. This book continues a series called "Logic at the Crossroads" whose title reflects a view that the deep insights from the classical phase of mathematical logic can form a harmonious mixture with a new, more ambitious research agenda of understanding and enhancing human reasoning and intelligent interaction. The (...) editors have gathered together articles from active authors in this new area that explore dynamic logical aspects of norms, reasons, preferences and beliefs in human agency, human interaction and groups. The book pays a special tribute to Professor Rohit Parikh, a pioneer in this movement. (shrink)

This book offers a state-of-the-art introduction to the basic techniques and results of neighborhood semantics for modal logic. In addition to presenting the relevant technical background, it highlights both the pitfalls and potential uses of neighborhood models – an interesting class of mathematical structures that were originally introduced to provide a semantics for weak systems of modal logic. In addition, the book discusses a broad range of topics, including standard modal logic results ; bisimulations for neighborhood models and other model-theoretic (...) constructions; comparisons with other semantics for modal logic ; neighborhood semantics for first-order modal logic, applications in game theory ; applications in epistemic logic ; and non-normal modal logics with dynamic modalities. The book can be used as the primary text for seminars on philosophical logic focused on non-normal modal logics; as a supplemental text for courses on modal logic, logic in AI, or philosophical logic ; or as the primary source for researchers interested in learning about the uses of neighborhood semantics in philosophical logic and game theory. (shrink)

– We offer a new motivation for imprecise probabilities. We argue that there are propositions to which precise probability cannot be assigned, but to which imprecise probability can be assigned. In such cases the alternative to imprecise probability is not precise probability, but no probability at all. And an imprecise probability is substantially better than no probability at all. Our argument is based on the mathematical phenomenon of non-measurable sets. Non-measurable propositions cannot receive precise probabilities, but there is a natural (...) way for them to receive imprecise probabilities. The mathematics of non-measurable sets is arcane, but its epistemological import is far-reaching; even apparently mundane propositions are liable to be affected by non-measurability. The phenomenon of non-measurability dramatically reshapes the dialectic between critics and proponents of imprecise credence. Non-measurability offers natural rejoinders to prominent critics of imprecise credence. Non-measurability even reverses some of the critics’ arguments—by the very lights that have been used to argue against imprecise credences, imprecise credences are better than precise credences. (shrink)

We study the logic of so-called lexicographic or priority merge for multi-agent plausibility models. We start with a systematic comparison between the logical behavior of priority merge and the more standard notion of pooling through intersection, used to define, for instance, distributed knowledge. We then provide a sound and complete axiomatization of the logic of priority merge, as well as a proof theory in labeled sequents that admits cut. We finally study Moorean phenomena and define a dynamic resolution operator for (...) priority merge for which we also provide a complete set of reduction axioms. (shrink)

We study imagination as reality-oriented mental simulation (ROMS): the activity of simulating nonactual scenarios in one’s mind, to investigate what would happen if they were realized. Three connected questions concerning ROMS are: What is the logic, if there is one, of such an activity? How can we gain new knowledge via it? What is voluntary in it and what is not? We address them by building a list of core features of imagination as ROMS, drawing on research in cognitive psychology (...) and the philosophy of mind. We then provide a logic of imagination as ROMS which models such features, combining techniques from epistemic logic, action logic, and subject matter semantics. Our logic comprises a modal propositional language with non-monotonic imagination operators, a formal semantics, and an axiomatization. (shrink)

According to the principle of Conjunction Closure, if one has justification for believing each of a set of propositions, one has justification for believing their conjunction. The lottery and preface paradoxes can both be seen as posing challenges for Closure, but leave open familiar strategies for preserving the principle. While this is all relatively well-trodden ground, a new Closure-challenging paradox has recently emerged, in two somewhat different forms, due to Backes :3773–3787, 2019a) and Praolini :715–726, 2019). This paradox synthesises elements (...) of the lottery and the preface and is designed to close off the familiar Closure-preserving strategies. By appealing to a normic theory of justification, I will defend Closure in the face of this new paradox. Along the way I will draw more general conclusions about justification, normalcy and defeat, which bear upon what Backes :2877–2895, 2019b) has dubbed the ‘easy defeat’ problem for the normic theory. (shrink)

Several theorists have observed that attitude reports have what we call “revisionist” uses. For example, even if Pete has never met Ann and has no idea that she exists, Jane can still say to Jim ‘Pete believes Ann can learn to play tennis in ten lessons’ if Pete believes all 6-year-olds can learn to play tennis in ten lessons and it is part of Jane and Jim’s background knowledge that Ann is a 6-year-old. Jane’s assertion seems acceptable because the claim (...) she reports Pete as believing is entailed by Pete’s beliefs if they are revised in light of Jane and Jim’s background knowledge. We provide a semantic theory of revisionist reports based on this idea. We observe that the admissible “revisions” are limited in a striking way. Jane cannot say ‘Pete thinks Ann is a 6-year-old and can play tennis in ten lessons’ in the same context that she can say ‘Pete believes Ann can learn to play tennis ten lessons’, even though this too follows from Jane and Jim’s background knowledge together with what Pete believes. Our theory predicts the infelicity of these latter reports. It also has the resources to predict the truth of “exported” attitude reports and casts the relationship between these reports and “singular thought” in a new light. We conclude by discussing how revisionist reports make trouble for a simplistic view of the connection between the relations expressed by attitude verbs in natural language and the relations of most interest to philosophers of mind and cognitive science. (shrink)

I present a possible worlds semantics for a hyperintensional belief revision operator, which reduces the logical idealization of cognitive agents affecting similar operators in doxastic and epistemic logics, as well as in standard AGM belief revision theory. (Revised) belief states are not closed under classical logical consequence; revising by inconsistent information does not perforce lead to trivialization; and revision can be subject to ‘framing effects’: logically or necessarily equivalent contents can lead to different revisions. Such results are obtained without resorting (...) to non-classical logics, or to non-normal or impossible worlds semantics. The framework combines, instead, a standard semantics for propositional S5 with a simple mereology of contents. (shrink)

In recent work, Stalnaker proposes a logical framework in which belief is realized as a weakened form of knowledge. Building on Stalnaker’s core insights, we employ topological tools to refine and, we argue, improve on this analysis. The structure of topological subset spaces allows for a natural distinction between what is known and what is knowable; we argue that the foundational axioms of Stalnaker’s system rely intuitively on both of these notions. More precisely, we argue that the plausibility of the (...) principles Stalnaker proposes relating knowledge and belief relies on a subtle equivocation between an “evidence-in-hand” conception of knowledge and a weaker “evidence-out-there” notion of what could come to be known. Our analysis leads to a trimodal logic of knowledge, knowability, and belief interpreted in topological subset spaces in which belief is definable in terms of knowledge and knowability. We provide a sound and complete axiomatization for this logic as well as its uni-modal belief fragment. We then consider weaker logics that preserve suitable translations of Stalnaker’s postulates, yet do not allow for any reduction of belief. We propose novel topological semantics for these irreducible notions of belief, generalizing our previous semantics, and provide sound and complete axiomatizations for the corresponding logics. (shrink)

A fictional text is commonly viewed as constituting an invitation to play a certain game of make-believe, with the individual sentences written by the author providing the propositions we are to imagine and/or accept as true within the fiction. However, we can’t always take the text at face value. What narratologists call ‘unreliable narrators’ may present a confused or misleading picture of the fictional world. Meanwhile there has been a debate in philosophy about so-called ‘imaginative resistance’ in which we are (...) inclined to resist imagining (or even accepting as true in the fiction) what’s explicitly stated in the text. But if we can’t take the text’s word for it, how do we determine what’s true in a fiction? We propose an account of fiction interpretation in a dynamic setting (a version of DRT with a mechanism for opening, updating, and closing temporary ‘workspaces’) and combine this framework with belief revision logic. With these tools in hand we turn to modelling imaginative resistance and unreliable narrators. (shrink)

We present a framework for epistemic logic, modeling the logical aspects of System 1 and System 2 cognitive processes, as per dual process theories of reasoning. The framework combines non-normal worlds semantics with the techniques of Dynamic Epistemic Logic. It models non-logically-omniscient, but moderately rational agents: their System 1 makes fast sense of incoming information by integrating it on the basis of their background knowledge and beliefs. Their System 2 allows them to slowly, step-wise unpack some of the logical consequences (...) of such knowledge and beliefs, by paying a cognitive cost. The framework is applied to three instances of limited rationality, widely discussed in cognitive psychology: Stereotypical Thinking, the Framing Effect, and the Anchoring Effect. (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.

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

Since the early 1980s, logical theories of belief revision have offered formal methods for the transformation of knowledge bases or “corpora” of data and beliefs. Early models have dealt with unconditional acceptance and integration of potentially belief-contravening pieces of information into the existing corpus. More recently, models of “non-prioritized” revision were proposed that allow the agent rationally to refuse to accept the new information. This paper introduces a refined method for changing beliefs by specifying constraints on the relative plausibility of (...) propositions. Like the earlier belief revision models, the method proposed is a qualitative one, in the sense that no numbers are needed in order to specify the posterior plausibility of the new information. We use reference beliefs in order to determine the degree of entrenchment of the newly accepted piece of information. We provide two kinds of semantics for this idea, give a logical characterization of the new model, study its relation with other operations of belief revision and contraction, and discuss its intuitive strengths and weaknesses. (shrink)

Darwiche and Pearl’s seminal 1997 article outlined a number of baseline principles for a logic of iterated belief revision. These principles, the DP postulates, have been supplemented in a number of alternative ways. Most suggestions have resulted in a form of ‘reductionism’ that identifies belief states with orderings of worlds. However, this position has recently been criticised as being unacceptably strong. Other proposals, such as the popular principle (P), aka ‘Independence’, characteristic of ‘admissible’ operators, remain commendably more modest. In this (...) paper, we supplement the DP postulates and (P) with a number of novel conditions. While the DP postulates constrain the relation between a prior and a posterior conditional belief set, our new principles notably govern the relation between two posterior conditional belief sets obtained from a common prior by different revisions. We show that operators from the resulting family, which subsumes both lexicographic and restrained revision, can be represented as relating belief states associated with a ‘proper ordinal interval’ (POI) assignment, a structure more fine-grained than a simple ordering of worlds. We close the paper by noting that these operators satisfy iterated versions of many AGM era postulates, including Superexpansion, that are not sound for admissible operators in general. (shrink)

This research is published within the project ‘The Logic of Conceivability’, funded by the European Research Council, Grant Number 681404.

This paper presents a uniform semantic treatment of nonmonotonic inference operations that allow for inferences from infinite sets of premises. The semantics is formulated in terms of selection functions and is a generalization of the preferential semantics of Shoham (1987), (1988), Kraus, Lehman, and Magidor (1990) and Makinson (1989), (1993). A selection function picks out from a given set of possible states (worlds, situations, models) a subset consisting of those states that are, in some sense, the most preferred ones. A (...) proposition α is a nonmonotonic consequence of a set of propositions Γ iff α holds in all the most preferred Γ-states. In the literature on revealed preference theory, there are a number of well-known theorems concerning the representability of selection functions, satisfying certain properties, in terms of underlying preference relations. Such theorems are utilized here to give corresponding representation theorems for nonmonotonic inference operations. At the end of the paper, the connection between nonmonotonic inference and belief revision, in the sense of Alchourrón, Gärdenfors, and Makinson, is explored. In this connection, infinitary belief revision operations that allow for the revision of a theory with a possibly infinite set of propositions are introduced and characterized axiomatically. (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)

The logic of Conditional Beliefs has been introduced by Board, Baltag, and Smets to reason about knowledge and revisable beliefs in a multi-agent setting. In this article both the semantics and the proof theory for this logic are studied. First, a natural semantics forCDLis defined in terms of neighbourhood models, a multi-agent generalisation of Lewis’ spheres models, and it is shown that the axiomatization ofCDLis sound and complete with respect to this semantics. Second, it is shown that the neighbourhood semantics (...) is equivalent to the original one defined in terms of plausibility models, by means of a direct correspondence between the two types of models. On the basis of neighbourhood semantics, a labelled sequent calculus forCDLis obtained. The calculus has strong proof-theoretic properties, in particular admissibility of contraction and cut, and it provides a decision procedure for the logic. Furthermore, its semantic completeness is used to obtain a constructive proof of the finite model property of the logic. Finally, it is shown that other doxastic operators can be easily captured within neighbourhood semantics. This fact provides further evidence of the naturalness of neighbourhood semantics for the analysis of epistemic/doxastic notions. (shrink)

The well-known formal semantics of conditionals due to Stalnaker Studies in logical theory, Blackwell, Oxford, 1968), Lewis, and Gärdenfors The logic and 1140 epistemology of scientific change, North-Holland, Amsterdam, 1978, Knowledge in flux, MIT Press, Cambridge, 1988) all fail to distinguish between trivially and nontrivially true indicative conditionals. This problem has been addressed by Rott :345–370, 1986) in terms of a strengthened Ramsey Test. In this paper, we refine Rott’s strengthened Ramsey Test and the corresponding analysis of explanatory relations. We (...) show that our final analysis captures the presumed asymmetry between explanans and explanandum much better than Rott’s original analysis. (shrink)

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

In this paper, we compare and contrast two methods for the revision of qualitative beliefs. The first method is generated by a simplistic diachronic Lockean thesis requiring coherence with the agent’s posterior credences after conditionalization. The second method is the orthodox AGM approach to belief revision. Our primary aim is to determine when the two methods may disagree in their recommendations and when they must agree. We establish a number of novel results about their relative behavior. Our most notable finding (...) is that the inverse of the golden ratio emerges as a non-arbitrary bound on the Bayesian method’s free-parameter—the Lockean threshold. This “golden threshold” surfaces in two of our results and turns out to be crucial for understanding the relation between the two methods. (shrink)

This paper develops an account of the meaning of `ought', and the distinction between weak necessity modals (`ought', `should') and strong necessity modals (`must', `have to'). I argue that there is nothing specially ``strong'' about strong necessity modals per se: uses of `Must p' predicate the (deontic/epistemic/etc.) necessity of the prejacent p of the actual world (evaluation world). The apparent ``weakness'' of weak necessity modals derives from their bracketing whether the necessity of the prejacent is verified in the actual world. (...) `Ought p' can be accepted without needing to settle that the relevant considerations (norms, expectations, etc.) that actually apply verify the necessity of p. I call the basic account a modal-past approach to the weak/strong necessity modal distinction (for reasons that become evident). Several ways of implementing the approach in the formal semantics/pragmatics are critically examined. The account systematizes a wide range of linguistic phenomena: it generalizes across flavors of modality; it elucidates a special role that weak necessity modals play in discourse and planning; it captures contrasting logical, expressive, and illocutionary properties of weak and strong necessity modals; and it sheds light on how a notion of `ought' is often expressed in other languages. These phenomena have resisted systematic explanation. In closing I briefly consider how linguistic inquiry into differences among necessity modals may improve theorizing on broader philosophical issues. (shrink)

Nearly a decade has past since Grove gave a semantics for the AGM postulates. The semantics, called sphere semantics, provided a new perspective of the area of study, and has been widely used in the context of theory or belief change. However, the soundness proof that Grove gives in his paper contains an error. In this note, we will point this out and give two ways of repairing it.

This paper reorganizes and further develops the theory of partial meet contraction which was introduced in a classic paper by Alchourron, Gardenfors, and Makinson. Our purpose is threefold. First, we put the theory in a broader perspective by decomposing it into two layers which can respectively be treated by the general theory of choice and preference and elementary model theory. Second, we reprove the two main representation theorems of AGM and present two more representation results for the finite case that (...) "lie between" the former, thereby partially answering an open question of AGM. Our method of proof is uniform insofar as it uses only one form of "revealed preference", and it explains where and why the finiteness assumption is needed. Third, as an application, we explore the logic characterizing theory contractions in the finite case which are governed by the structure of simple and prioritized belief bases. (shrink)

Richard Bradley has initiated a new debate, with Brian Hill and Jake Chandler as further participants, about the implications of a number of so-called triviality results surrounding the Ramsey test for conditionals. I comment on this debate and argue that ‘Inclusion’ and ‘Preservation’, which were originally introduced as postulates for the rational revision of factual beliefs, have little to recommend them in the first place when extended to languages containing conditionals. I question the philosophical method of postulation that was applied (...) in the new debate, and instead base my arguments on explicit representations of belief states and canonical constructions of belief state revisions. (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)

In this paper we study AGM contraction and revision of rules using input/output logical theories. We replace propositional formulas in the AGM framework of theory change by pairs of propositional formulas, representing the rule based character of theories, and we replace the classical consequence operator Cn by an input/output logic. The results in this paper suggest that, in general, results from belief base dynamics can be transferred to rule base dynamics, but that a similar transfer of AGM theory change to (...) rule change is much more problematic. First, we generalise belief base contraction to rule base contraction, and show that two representation results of Hansson still hold for rule base contraction. Second, we show that the six so-called basic postulates of AGM contraction are consistent only for some input/output logics, but not for others. In particular, we show that the notorious recovery postulate can be satisfied only by basic output, but not by simple-minded output. Third, we show how AGM rule revision can be defined in terms of AGM rule contraction using the Levi identity. We highlight various topics for further research. (shrink)

A set of sentential revision operations can be generated in a select-direct way within a new framework for belief change named descriptor revision firstly introduced in Hansson [8]. In this paper, we adopt another constructive approach to these operations, based on a relation \ on sentences named believability relation. Intuitively, \ means that the subject is at least as prone to believe or accept \ as to believe or accept \. We demonstrate that so called H-believability relations and basic believability (...) relations, the second of which the is axiomatically characterized with a set of weak postulates, are faithful alternative models for two typical select-direct sentential revision operations. Then we investigate additional postulates on believability relations that correlate with properties of the generated revision operations. Finally, we show that traditional AGM revision operations can be reconstructed from a strengthened variant of the basic believability relation and there is a close connection between this relation and the standard epistemic entrenchment relation. (shrink)

After a number of decades of research into the dynamics of rational belief, the belief revision theory community remains split on the appropriate handling of sequences of changes in view, the issue of so-called iterated revision. It has long been suggested that the matter is at least partly settled by facts pertaining to the results of various single revisions of one’s initial state of belief. Recent work has pushed this thesis further, offering various strong principles that ultimately result in a (...) wholesale reduction of iterated to one-shot revision. The present paper offers grounds to hold that these principles should be significantly weakened and that the reductionist thesis should ultimately be rejected. Furthermore, the considerations provided suggest a close connection between the logic of iterated belief change and the logic of evidential relevance. (shrink)

One of the standard principles of rationality guiding traditional accounts of belief change is the principle of minimal change: a reasoner's belief corpus should be modified in a minimal fashion when assimilating new information. This rationality principle has stood belief change in good stead. However, it does not deal properly with all belief change scenarios. We introduce a novel account of belief change motivated by one of Grice's maxims of conversational implicature: the reasoner's belief corpus is modified in a minimal (...) fashion to assimilate exactly the new information. In this form of belief change, when the reasoner revises by new information p ∨ q their belief corpus is modified so that p∨q is believed but stronger propositions like p∧q are not, no matter what beliefs are in the reasoner's initial corpus. We term this conservative belief change since the revised belief corpus is a conservative extension of the original belief corpus given the new information. (shrink)

Deontic Logic goes back to Ernst Mally’s 1926 work, Grundgesetze des Sollens: Elemente der Logik des Willens [Mally. E.: 1926, Grundgesetze des Sollens: Elemente der Logik des Willens, Leuschner & Lubensky, Graz], where he presented axioms for the notion ‘p ought to be the case’. Some difficulties were found in Mally’s axioms, and the field has much developed. Logic of Knowledge goes back to Hintikka’s work Knowledge and Belief [Hintikka, J.: 1962, Knowledge and Belief: An Introduction to the Logic of (...) the Two Notions, Cornell University Press] in which he proposed formal logics of knowledge and belief. This field has also developed quite a great deal and is now the subject of the TARK conferences. However, there has been relatively little work combining the two notions of knowledge (belief) with the notion of obligation. (See, however, [Lomuscio, A. and Sergot, M.: 2003, Studia Logica 75 63–92; Moore, R. C.: 1990, In J. F. Allen, J. Hendler and A. Tate (eds.), Readings in Planning, Morgan Kaufmann Publishers, San Mateo, CA]) In this paper we point out that an agent’s obligations are often dependent on what the agent knows, and indeed one cannot reasonably be expected to respond to a problem if one is not aware of its existence. For instance, a doctor cannot be expected to treat a patient unless she is aware of the fact that he is sick, and this creates a secondary obligation on the patient or someone else to inform the doctor of his situation. In other words, many obligations are situation dependent, and only apply in the presence of the relevant information. Thus a case for combining Deontic Logic with the Logic of Knowledge is clear. We introduce the notion of knowledge based obligation and offer an S5, history based Kripke semantics to express this notion, as this semantics enables us to represent how information is transmitted among agents and how knowledge changes over time as a result of communications. We consider both the case of an absolute obligation (although dependent on information) as well as the (defeasible) notion of an obligation which may be over-ridden by more relevant information. For instance a physician who is about to inject a patient with drug d may find out that the patient is allergic to d and that she should use d′ instead. Dealing with the second kind of case requires a resort to non-monotonic reasoning and the notion of justified belief which is stronger than plain belief, but weaker than absolute knowledge in that it can be over-ridden. This notion of justified belief also creates a derived notion of default obligation where an agent has, as far as the agent knows, an obligation to do some action a. A dramatic application of this notion is our analysis of the Kitty Genovese case where, in 1964, a young woman was stabbed to death while 38 neighbours watched from their windows but did nothing. The reason was not indifference, but none of the neighbours had even a default obligation to act, even though, as a group, they did have an obligation to take some action to protect Kitty. (shrink)

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

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

A dynamic semantics for iffy oughts offers an attractive alternative to the folklore that Chisholm's paradox enforces an unhappy choice between the intuitive inference rules of factual and deontic detachment. The first part of the story told here shows how a dynamic theory about ifs and oughts gives rise to a nonmonotonic perspective on deontic discourse and reasoning that elegantly removes the air of paradox from Chisholm's puzzle without sacrificing any of the two detachment principles. The second part of the (...) story showcases two bonus applications of the framework suggested here: it offers a response to Forrester's gentle murder paradox and avoids Kolodny and MacFarlane's miners paradox about deontic reasoning under epistemic uncertainty. A comparison between the dynamic semantic proposal made in this paper and a more conservative approach combining a static semantics with a dynamic pragmatics is provided. (shrink)

This essay develops a joint theory of rational (all-or-nothing) belief and degrees of belief. The theory is based on three assumptions: the logical closure of rational belief; the axioms of probability for rational degrees of belief; and the so-called Lockean thesis, in which the concepts of rational belief and rational degree of belief figure simultaneously. In spite of what is commonly believed, this essay will show that this combination of principles is satisfiable (and indeed nontrivially so) and that the principles (...) are jointly satisfied if and only if rational belief is equivalent to the assignment of a stably high rational degree of belief. Although the logical closure of belief and the Lockean thesis are attractive postulates in themselves, initially this may seem like a formal “curiosity”; however, as will be argued in the rest of the essay, a very reasonable theory of rational belief can be built around these principles that is not ad hoc and that has various philosophical features that are plausible independently. In particular, this essay shows that the theory allows for a solution to the Lottery Paradox, and it has nice applications to formal epistemology. The price that is to be paid for this theory is a strong dependency of belief on the context, where a context involves both the agent's degree of belief function and the partitioning or individuation of the underlying possibilities. But as this essay argues, that price seems to be affordable. (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)

This paper combines various structures representing degrees of belief, degrees of disbelief, and degrees of non-belief (degrees of expectations) into a unified whole. The representation uses relations of comparative necessity and possibility, as well as non-probabilistic functions assigning numerical values of necessity and possibility. We define all-encompassing necessity structures which have weak expectations (mere hypotheses, guesses, conjectures, etc.) occupying the lowest ranks and very strong, ineradicable ('a priori') beliefs occupying the highest ranks. Structurally, there are no differences from the top (...) to the bottom. I argue that belief is a vague notion, and that thresholds for belief, if there are any, are context-dependent. (shrink)