Most of the work in default logic is about default theories that are completely specified. In this category are the proposals of appropriate semantics for default logic, the characterizations of the complexity of reasoning with a default theory, the algorithms for finding consequences of default theories, etc. Relatively little attention has been paid to the process of building a default theory, and most of the work on this topic is about translating knowledge bases from other formalisms (such as circumscription, autoepistemic (...) logic, and action description languages) into default logic. This paper is about expressing knowledge in default logic. In particular, we assume that defaults are initially formulated as normal, and are then corrected using specific inference examples. (shrink)

According to the Ramsey Test, conditionals reflect changes of beliefs: α > β is accepted in a belief state iff β is accepted in the minimal revision of it that is necessary to accommodate α. Since Gärdenfors’s seminal paper of 1986, a series of impossibility theorems (“triviality theorems”) has seemed to show that the Ramsey test is not a viable analysis of conditionals if it is combined with AGM-type belief revision models. I argue that it is possible to endorse that (...) Ramsey test for conditionals while staying true to the spirit of AGM. A main focus lies on AGM’s condition of Preservation according to which the original belief set should be fully retained after a revision by information that is consistent with it. I use concrete representations of belief states and (iterated) revisions of belief states as semantic models for (nested) conditionals. Among the four most natural qualitative models for iterated belief change, two are identified that indeed allow us to combine the Ramsey test with Preservation in the language containing only flat conditionals of the form α > β. It is shown, however, that Preservation for this simple language enforces a violation of Preservation for nested conditionals of the form α > (β > γ). In such languages, no two belief sets are ordered by strict subset inclusion. I argue that it has been wrong right from the start to expect that Preservation holds in languages containing nested conditionals. (shrink)

This paper describes an approach for reasoning in a dynamic domain with nondeterministic actions in which an agent’s beliefs correspond to the simplest, or most plausible, course of events consistent with the agent’s observations and beliefs. The account is based on an epistemic extension of the situation calculus, a first-order theory of reasoning about action that accommodates sensing actions. In particular, the account is based on a qualitative theory of nondeterminism. Our position is that for commonsense reasoning, the world is (...) most usefully regarded as deterministic, and that nondeterminism is an epistemic phenomenon, arising from an agent’s limited awareness and perception. The account offers several advantages: an agent has a set of categorical beliefs, yet can deal with equally-likely outcomes or with outcomes of differing plausibility. The agent maintains as its set of contingent beliefs the most plausible, or simplest, picture of the world, consistent with its beliefs and actions it believes it executed; yet it may modify these in light of later information. (shrink)

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

In this paper I propose violation games as the basis of formal logics to represent and reason about norms, i.e. as the foundation of deontic logic. Deontic logic is an applied non-classical logic reflecting a way in which we conceptualize normative reasoning. By introducing violation games as a fundamental principle of deontic logic, I am introducing a new way of looking at familiar problems in normative reasoning, with the aim of introducing a new approach for handling norms in intelligent systems.

ABSTRACT The major approaches to belief revision and non monotonic reasoning proposed in the literature differ along a number of dimensions, including whether they are ?syntax- based? or ?semantic-based?, ?foundational? or ?coherentist?, ?consistence-restoring? or ?inconsistency-tolerant?. Our contribution towards clarifying the connections between these various approaches is threefold: ?We show that the two main approaches to belief revision, the foundations and coherence theories, are mathematically equivalent, thus answering a question left open in [Gar90, Doy92], The distinction between syntax-based approaches to revision (...) and approaches based on (semantic) preferential structures falls along similar lines, and their expressive equivalence is a consequence of this result. ?We formally clarify the connection between belief revision and non monotonic reasoning, in a particularly simple way which also throws light on the connection between consistence- restoring and reasoning-from-inconsistency approaches [BDP95]. ?As a direct application of the above, we show that Poole's (syntax-based) system of default reasoning and Shoham's preferential semantic for non monotonic reasoning are also expressively equivalent, in that they can represent the same set of non monotonic consequence relations. (shrink)

In this paper we report preliminary results on how people revise or update a previously held set of beliefs. When intelligent agents learn new things which conflict with their current belief set, they must revise their belief set. When the new information does not conflict, they merely must update their belief set. Various AI theories have been proposed to achieve these processes. There are two general dimensions along which these theories differ: whether they are syntactic-based or model-based, and what constitutes (...) a minimal change of beliefs. This study investigates how people update and revise semantically equivalent but syntactically distinct belief sets, both in symbolic-logic problems and in quasi-real-world problems. Results indicate that syntactic form affects belief revision choices. In addition, for the symbolic problems, subjects update and revise semantically-equivalent belief sets identically, whereas for the quasi-real-world problems they both update and revise differently. Further, contrary to earlier studies, subjects are sometimes reluctant to accept that a sentence changes from false to true, but they are willing to accept that it would change from true to false. (shrink)

We introduce a new operator – belief fusion– which aggregates the beliefs of two agents, each informed by a subset of sources ranked by reliability. In the process we definepedigreed belief states, which enrich standard belief states with the source of each piece of information. We note that the fusion operator satisfies the invariants of idempotence, associativity, and commutativity. As a result, it can be iterated without difficulty. We also define belief diffusion; whereas fusion generally produces a belief state with (...) more information than is possessed by either of its two arguments, diffusion produces a state with less information. Fusion and diffusion are symmetric operators, and together define a distributive lattice. Finally, we show that AGM revision can be viewed as fusion between a novice and an expert. (shrink)

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

People use commonsense science knowledge to flexibly explain, predict, and manipulate the world around them, yet we lack computational models of how this commonsense science knowledge is represented, acquired, utilized, and revised. This is an important challenge for cognitive science: Building higher order computational models in this area will help characterize one of the hallmarks of human reasoning, and it will allow us to build more robust reasoning systems. This paper presents a novel assembled coherence theory of human conceptual change, (...) whereby people revise beliefs and mental models by constructing and evaluating explanations using fragmentary, globally inconsistent knowledge. We implement AC theory with Timber, a computational model of conceptual change that revises its beliefs and generates human-like explanations in commonsense science. Timber represents domain knowledge using predicate calculus and qualitative model fragments, and uses an abductive model formulation algorithm to construct competing explanations for phenomena. Timber then scores competing explanations with respect to previously accepted beliefs, using a cost function based on simplicity and credibility, identifies a low-cost, preferred explanation and accepts its constituent beliefs, and then greedily alters previous explanation preferences to reduce global cost and thereby revise beliefs. Consistency is a soft constraint in Timber; it is biased to select explanations that share consistent beliefs, assumptions, and causal structure with its other, preferred explanations. In this paper, we use Timber to simulate the belief changes of students during clinical interviews about how the seasons change. We show that Timber produces and revises a sequence of explanations similar to those of the students, which supports the psychological plausibility of AC theory. (shrink)

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)

There have been a number of publications in recent years on generalising the AGM paradigm to the Horn fragment of propositional logic. Most of them focused on adapting AGM contraction and revision to the Horn setting. It remains an open question whether the adapted Horn contraction and Horn revision are inter-definable as in the AGM case through the Levi and Harper identities. In this paper, we give a positive answer by providing methods for generating contraction and revision from their dual (...) operations. Noticeably, we cannot apply the Levi and Harper identities directly in such methods as the Horn fragment does not fully support negation. To overcome this difficulty, a Horn approximation technique called Horn strengthening is used. We show that Horn contraction generated from Horn revision is always plausible whereas Horn revision generated from Horn contraction is, in general, implausible and, to regain plausibility, the generating contraction has to be properly restricted. (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)

Intelligent agents are often faced with the problem of trying to combine possibly conflicting pieces of information obtained from different sources into a coherent view of the world. We propose a framework for the modelling of such combination operations with roots in the work of Spohn [Spo88, Spo91]. We construct a number of combination operations and we measure them against various properties that such operations ought to satisfy. We conclude by discussing the connection between combination operations and the use of (...) infobases [Mey99, MLH00]. (shrink)

The purpose of this article is to introduce a class of distance-based iterated revision operators generated by minimizing the geodesic distance on a graph. Such operators correspond bijectively to metrics and have a simple finite presentation. As distance is generated by distinguishability, our framework is appropriate for modelling contexts where distance is generated by threshold, and therefore, when measurement is erroneous.

We show in this paper that the AGM postulates are too weak to ensure the rational preservation of conditional beliefs during belief revision, thus permitting improper responses to sequences of observations. We remedy this weakness by proposing four additional postulates, which are sound relative to a qualitative version of probabilistic conditioning. Contrary to the AGM framework, the proposed postulates characterize belief revision as a process which may depend on elements of an epistemic state that are not necessarily captured by a (...) belief set. We also show that a simple modification to the AGM framework can allow belief revision to be a function of epistemic states. We establish a model-based representation theorem which characterizes the proposed postulates and constrains, in turn, the way in which entrenchment orderings may be transformed under iterated belief revision. (shrink)

We point out a simple but hitherto ignored link between the theoryof updates, the theory of counterfactuals, and classical modal logic: update is a classicalexistential modality, counterfactual is a classical universalmodality, and the accessibility relations corresponding to these modalities are inverses. The Ramsey Rule (often thought esoteric) is simply an axiomatisation of this inverse relationship. We use this fact to translate between rules for updates andrules for counterfactuals. Thus, Katsuno and Mendelzons postulatesU1--U8 are translated into counterfactual rules C1--C8(Table VII), and (...) many of the familiar counterfactual rulesare translated into rules for updates (Table VIII). Ourconclusions are summarised in Table V. (shrink)

Belief revision theories standardly endorse a principle of intensionality to the effect that ideal doxastic agents do not discriminate between pieces of information that are equivalent within classical logic. I argue that this principle should be rejected. Its failure, on my view, does not require failures of logical omniscience on the part of the agent, but results from a view of the update as _mighty_: as encoding what the agent learns might be the case, as well as what must be. (...) The view is motivated by consideration of a puzzle case, obtained by transposing into the context of belief revision a kind of scenario that Kit Fine has used to argue against intensionalism about counterfactuals. Employing the framework of truthmaker semantics, I go on to develop a novel account of belief revision, based on a conception of the update as mighty, which validates natural hyperintensional counterparts of the usual AGM postulates. (shrink)

ABSTRACT The major approaches to belief revision and non monotonic reasoning proposed in the literature differ along a number of dimensions, including whether they are “syntax- based” or “semantic-based”, “foundational” or “coherentist”, “consistence-restoring” or “inconsistency-tolerant”. Our contribution towards clarifying the connections between these various approaches is threefold: •We show that the two main approaches to belief revision, the foundations and coherence theories, are mathematically equivalent, thus answering a question left open in [Gar90, Doy92], The distinction between syntax-based approaches to revision (...) and approaches based on (semantic) preferential structures falls along similar lines, and their expressive equivalence is a consequence of this result. •We formally clarify the connection between belief revision and non monotonic reasoning, in a particularly simple way which also throws light on the connection between consistence- restoring and reasoning-from-inconsistency approaches [BDP95]. •As a direct application of the above, we show that Poole's (syntax-based) system of default reasoning and Shoham's preferential semantic for non monotonic reasoning are also expressively equivalent, in that they can represent the same set of non monotonic consequence relations. (shrink)

Belief revision (BR) and truthlikeness (TL) emerged independently as two research programmes in formal methodology in the 1970s. A natural way of connecting BR and TL is to ask under what conditions the revision of a belief system by new input information leads the system towards the truth. It turns out that, for the AGM model of belief revision, the only safe case is the expansion of true beliefs by true input, but this is not very interesting or realistic as (...) a model of theory change in science. The new accounts of non-prioritized belief revision do not seem more promising in this respect, and the alternative BR account of updating by imaging leads to other problems. Still, positive results about increasing truthlikeness by belief revision may be sought by restricting attention to special kinds of theories. Another approach is to link truthlikeness to epistemic matters by an estimation function which calculates expected degrees of truthlikeness relative to evidence. Then we can study how the expected truthlikeness of a theory changes when probabilities are revised by conditionalization or imaging. Again, we can ask under what conditions such changes lead our best theories towards the truth. (shrink)

We examine carefully the rationale underlying the approaches to belief change taken in the literature, and highlight what we view as methodological problems. We argue that to study belief change carefully, we must be quite explicit about the ontology or scenario underlying the belief change process. This is something that has been missing in previous work, with its focus on postulates. Our analysis shows that we must pay particular attention to two issues that have often been taken for granted: the (...) first is how we model the agent's epistemic state. (Do we use a set of beliefs, or a richer structure, such as an ordering on worlds? And if we use a set of beliefs, in what language are these beliefs are expressed?) We show that even postulates that have been called beyond controversy are unreasonable when the agent's beliefs include beliefs about her own epistemic state as well as the external world. The second is the status of observations. (Are observations known to be true, or just believed? In the latter case, how firm is the belief?) Issues regarding the status of observations arise particularly when we consider iterated belief revision, and we must confront the possibility of revising by and then by ¬. (shrink)

Merging beliefs depends on the relative reliability of their sources. When this is information is absent, assuming equal reliability is unwarranted. The solution proposed in this article is that every reliability profile is possible, and only what holds according to all of them is accepted. Alternatively, one source is completely reliable, but which one is not specified. These two cases motivate two existing forms of merging: maxcons-based merging and disjunctive merging.

The problem of knowledge evolution has received considerable attention over the years. Mainly, the study of the dynamics of knowledge has been addressed in the area of Belief Revision, a field emerging as the convergence of the efforts in Philosophy, Logic, and more recently Computer Science, where research efforts usually involve “flat” knowledge bases where there is no additional information about the formulas stored in it. Even when this may be a good fit for particular applications, in many real-world scenarios (...) different information items may be attached to formulas. For instance, when the reliability of the source of the piece of information is attached to it as a measure of some quality (e.g., strength) of the piece of information itself, or when some characteristic informs us on the desirability of the item (e.g., the potential benefit that could be obtained from it). If this type of information is available, we can use it to guide how the belief base is to be modified when new information arrives. In this work, we present a novel approach to the contraction of knowledge bases where formulas have values attached that measure some quality linked to those formulas, exploiting it to define their desirability, and uses such desirability to define which formulas need to be removed to solve conflicts. In this context, we introduce a set of properties for contraction operators by extending classic approaches. We also show how the local treatment of minimal conflicts can induce some counter-intuitive contractions, and we present a way to avoid them by considering optimal resolutions of conflicts using the additional information encoded. We show how the proposed formalization captures any contraction that is optimal under a set of features. Finally, we present a refinement based on the identification of related minimal conflicts that performs contraction in optimal ways without looking into the entire knowledge base. The approach is based on the use of the accrual of beliefs where several formulas collaboratively use their respective values to prevail in the resolution of conflicts. (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 paper is part of an on-going programme on the study of the logical aspects of social network formation. It recalls the so-called social network model, discussing the properties of a notion of closeness between agents ; then introduces an extended social network model in which different agents might assign different values to different traits, discussing the properties of the notion of weighted closeness that arises. These notions are used to define social network creation operations by means of a threshold (...) strategy. The paper studies the properties of the social networks the updates create, providing sound and complete axiom systems for formal languages describing these updates’ effects. (shrink)