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)

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)

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)

In their recently published book Nudge (2008) Richard H. Thaler and Cass R. Sunstein (T&S) defend a position labelled as ‘libertarian paternalism’. Their thinking appeals to both the right and the left of the political spectrum, as evidenced by the bedfellows they keep on either side of the Atlantic. In the US, they have advised Barack Obama, while, in the UK, they were welcomed with open arms by the David Cameron's camp (Chakrabortty 2008). I will consider the following questions. What (...) is Nudge? How is it different from social advertisement? Does Nudge induce genuine preference change? Does Nudge build moral character? Is there a moral difference between the use of Nudge as opposed to subliminal images to reach policy objectives? And what are the moral constraints on Nudge? (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)

Given the role consensus is supposed to play in the social aspects of inquiry and deliberation, it is important that we may always identify a consensus as the basis of joint inquiry and deliberation. However, it turns out that if we think of an agent revising her beliefs to reach a consensus, then, on the received view of belief revision, AGM belief revision theory, certain simple and compelling consensus positions are not always available.

We provide a formal study of belief retraction operators that do not necessarily satisfy the postulate. Our intuition is that a rational description of belief change must do justice to cases in which dropping a belief can lead to the inclusion, or ‘liberation’, of others in an agent's corpus. We provide two models of liberation via retraction operators: ρ-liberation and linear liberation. We show that the class of ρ-liberation operators is included in the class of linear ones and provide axiomatic (...) characterisations for each class. We show how any retraction operator can be ‘converted’ into either a withdrawal operator ) or a revision operator via the Harper Identity and the Levi Identity respectively. (shrink)

Specified meet contraction is the operation defined by the identity where ∼ is full meet contraction and f is a sentential selector, a function from sentences to sentences. With suitable conditions on the sentential selector, specified meet contraction coincides with the partial meet contractions that yield a finite-based contraction outcome if the original belief set is finite-based. In terms of cognitive realism, specified meet contraction has an advantage over partial meet contraction in that the selection mechanism operates on sentences rather (...) than on temporary infinite structures (remainders) that are cognitively inaccessible. Specified meet contraction provides a versatile framework in which other types of contraction, such as severe withdrawal and base-generated contraction, can be expressed with suitably chosen properties of the sentential selector. (shrink)

A model of coherentist belief contraction is constructed. The outcome of belief contraction is required to be one of the coherent subsets of the original belief set, and a set of plausible properties is proposed for this set of coherent subsets. The contraction operators obtained in this way are shown to coincide with well-known belief base operations. This connection between coherentist and "foundationalist" approaches to belief change has important implications for the philosophical interpretation of models of belief change.

The contributions to the Special Issue on Multiple Belief Change, Iterated Belief Change and Preference Aggregation are divided into three parts. Four contributions are grouped under the heading "multiple belief change" (Part I, with authors M. Falappa, E. Fermé, G. Kern-Isberner, P. Peppas, M. Reis, and G. Simari), five contributions under the heading "iterated belief change" (Part II, with authors G. Bonanno, S.O. Hansson, A. Nayak, M. Orgun, R. Ramachandran, H. Rott, and E. Weydert). These papers do not only pick (...) up the particular questions raised, but also extend and modify the framework of Alchourrón, Gärdenfors and Makinson. Part III deals with preference aggregation and consists of one contribution (by F. Herzberg and D. Eckert). (shrink)

We propose a new class of multiple contraction operations — the system of spheres-based multiple contractions — which are a generalization of Grove’s system of spheres-based (singleton) contractions to the case of contractions by (possibly non-singleton) sets of sentences. Furthermore, we show that this new class of functions is a subclass of the class of the partial meet multiple contractions.

In a recent article, Zhang and Foo generalized the AGM postulates for contraction to include infinite epistemic input. The new type of belief change is called set contraction. Zhang and Foo also introduced a constructive model for set contraction, called nicely ordered partition, as a generalization of epistemic entrenchment. It was shown however that the functions induced from nicely ordered partitions do not quite match the postulates for set contraction. The mismatch was fixed with the introduction of an extra condition (...) called the limit postulate. The limit postulate establishes a connection between contraction by infinite epistemic input and contraction by finite epistemic input (reducing the former to the latter) and it is appealing both on mathematical and on conceptual grounds. It is debatable however whether the limit postulate can be adopted as a general feature of rationality in set contraction. Instead we propose that the limit postulate is viewed as a condition characterizing an important special case of set contraction functions. With this reading in mind, in this article we introduce an alternative generalization of epistemic entrenchment, based on the notion of comparative possibility. We prove that the functions induced from comparative possibility preorders precisely match those satisfying the postulates for set contraction (without the limit postulate). The relationship between comparative possibility and epistemic entrenchment is also investigated. Finally, we formulate necessary and sufficient conditions under which the functions induced from comparative possibility preorders coincide with the special class of contraction functions characterized by the limit postulate. (shrink)

Theory change is a central concern in contemporary epistemology and philosophy of science. In this paper, we investigate the relationships between two ongoing research programs providing formal treatments of theory change: the (post-Popperian) approach to verisimilitude and the AGM theory of belief change. We show that appropriately construed accounts emerging from those two lines of epistemological research do yield convergences relative to a specified kind of theories, here labeled “conjunctive”. In this domain, a set of plausible conditions are identified which (...) demonstrably capture the verisimilitudinarian effectiveness of AGM belief change, i.e., its effectiveness in tracking truth approximation. We conclude by indicating some further developments and open issues arising from our results. (shrink)

The process [by which any individual settles into new opinions] is always the same. The individual has a stock of old opinions already, but he meets a new experience that puts them to a strain…. The result is an inward trouble to which his mind till then had been a stranger, and from which he seeks to escape by modifying his previous mass of opinions. He saves as much of it as he can, for in this matter of belief we (...) are all extreme conservatives. So he tries to change first this opinion, and then that (for they resist change very variously), until at last some new idea comes up which he can graft upon the ancient stock with a minimum of disturbance of the latter, some idea that mediates between the stock and the new experience and runs them into one most felicitously and expediently.The new idea is then adopted as the true one. It preserves the older stock of truths with a minimum of modification, stretching them just enough to make them admit the novelty, but conceiving that in ways as familiar as the case leaves possible. (William James, Lectures on Pragmatism, 1907). (shrink)

Starting from the sixties of the past century theory change has become a main concern of philosophy of science. Two of the best known formal accounts of theory change are the post-Popperian theories of verisimilitude (PPV for short) and the AGM theory of belief change (AGM for short). In this paper, we will investigate the conceptual relations between PPV and AGM and, in particular, we will ask whether the AGM rules for theory change are effective means for approaching the truth, (...) i.e., for achieving the cognitive aim of science pointed out by PPV. First, the key ideas of PPV and AGM and their application to a particular kind of propositional theories - the so called "conjunctive propositions" - will be illustrated. Afterwards, we will prove that, as far as conjunctive propositions are concerned, AGM belief change is an effective tool for approaching the truth. (shrink)

First, ranking functions are argued to be superior to AGM belief revision theory in two crucial respects. Second, it is shown how ranking functions are uniquely reflected in iterated belief change. More precisely, conditions on threefold contractions are specified which suffice for representing contractions by a ranking function uniquely up to multiplication by a positive integer. Thus, an important advantage AGM theory seemed to have over ranking functions proves to be spurious.

I argue that the analysis most capable of systematising our intuitions about coherence as a relation is one according to which a set of beliefs, A, coheres with another set, B, if and only if the set-theoretical union of A and B is a coherent set. The second problem I consider is the role of coherence in epistemic justification. I submit that there are severe problems pertaining to the idea, defended most prominently by Keith Lehrer, that justification amounts to coherence (...) with an acceptance system. Instead I advance a more dynamic approach according to which the problem of justification is the problem of how to merge new information with old coherently, a process which is seen to be closely connected with relational coherence. (shrink)

This paper presents a theory of belief revision that allows people to come tobelieve in contradictions. The AGM theory of belief revision takes revision,in part, to be consistency maintenance. The present theory replacesconsistency with a weaker property called coherence. In addition to herbelief set, we take a set of statements that she rejects. These two sets arecoherent if they do not overlap. On this theory, belief revision maintains coherence.

It was shown that finite P-recovery holds for partial meet package contraction in Furhmann and Hansson (1994). However, it is not known if recovery holds for partial meet package contraction in the infinite case. In this paper, I show that recovery does not hold for partial meet package contraction in the infinite case.

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

Changing preferencesis a phenomenonoften invoked but rarely properlyaccounted for. Throughout the history of the social sciences, researchers have come against the possibility that their subjects’ preferenceswere affected by the phenomenato be explainedor by otherfactorsnot taken into accountin the explanation.Sporadically, attempts have been made to systematically investigate these in uences, but none of these seems to have had a lasting impact. Today we are still not much further with respect to preference change than we were at the middle of the last (...) century. This anthology hopes to provide a new impulse for research into this important subject. In particular, we have chosen two routes to amplify this impulse. First, we stress the use of modellingtechniquesfamiliar from economicsand decision theory. Instead of constructing complex, all-encompassing theories of preference change, the authors of this volume start with very simple, formal accounts of some possible and hopefully plausible mechanism of preference change. Eventually, these models may nd their way into larger, empirically adequate theories, but at this stage, we think that the most importantwork lies in building structure.Secondly,we stress the importance of interdisciplinary exchange. Only by drawing together experts from different elds can the complex empirical and theoretical issues in the modelling of preference change be adequately investigated. (shrink)

Modern belief revision theory is based to a large extent on partial meet contraction that was introduced in the seminal article by Carlos Alchourrón, Peter Gärdenfors, and David Makinson that appeared in 1985. In the same year, Alchourrón and Makinson published a significantly different approach to the same problem, called safe contraction. Since then, safe contraction has received much less attention than partial meet contraction. The present paper summarizes the current state of knowledge on safe contraction, provides some new results (...) and offers a list of unsolved problems that are in need of investigation. (shrink)

Belief revision from the point of view of doxastic logic. Logic Journal of the IGPL, 3(4), 535–553. Segerberg, K. (1995). Conditional action. In G. Crocco, L. Fariñas, & A. Herzig (Eds.), Conditionals: From philosophy to computer science, Studies ...

This paper generalises classical revision theory of the AGM brand to sets of norms. This is achieved substituting input/output logic for classical logic and tracking the changes. Operations of derogation and amendment—analogues of contraction and revision—are defined and characterised, and the precise relationship between contraction and derogation, on the one hand, and derogation and amendment on the other, is established. It is argued that the notion of derogation, in particular, is a very important analytical tool, and that even core deontic (...) concepts such as that of permission resists a satisfactory analysis without it. By way of illustration the last section of the paper analyses the much debated concept of positive permission, of which there turns out to be more than one kind. (shrink)

Generalizations of partial meet contraction are introduced that start out from the observation that only some of the logically closed subsets of the original belief set are at all viable as contraction outcomes. Belief contraction should proceed by selection among these viable options. Several contraction operators that are based on such selection mechanisms are introduced and then axiomatically characterized. These constructions are more general than the belief base approach. It is shown that partial meet contraction is exactly characterized by adding (...) to one of these constructions the condition that all logically closed subsets of the belief set can be obtained as the outcome of a single (multiple) contraction. Examples are provided showing the counter-intuitive consequences of that condition, thus confirming the credibility of the proposed generalization of the AGM framework. (shrink)

We propose a revision operator on a stratified belief base, i.e., a belief base that stores beliefs in different strata corresponding to the value an agent assigns to these beliefs. Furthermore, the operator will be defined as to perform the revision in such a way that information is never lost upon revision but stored in a stratum or layer containing information perceived as having a lower value. In this manner, if the revision of one layer leads to the rejection of (...) some information to maintain consistency, instead of being withdrawn it will be kept and introduced in a different layer with lower value. Throughout this development we will follow the principle of minimal change, being one of the important principles proposed in belief change theory, particularly emphasized in the AGM model. Regarding the reasoning part from the stratified belief base, the agent will obtain the inferences using an argumentative formalism. Thus, the argumentation framework will decide which information prevails when sentences of different layers are used for entailing conflicting beliefs. We will also illustrate how inferences are changed and how the status of arguments can be modified after a revision process. (shrink)

A representation theorem is obtained for contraction operators that are based on Levi's recent proposal that selection functions should be applied to the set of saturatable contractions, rather than to maximal subsets as in the AGM framework. Furthermore, it is shown that Levi's proposal to base the selection on a weakly monotonic measure of informational value guarantees the satisfaction of both of Gärdenfors' supplementary postulates for contraction. These results indicate that Levi has succeeded in constructing a well-behaved operation of contraction (...) that does not satisfy the postulate of recovery. (shrink)

This paper extends the AGM theory of belief revision to accommodate infinitary belief change. We generalize both axiomatization and modeling of the AGM theory. We show that most properties of the AGM belief change operations are preserved by the generalized operations whereas the infinitary belief change operations have their special properties. We prove that the extended axiomatic system for the generalized belief change operators with a Limit Postulate properly specifies infinite belief change. This framework provides a basis for first-order belief (...) revision and the theory of revising a belief state by a belief state. (shrink)

The most controversial condition that the AGM theory of rational belief change places on belief contraction is the recovery condition. The condition is controversial because of a series of putative counterexamples due (separately) to I. Levi and S. O. Hansson. In this paper we show that the conflicts that Levi and Hansson arrange between AGM contraction and our intuitions about how to give up beliefs are merely apparent. We argue that these conflicts disappear once we attend more closely to the (...) identification of the beliefs contracted away in each counterexample case. Since, on our view, speakers" belief contraction intentions are often more complicated than they may first appear, we are led to develop apparatus for thinking about the communication and identification of those intentions. Our argument refocuses attention on the difficult question of how to apply the AGM theory to particular cases. (shrink)

This paper focuses on the extension of AGM that allows change for a belief base by a set of sentences instead of a single sentence. In [FH94], Fuhrmann and Hansson presented an axiomatic for Multiple Contraction and a construction based on the AGM Partial Meet Contraction. We propose for their model another way to construct functions: Multiple Kernel Contraction, that is a modification of Kernel Contraction, proposed by Hansson [Han94] to construct classical AGM contractions and belief base contractions. This construction (...) works out the unsolved problem pointed out by Hansson in [Han99, pp. 369]. (shrink)

The postulate of Recovery, among the six postulates for theory contraction, formulated and studied by Alchourrón, Gärdenfors and Makinson is the one that has provoked most controversy. In this article we construct withdrawal functions that do not satisfy Recovery, but try to preserve minimal change, and relate these withdrawal functions with the AGM contraction functions.

Traditionally, belief change is modelled as the construction of a belief set that satisfies a success condition. The success condition is usually that a specified sentence should be believed or not believed. Furthermore, most models of belief change employ a select-and-intersect strategy. This means that a selection is made among primary objects that satisfy the success condition, and the intersection of the selected objects is taken as outcome of the operation. However, the select-and-intersect method is difficult to justify, in particular (...) since the primary objects are not themselves plausible outcome candidates. Some of the most controversial features of belief change theory, such as recovery and the impossibility of Ramsey test conditionals, are closely connected with the select-and-intersect method. It is proposed that a selection mechanism should instead operate directly on the potential outcomes, and select only one of them. In this way many of the problems that are associated with the select-and-intersect method can be avoided. This model is simpler than previous models in the important Ockhamist sense of doing away with intermediate, cognitively inaccessible objects. However, the role of simplicity as a choice criterion in the direct selection among potential outcomes is left as an open issue. (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)

The 1985 paper by Carlos Alchourrón (1931–1996), Peter Gärdenfors, and David Makinson (AGM), "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 twentyfive 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 can often specify how we would contract by a certain sentence by saying that this contraction would coincide with some other contraction that we know how to perform. We can for instance clarify that our contraction by p&q would coincide with our contraction by p, or by q, or by {p, q}. In a framework where the set of potential outcomes is known, some contractions are “self-evident” in the sense that there is only one serious candidate that can be (...) the outcome of such a contraction. Contraction by a specific contractee (sentence or set of sentences to be contracted) is bootstrapped if it is specified by saying that it coincides with some such self-evident contraction. For a wide range of (multiple) contraction operators, contractions by any contractee can be bootstrapped. This means that the selection mechanism (selection function, incision function, etc.) can be replaced by a function called a bootstrapping selector that assigns to each contractee some “self-evident” contractee that yields the same outcome. With bootstrapping we can eliminate traditional extralogical components in contraction (e.g., selection functions) and replace them by bootstrapping selectors that reflect more closely the ways in which we actually reason and argue about belief contraction. (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)

Blockage contraction is an operation of belief contraction that acts directly on the outcome set, i.e. the set of logically closed subsets of the original belief set K that are potential contraction outcomes. Blocking is represented by a binary relation on the outcome set. If a potential outcome X blocks another potential outcome Y, and X does not imply the sentence p to be contracted, then Y ≠ K ÷ p. The contraction outcome K ÷ p is equal to the (...) (unique) inclusion-maximal unblocked element of the outcome set that does not imply p. Conditions on the blocking relation are specified that ensure the existence of such a unique inclusion-maximal set for all sentences p. Blockage contraction is axiomatically characterized and its relations to AGM-style operations are investigated. In a finite-based framework, every transitively relational partial meet contraction is also a blockage contraction. (shrink)

The problem of how to remove information from an agent's stock of beliefs is of paramount concern in the belief change literature. An inquiring agent may remove beliefs for a variety of reasons: a belief may be called into doubt or the agent may simply wish to entertain other possibilities. In the prominent AGM framework for belief change, upon which the work here is based, one of the three central operations, contraction, addresses this concern (the other two deal with the (...) incorporation of new information). Makinson has generalised this work by introducing the notion of a withdrawal operation. Underlying the account proffered by AGM is the idea of rational belief change. A belief change operation should be guided by certain principles or integrity constraints in order to characterise change by a rational agent. One of the most noted principles within the context of AGM is the Principle of Informational Economy. However, adoption of this principle in its purest form has been rejected by AGM leading to a more relaxed interpretation. In this paper, we argue that this weakening of the Principle of Informational Economy suggests that it is only one of a number of principles which should be taken into account. Furthermore, this weakening points toward a Principle of Indifference. This motivates the introduction of a belief removal operation that we call severe withdrawal. We provide rationality postulates for severe withdrawal and explore its relationship with AGM contraction. Moreover, we furnish possible worlds and epistemic entrenchment semantics for severe withdrawals. (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)

In the logic of theory change, the standard model is AGM, proposed by Alchourrón et al. (J Symb Log 50:510–530, 1985 ). This paper focuses on the extension of AGM that accounts for contractions of a theory by a set of sentences instead of only by a single sentence. Hansson (Theoria 55:114–132, 1989 ), Fuhrmann and Hansson (J Logic Lang Inf 3:39–74, 1994 ) generalized Partial Meet Contraction to the case of contractions by (possibly non-singleton) sets of sentences. In this (...) paper we present the possible worlds semantics for partial meet multiple contractions. (shrink)

A model of coherentist belief contraction is constructed. The outcome of belief contraction is required to be one of the coherent subsets of the original belief set, and a set of plausible properties is proposed for this set of coherent subsets. The contraction operators obtained in this way are shown to coincide with well-known belief base operations. This connection between coherentist and foundationalist approaches to belief change has important implications for the philosophical interpretation of models of belief change.

Multiple contraction (simultaneous contraction by several sentences) and iterated contraction are investigated in the framework of specified meet contraction (s.m.c.) that is extended for this purpose. Multiple contraction is axiomatized, and so is finitely multiple contraction (contraction by a finite set of sentences). Two ways to reduce finitely multiple contraction to contraction by single sentences are introduced. The reduced operations are axiomatically characterized and their properties are investigated. Furthermore, it is shown how iterated contraction can be reduced to single-step, single-sentence (...) contraction. However, in this framework the outcome of iterated contraction depends unavoidably on the order in which the inputs are received. This order-dependence makes it impossible to treat two inputs on an equal footing. Therefore it is often preferable to perform changes involving several pieces of information as multiple rather than iterated change. (shrink)

Full meet contraction, that was devised by Carlos Alchourrón and David Makinson in the early 1980' s, has often been overlooked since it is not in itself a plausible contraction operator. However, it is a highly useful building-block in the construction of composite contraction operators. In particular, all plausible contraction operators can be reconstructed so that the outcome of contracting a belief set K by a sentence p is defined as K ∼ f, where ∼ is full meet contraction and (...) f a sentential selector, i.e. a function to and from sentences. This paper investigates the logic of full meet contraction. Seven properties of this operation are presented that contribute to making it useful as a building-block: Full meet contraction is a purely logical operation. It retains finitebasedness of the belief set. It is the inclusion-maximal contraction that removes all sentences that can contribute to implying the input sentence. It is the inclusion-maximal contraction that removes all non-tautologous consequences of the input sentence. Almost all contractions can be reconstructed as full meet contraction. Full meet contraction allows for recovery of the input sentence. Full meet contraction provides a unified account of multiple and singleton contraction. La llamada full meet contraction, creada por Carlos Alchourrón y David Makinson en los comienzos de los ' 80, ha sido a menudo desestimada puesto que ella no constituye un operador de contracción plausible. De todas formas ella es altamente útil en la construcción de operadores de contracción compuestos. En particular, todos los operadores de contracción plausibles pueden ser reconstruidos de forma tal que la contracción de un conjunto de creencias K por una sentencia p sea definida como K ∼ f, donde ∼ es una full meet contraction y f un selector de sentencias, i.e., una función de sentencias a sentencias. En este trabajo investigamos la lógica de la full meet contraction. Se presentan siete propiedades de esta operación que contribuyen a hacerla útil como building-block: Full meet contraction es una operación puramente lógica. Ella retiene la finit- basednes del conjunto de creencias. Ella es la máxima-inclusiva de las contracciones que elimina todas las sentencias que pueden contribuir a implicar la input-sentence. Es la contracción maximal inclusiva que elimina todas las consecuencias no tautológicas de la input-sentence. Casi todas las contracciones pueden ser reconstruidas como full-meet contractions. Full meet contraction permite la recuperación de la input-sentence. Full meet contracción da cuenta en forma unificada de las contracciones múltiples y singulares. (shrink)