The theory of theory change due to Alchourrón, Gärdenfors and Makinson ("AGM") has been widely known as being characterized by two sets of postulates, one being very weak and the other being very strong. Commenting on the three classic constructions of partial meet contraction, safe contraction and entrenchment-based construction, I argue that three intermediate levels can be distinguished that play decisive roles within the AGM theory.

Understanding the logical behavior of propositional attitudes, i.e. the mental states that we entertain with propositions (such as knowledge, belief, supposition, imagination, etc.), requires careful consideration of what such attitudes are about: their topic. This is the core intuition of Francesco Berto’s work, a book that fits into one of the most interesting and rich debates of recent decades, ranging over a wide variety of disciplines: from formal semantics to epistemology and even cognitive psychology. But above all, Berto’s book makes (...) a substantial contribution to what Daniel Nolan calls the hyperintensional revolution. In addition to being an original and ambitious proposal in the area of epistemic logic, the book can also be considered an excellent and in-depth introduction to many of the most interesting problems in the contemporary debate. (shrink)

The volume analyses and develops David Makinson’s efforts to make classical logic useful outside its most obvious application areas. The book contains chapters that analyse, appraise, or reshape Makinson’s work and chapters that develop themes emerging from his contributions. These are grouped into major areas to which Makinsons has made highly influential contributions and the volume in its entirety is divided into four sections, each devoted to a particular area of logic: belief change, uncertain reasoning, normative systems and the resources (...) of classical logic. Among the contributions included in the volume, one chapter focuses on the “inferential preferential method”, i.e. the combined use of classical logic and mechanisms of preference and choice and provides examples from Makinson’s work in non-monotonic and defeasible reasoning and belief revision. One chapter offers a short autobiography by Makinson which details his discovery of modern logic, his travels across continents and reveals his intellectual encounters and inspirations. The chapter also contains an unusually explicit statement on his views on the role of logic in philosophy. (shrink)

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

A model of inductive inquiry is defined within the context of first‐order logic. The model conceives of inquiry as a game between Nature and a scientist. To begin the game, a nonlogical vocabulary is agreed upon by the two players, along with a partition of a class of countable structures for that vocabulary. Next, Nature secretly chooses one structure from some cell of the partition. She then presents the scientist with a sequence of facts about the chosen structure. With each (...) new datum the scientist announces a guess about the cell to which the chosen structure belongs. To succeed in his or her inquiry, the scientist’s successive conjectures must be correct all but finitely often, that is, the conjectures must converge in the limit to the correct cell. Different kinds of scientists can be investigated within this framework. At opposite ends of the spectrum are dumb scientists that rely on the strategy of “induction by enumeration,” and smart scientists that rely on an operator of belief revision. We report some results about the scope and limits of these two inductive strategies. (shrink)

A model of inductive inquiry is defined within the context of first‐order logic. The model conceives of inquiry as a game between Nature and a scientist. To begin the game, a nonlogical vocabulary is agreed upon by the two players, along with a partition of a class of countable structures for that vocabulary. Next, Nature secretly chooses one structure from some cell of the partition. She then presents the scientist with a sequence of facts about the chosen structure. With each (...) new datum the scientist announces a guess about the cell to which the chosen structure belongs. To succeed in his or her inquiry, the scientist’s successive conjectures must be correct all but finitely often, that is, the conjectures must converge in the limit to the correct cell. Different kinds of scientists can be investigated within this framework. At opposite ends of the spectrum are dumb scientists that rely on the strategy of “induction by enumeration,” and smart scientists that rely on an operator of belief revision. We report some results about the scope and limits of these two inductive strategies. (shrink)

Choice revision is a sort of non-prioritized multiple revision, in which the agent partially accepts the new information represented by a set of sentences. We investigate the construction of choice revision based on a new approach to belief change called descriptor revision. We prove that each of two variants of choice revision based on such construction is axiomatically characterized with a set of plausible postulates, assuming that the object language is finite. Furthermore, we introduce an alternative modelling for choice revision, (...) which is based on a type of relation on sets of sentences, named multiple believability relation. We show without assuming a finite language that choice revision constructed from such relations is axiomatically characterized with the same sets of postulates that we proposed for the choice revision based on descriptor revision, whenever the relations satisfy certain rationality conditions. (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)

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

In this paper, I set out a new Kantian approach to resolving conflicts between moral obligations for highly autonomous machine agents. First, I argue that efforts to build explicitly moral autonomous machine agents should focus on what Kant refers to as duties of right, which are duties that everyone could accept, rather than on duties of virtue (or “ethics”), which are subject to dispute in particular cases. “Moral” machines must first be rightful machines, I argue. I then show how this (...) shift in focus from ethics to a standard of public right resolves the conflicts in what is known as the "trolley problem" for autonomous ma-chine agents. Finally, I consider how a deontic logic suitable for capturing duties of right might meet Kant’s requirement that rightfully enforceable obligations be consistent in a system of equal freedom under universal law. (shrink)

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

ABSTRACT The well-known AGM-theory-contraction and theory-revision, due to Alchourrón, Gärdenfors and Makinson, relies heavily on the so-called postulate of recovery. This postulate is supposed to capture the requirement of “minimum mutilation”; but it does not. Recovery can be satisfied even when there is more mutilation than is necessary. Recovery also ensures that very often too little is given up in a contraction, in this paper I bring out clearly the deficiencies of the AGM-theory in these two regards, showing how it (...) is doubly off-beam. I show that some of the most serious inadequacies of the AGM-theory derive from early claims in some of its founding contributions, claims that have not been seriously questioned within the tradition since. The upshot of these investigations is that recovery cannot, and should not, be recovered. Theory contraction is hysteretic. Whether the AGM-theory can now recover is a good question. (shrink)

The Theory of theory change has contraction and revision as its central notions. Of these, contraction is the more fundamental. The best-known theory, due to Alchourrón, Gärdenfors, and Makinson, is based on a few central postulates. The most fundamental of these is the principle of recovery: if one contracts a theory with respect to a sentence, and then adds that sentence back again, one recovers the whole theory. Recovery is demonstrably false. This paper shows why, and investigates how one can (...) nevertheless characterize contraction in a theoretically fruitful way. The theory proposed lends itself to implementation, which in turn could yield new theoretical insights. The Main proposal is a ‘staining algorithm’ which identifies which sentences to reject when contracting a theory. The algorithm requires one to be clear about the structure of reasons one has for including sentences within one's theory. (shrink)

I reformulate the AGM-account of contraction (which would yield an account also of revision). The reformulation involves using introduction and elimination rules for relational notions. Then I investigate the extent to which the two main methods of partial meet contraction and safe contraction can be employed for theories closed under intuitionistic consequence.

In this paper we propose an approach to multi-source belief revision where the trust or credibility assigned to informant agents can be revised. In our proposal, the credibility of each informant represented as a strict partial order among informant agents, will be maintained in a repository called credibility base. Upon arrival of new information concerning the credibility of its peers, an agent will be capable of revising this strict partial order, changing the trust assigned to its peers accordingly. Our goal (...) is to formalize a set of change operators over the credibility base: expansion, contraction, prioritized, and non-prioritized revision. These operators will provide the capability of dynamically modifying the credibility of informants considering the reliability of the information. This dynamics will reflect a new perception of trust assigned to the informant, or extend the set of informants by admitting the addition of new informant agents. (shrink)

Quine's holistic empiricist account of scientific inquiry can be characterized by three constitutive principles: *noncontradiction*, *universal revisability* and *pragmatic ordering*. We show that these constitutive principles cannot be regarded as statements within a holistic empiricist's scientific theory of the world. This claim is a corollary of our refutation of Katz's [1998, 2002] argument that holistic empiricism suffers from what he calls the Revisability Paradox. According to Katz, Quine's empiricism is incoherent because its constitutive principles cannot themselves be rationally revised. Using (...) Gärdenfors and Makinson's logic of belief revision based on epistemic entrenchment, we argue that Katz wrongly assumes that the constitutive principles are *statements* within a holistic empiricist's theory of the world. Instead, we show that constitutive principles are best seen as *properties* of a holistic empiricist's theory of scientific inquiry and we submit that, without Katz's mistaken assumption, the paradox cannot be formulated. We argue that our perspective on the status of constitutive principles is perfectly in line with Quinean orthodoxy. In conclusion, we compare our findings with van Fraassen's [2002] argument that we should think of empiricism as a stance, rather than as a doctrine. (shrink)

This paper presents a belief revision operator that considers time intervals for modelling norm change in the law. This approach relates techniques from belief revision formalisms and time intervals with temporalised rules for legal systems. Our goal is to formalise a temporalised belief base and corresponding timed derivation, together with a proper revision operator. This operator may remove rules when needed or adapt intervals of time when contradictory norms are added in the system. For the operator, both constructive definition and (...) an axiomatic characterisation by representation theorems are given. (shrink)

The expansion or revision of false theories by true evidence does not always increase their verisimilitude. After a comparison of different notions of verisimilitude the relation between verisimilitude and belief expansion or revision is investigated within the framework of the relevant element account. We are able to find certain interesting conditions under which both the expansion and the revision of theories by true evidence is guaranteed to increase their verisimilitude.

This article proposes a formal analysis of a fundamental aspect of legal reasoning: dealing with normative conflicts. Firstly, examples are illustrated concerning the dynamics of legal systems, the application of rules and exceptions, and the semantic indeterminacy of legal sources. Then two approaches to cope with conflicting information are presented: the preferred theories of Brewka, and the belief change functions of Alchourrón, Gärdenfors, and Makinson. The relations between those approaches are closely examined, and some aspects of a model of reasoning (...) with normative conflicts are outlined. Since this model takes into account an ordering of the involved regulations, criteria to order legal norms are finally specified. (shrink)

Naturalised realism’ is presented as a version of realism which is more compatible with the history of science than convergent or explanationist forms of realism. The account is unpacked according to four theses: 1) Whether realism is warranted with regards to a particular theory depends on the kind and quality of evidence available for that theory; 2) Reference is about causal interaction with the world; 3) Most of science happens somewhere in between instrumentalism and scientific realism on a continuum of (...) stances towards the status of theories; 4) The degree to which realism is warranted has something to do with the degree to which theories successfully refer, rather than with the truth of theories. (shrink)

In their unifying theory to model uncertainty, Friedman and Halpern (1995–2003) applied plausibility measures to default reasoning satisfying certain sets of axioms. They proposed a distinctive condition for plausibility measures that characterizes “qualitative” reasoning (as contrasted with probabilistic reasoning). A similar and similarly fundamental, but more general and thus stronger condition was independently suggested in the context of “basic” entrenchment-based belief revision by Rott (1996–2003). The present paper analyzes the relation between the two approaches to formalizing basic notions of plausibility (...) as used in qualitative default reasoning. While neither approach is a special case of the other, translations can be found that elucidate their relationship. I argue that Rott’s notion of plausibility allows for a more modular set-up and has a better philosophical motivation than that of Friedman and Halpern. (shrink)

A sentence A is epistemically less entrenched in a belief state K than a sentence B if and only if a person in belief state K who is forced to give up either A or B will give up A and hold on to B. This is the fundamental idea of epistemic entrenchment as introduced by Gärdenfors (1988) and elaborated by Gärdenfors and Makinson (1988). Another distinguishing feature of relations of epistemic entrenchment is that they permit particularly simple and elegant (...) construction recipes for minimal changes of belief states. These relations, however, are required to satisfy rather demanding conditions. In the present paper we liberalize the concept of epistemic entrenchment by removing connectivity, minimality and maximality conditions. Correspondingly, we achieve a liberalization of the concept of rational belief change that does no longer presuppose the postulates of success and rational monotony. We show that the central results of Gärdenfors and Makinson are preserved in our more flexible setting. Moreover, the generalized concept of epistemic entrenchment turns out to be applicable also to relational and iterated belief changes. (shrink)

We distinguish the set of explicit beliefs of a reasoner, his "belief base", from the beliefs that are merely implicit. Syntax-based belief change governed by the structure of the belief base and the ranking ("prioritization") of its elements is reconstructed with the help of an epistemic entrenchment relation in the style of Gärdenfors and Makinson. Though priorities are essentially different from entrenchments, distinguished relations of epistemic entrenchment may be obtained from prioritized belief bases by a number of different constructions. An (...) approximate reconstruction of syntax-based belief change is possible, which can be strengthened to a strict identity in some important special cases. A competitive interpretation and a minimal change interpretation of the basic idea of entrenchment are discussed. It is argued that entrenchment essentially involves multiple belief changes, i.e., changes by sets of sentences. (shrink)

The impact of our desires and preferences upon our ordinary, everyday beliefs is well-documented [Gilovich, T. . How we know what isn’t so: The fallibility of human reason in everyday life. New York: The Free Press.]. The influence of such motivational factors on delusions, which are instances of pathological misbelief, has tended however to be neglected by certain prevailing models of delusion formation and maintenance. This paper explores a distinction between two general classes of theoretical explanation for delusions; the motivational (...) and the deficit. Motivational approaches view delusions as extreme instances of self-deception; as defensive attempts to relieve pain and distress. Deficit approaches, in contrast, view delusions as the consequence of defects in the normal functioning of belief mechanisms, underpinned by neuroanatomical or neurophysiological abnormalities. It is argued that although there are good reasons to be sceptical of motivational theories , recent experiments confirm that motives are important causal forces where delusions are concerned. It is therefore concluded that the most comprehensive account of delusions will involve a theoretical unification of both motivational and deficit approaches. (shrink)

The process of completing, correcting and prioritising specifications is an essential but very complex task for the maintenance and improvement of software systems. The preservation of functionalities and the ability to accommodate changes are main objectives of the software development cycle to guarantee system reliability. Logical theories able to fully model such processes are still insufficient. In this paper we propose a full formalisation of such operations on software systems inspired by the Alchourrón–Gärdenfors–Makinson paradigm for belief revision of human epistemic (...) states. We represent specifications as finite sets of formulas equipped with a priority relation that models functional entrenchment of properties. We propose to handle specification incompleteness through ordered expansion, inconsistency through ordered safe contraction and prioritisation through revision with reordering, and model all three in an algorithmic fashion. We show how the system satisfies basic properties of the AGM paradigm, including Levi’s and Harper’s identities. We offer a concrete example and complexity results for the inference and model checking problems on revision. We conclude by describing resilience and evolvability of software systems based on such revision operators. (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 properties of belief revision operators are known to have an informal semantics which relates them to the axioms of conditional logic. The purpose of this paper is to make this connection precise via the model theory of conditional logic. A semantics for conditional logic is presented, which is expressed in terms of algebraic models constructed ultimately out of revision operators. In addition, it is shown that each algebraic model determines both a revision operator and a logic, that are related (...) by virtue of the stable Ramsey test. (shrink)

In this paper it is argued that, in order to solve the problem of iterated belief change, both the belief state and its input should be represented as epistemic entrenchment (EE) relations. A belief revision operation is constructed that updates a given EE relation to a new one in light of an evidential EE relation. It is shown that the operation in question satisfies generalized versions of the Gärdenfors revision postulates. The account offered is motivated by Spohn's ordinal conditionalization functions, (...) and can be seen as the Jeffrization of a proposal considered by Rott. (shrink)

This paper is concerned with the construction of a base contraction (revision) operation such that the theory contraction (revision) operation generated by it will be fully AGM-rational. It is shown that the theory contraction operation generated by Fuhrmann's minimal base contraction operation, even under quite strong restrictions, fails to satisfy the "supplementary postulates" of belief contraction. Finally Fuhrmann's construction is appropriately modified so as to yield the desired properties. The new construction may be described as involving a modification of safe (...) (base) contraction so as to make it maxichoice. (shrink)

In this paper, it is argued that both the belief state and its input should be represented as epistemic entrenchment (EE) relations. A belief revision operation is constructed that updates a given EE relation to a new one in light of an evidential EE relation, and an axiomatic characterization of this operation is given. Unlike most belief revision operations, the one developed here can handle both multiple belief revision and iterated belief revision.

As lawmakers produce norms, the underlying normative system is affected showing the intrinsic dynamism of law. Through undertaken actions of legal change, the normative system is continuously modified. In a usual legislative practice, the time for an enacted legal provision to be in force may differ from that of its inclusion to the legal system, or from that in which it produces legal effects. Even more, some provisions can produce effects retroactively in time. In this article we study a simulation (...) of such process through the formalisation of a temporalised logical framework upon which a novel belief revision model tackles the dynamic nature of law. Represented through intervals, the temporalisation of sentences allows differentiating the temporal parameters of norms. In addition, a proposed revision operator allows assessing change to the legal system by including a new temporalised literal while preserving the time-based consistency. This can be achieved either by pushing out conflictive pieces of pre-existing norms or through the modification of intervals in which such norms can be either in force, or produce effects. Finally, the construction of the temporalised revision operator is axiomatically characterised and its rational behavior proved through a corresponding representation theorem. (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)

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

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

Describes and discusses the rather special behaviour of one of the postulates in the AGM account of theory change.

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.

In a previous paper we developed a general theory of input/output logics. These are operations resembling inference, but where inputs need not be included among outputs, and outputs need not be reusable as inputs. In the present paper we study what happens when they are constrained to render output consistent with input. This is of interest for deontic logic, where it provides a manner of handling contrary-to-duty obligations. Our procedure is to constrain the set of generators of the input/output system, (...) considering only the maximal subsets that do not yield output conflicting with a given input. When inputs are authorised to reappear as outputs, both maxichoice revision in the sense of Alchourr6n/Makinson and the default logic of Poole emerge as special cases, and there is a close relation with Reiter default logic. However, our focus is on the general case where inputs need not be outputs. We show in what contexts the consistency of input with output may be reduced to its consistency with a truth-functional combination of components of generators, and under what conditions constrained output may be obtained by a derivation that is constrained at every step. (shrink)

This paper concerns the extent to which uncertain propositional reasoning can track probabilistic reasoning, and addresses kinematic problems that extend the familiar Lottery paradox. An acceptance rule assigns to each Bayesian credal state p a propositional belief revision method B p , which specifies an initial belief state B p (T) that is revised to the new propositional belief state B(E) upon receipt of information E. An acceptance rule tracks Bayesian conditioning when B p (E) = B p|E (T), for (...) every E such that p(E) > 0; namely, when acceptance by propositional belief revision equals Bayesian conditioning followed by acceptance. Standard proposals for uncertain acceptance and belief revision do not track Bayesian conditioning. The "Lockean" rule that accepts propositions above a probability threshold is subject to the familiar lottery paradox (Kyburg 1961), and we show that it is also subject to new and more stubborn paradoxes when the tracking property is taken into account. Moreover, we show that the familiar AGM approach to belief revision (Harper, Synthese 30(1-2):221-262, 1975; Alchourrón et al., J Symb Log 50:510-530, 1985) cannot be realized in a sensible way by any uncertain acceptance rule that tracks Bayesian conditioning. Finally, we present a plausible, alternative approach that tracks Bayesian conditioning and avoids all of the paradoxes. It combines an odds-based acceptance rule proposed originally by Levi (1996) with a non-AGM belief revision method proposed originally by Shoham (1987). (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)

Formal models of theory contraction entered the philosophicalliterature with the prototype model by Alchourrón, Gärdenfors,and Makinson (Alchourrón et al. 1985). One influential modelinvolves theory contraction with respect to a relation calledepistemic entrenchment which orders the propositions of a theoryaccording to their relative degrees of theoretical importance.Various postulates have been suggested for characterizingepistemic entrenchment formally. I argue here that threesuggested postulates produce inappropriately bizarre results whenapplied to scientific theories. I argue that the postulates callednoncovering, continuing up, and continuing down, implyrespectively that, (...) (i) no scientific law is more epistemicallyentrenched than any of its instances, (ii) two distinct instances ofthe same scientific law must have different degrees of epistemicentrenchment, and (iii) any two scientific laws must have differentdegrees of epistemic entrenchment. I also argue that continuingup and continuing down each lead to incoherency. (shrink)

Formal models of theory contraction entered the philosophicalliterature with the prototype model by Alchourrón, Gärdenfors,and Makinson (Alchourrón et al. 1985). One influential modelinvolves theory contraction with respect to a relation calledepistemic entrenchment which orders the propositions of a theoryaccording to their relative degrees of theoretical importance.Various postulates have been suggested for characterizingepistemic entrenchment formally. I argue here that threesuggested postulates produce inappropriately bizarre results whenapplied to scientific theories. I argue that the postulates callednoncovering, continuing up, and continuing down, implyrespectively that, (...) (i) no scientific law is more epistemicallyentrenched than any of its instances, (ii) two distinct instances ofthe same scientific law must have different degrees of epistemicentrenchment, and (iii) any two scientific laws must have differentdegrees of epistemic entrenchment. I also argue that continuingup and continuing down each lead to incoherency. (shrink)

Epistemic logic begins with the recognition that our everyday talk about knowing and believing has some systematic features that we can track and re‡ect upon. Epistemic logicians have studied and extended these glints of systematic structure in fascinating and important ways since the early 1960s. However, for one reason or another, mainstream epistemologists have shown little interest. It is striking to contrast the marginal role of epistemic logic in contemporary epistemology with the centrality of modal logic for metaphysicians. This article (...) is intended to help in correcting this oversight by presenting some important developments in epistemic logic and suggesting ways to understand their applicability to traditional epistemological problems. Obviously, by itself, tweaking the formal apparatus of epistemic logic does not solve traditional epistemological problems. Epistemic logic can help us to navigate through problems in a systematic fashion by unpacking the logic of the problematic concepts, it can also lead us to recognize problems that we had not anticipated. This is basically analogous to the role that modal logic has played in contemporary metaphysics. (shrink)

Kernel contraction is a natural nonrelational generalization of safe contraction. All partial meet contractions are kernel contractions, but the converse relationship does not hold. Kernel contraction is axiomatically characterized. It is shown to be better suited than partial meet contraction for formal treatments of iterated belief change.