Contractions on belief sets that have no finite representation cannot be finite in the sense that only a finite number of sentences is removed. However, such contractions can be delimited so that the actual change takes place in a logically isolated, finite-based part of the belief set. A construction that answers to this principle is introduced, and is axiomatically characterized. It turns out to coincide with specified meet contraction.

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)

Most belief change operators in the AGM tradition assume an underlying plausibility ordering over the possible worlds which is transitive and complete. A unifying structure for these operators, based on supplementing the plausibility ordering with a second, guiding, relation over the worlds was presented in Booth et al. (Artif Intell 174:1339-1368, 2010). However it is not always reasonable to assume completeness of the underlying ordering. In this paper we generalise the structure of Booth et al. (Artif Intell 174: 1339-1368, (...) 2010) to allow incomparabilities between worlds. We axiomatise the resulting class of belief removal functions, and show that it includes an important family of removal functions based on finite prioritised belief bases. (shrink)

It is well known that the computational complexity of propositional knowledge base revision is at the second level of polynomial hierarchy. A way to solve this kind of problems is to introduce approximate algorithms. In this paper, an approximate approach is introduced for belief change. Operators, which satisfy the AGM rational postulates, are defined to change belief sets or belief bases. Furthermore, approximate algorithms to implement the revision of finite belief bases are presented. (...) The time complexities of the approximate algorithms shown in this paper are at lower level than the time complexities of the existed approaches in literatures, although they may not generate the optimal solution, and this is meaningful from the theoretical point of view. (shrink)

This thesis proposes and presents two new models for belief representation and belief revision. The first model is the B-structures model which relies on a notion of partial language splitting and tolerates some amount of inconsistency while retaining classical logic. The model preserves an agent's ability to answer queries in a coherent way using Belnap's four-valued logic. Axioms analogous to the AGM axioms hold for this new model. The distinction between implicit and explicit beliefs is represented and psychologically (...) plausible, computationally tractable procedures for query answering and belief base revision are obtained. ;The second model presents a method for relevance sensitive non-monotonic inference from belief sequences which incorporates insights pertaining to prioritized inference and relevance sensitive, inconsistency tolerant belief revision. Our model uses a finite, logically open sequence of propositional formulas as a representation for beliefs and defines a notion of inference from maxiconsistent subsets of formulas guided by two orderings: a temporal sequencing and an ordering based on relevance relations between the conclusion and formulas in the sequence. The relevance relations are ternary as opposed to standard binary axiomatizations. The inference operation thus defined easily handles iterated revision by maintaining a revision history, blocks the derivation of inconsistent answers from a possibly inconsistent sequence and maintains the distinction between explicit and implicit beliefs. In doing so, it provides a finitely representable formalism and a plausible model of reasoning for automated agents. (shrink)

We study belief change in the branching-time structures introduced in Bonanno (Artif Intell 171:144–160, 2007 ). First, we identify a property of branching-time frames that is equivalent (when the set of states is finite) to AGM-consistency, which is defined as follows. A frame is AGM-consistent if the partial belief revision function associated with an arbitrary state-instant pair and an arbitrary model based on that frame can be extended to a full belief revision function that satisfies the (...) AGM postulates. Second, we provide a set of modal axioms that characterize the class of AGM-consistent frames within the modal logic introduced in Bonanno (Artif Intell 171:144–160, 2007 ). Third, we introduce a generalization of AGM belief revision functions that allows a clear statement of principles of iterated belief revision and discuss iterated revision both semantically and syntactically. (shrink)

In this paper I argue, based on a comparison of Spinoza's and Descartes‟s discussion of error, that beliefs are affirmations of the content of imagination that is not false in itself, only in relation to the object. This interpretation is an improvement both on the winning ideas reading and on the interpretation reading of beliefs. Contrary to the winning ideas reading it is able to explain belief revision concerning the same representation. Also, it does not need the assumption that (...) I misinterpret my otherwise correct ideas as the interpretation reading would have it. In the first section I will provide a brief overview of the notion of inherence and its role in Spinoza‟s discussion of the status of finite minds. Then by examining the relation between Spinoza‟s and Descartes‟ distinction of representations and attitudes, I show that affirmation can be identified with beliefs in Spinoza. Next, I will take a closer look at the identification of intellect and will and argue that Spinoza's identification of the two is based on the fact that Spinoza sees both as the active aspect of the mind. After that, I analyze Spinoza‟s comments on the different scopes of will and intellect, and argue that beliefs are affirmations of the imaginative content of the idea. Finally, through Spinoza‟s example of the utterance of mathematical error, I present my solution to the problem of inherence of false beliefs. (shrink)

We propose a new topological semantics for evidence, evidence-based justifications, belief, and knowledge. Resting on the assumption that an agent’s rational belief is based on the available evidence, we try to unveil the concrete relationship between an agent’s evidence, belief, and knowledge via a rich formal framework afforded by topologically interpreted modal logics. We prove soundness, completeness, decidability, and the finite model property for the associated logics, and apply this setting to analyze key epistemological issues such (...) as “no false lemma” Gettier examples, misleading defeaters, undefeated justification versus undefeated belief, as well as the defeasibility theories of knowledge. (shrink)

We present a method for relevance sensitive non-monotonic inference from belief sequences which incorporates insights pertaining to prioritized inference and relevance sensitive, inconsistency tolerant belief revision. Our model uses a finite, logically open sequence of propositional formulas as a representation for beliefs and defines a notion of inference from maxiconsistent subsets of formulas guided by two orderings: a temporal sequencing and an ordering based on relevance relations between the putative conclusion and formulas in the sequence. The relevance (...) relations are ternary (using context as a parameter) as opposed to standard binary axiomatizations. The inference operation thus defined easily handles iterated revision by maintaining a revision history, blocks the derivation of inconsistent answers from a possibly inconsistent sequence and maintains the distinction between explicit and implicit beliefs. In doing so, it provides a finitely presented formalism and a plausible model of reasoning for automated agents. (shrink)

We study the learning power of iterated belief revision methods. Successful learning is understood as convergence to correct, i.e., true, beliefs. We focus on the issue of universality: whether or not a particular belief revision method is able to learn everything that in principle is learnable. We provide a general framework for interpreting belief revision policies as learning methods. We focus on three popular cases: conditioning, lexicographic revision, and minimal revision. Our main result is that conditioning and (...) lexicographic revision can drive a universal learning mechanism, provided that the observations include only and all true data, and provided that a non-standard, i.e., non-well-founded prior plausibility relation is allowed. We show that a standard, i.e., well-founded belief revision setting is in general too narrow to guarantee universality of any learning method based on belief revision. We also show that minimal revision is not universal. Finally, we consider situations in which observational errors may occur. Given a fairness condition, which says that only finitely many errors occur, and that every error is eventually corrected, we show that lexicographic revision is still universal in this setting, while the other two methods are not. (shrink)

This paper investigates simple syntactic methods for revising prioritized belief bases, that are semantically meaningful in the frameworks of possibility theory and of Spohn''s ordinal conditional functions. Here, revising prioritized belief bases amounts to conditioning a distribution function on interpretations. The input information leading to the revision of a knowledge base can be sure or uncertain. Different types of scales for priorities are allowed: finite vs. infinite, numerical vs. ordinal. Syntactic revision is envisaged here as (...) a process which transforms a prioritized belief bases into a new prioritized belief base, and thus allows a subsequent iteration. (shrink)

Religious beliefs are often singled out for special treatment in secular liberal societies. Yet if a legal exemption is granted for a belief with a religious foundation, the question arises whether a similar, non‐religious moral belief must also be granted an exemption. I argue that common reasons for favoring religious over non‐religious beliefs fail to provide a convincing moral case for drawing a distinction of this nature. I focus on arguments concerning the role of religious beliefs in constituting (...) an individual's identity and the transcendental nature of religion, which lead me to consider in the final section the role of choice in religious belief. (shrink)

We prove that for any finite deduction structure there exists a unique concise-widest chain-preserved split. Based on this result, we propose a logical splitting strategy which enables an agent to split its belief structure such that all the original inference chains can be preserved. The significance of such logical splitting at least is four-fold: It can be used by an agent to separate its concerns appropriately, or even create smaller and smarter clones which could save time and efforts (...) in their deliberation computing; It will enable an agent to adjust its concerns dynamically based on its recognition of the current situation, which may further enable the agent to make rapid and rational decisions when situation shifting occurs; In periodic team synchronization domains where agents can periodically synchronize their behaviors with no restriction on communication, it can be employed as a critical process for maintaining the shared mental models among a team of agents; and It is helpful in alleviating the complexity of reasoning about relevant information, and in better anticipating both explicit and implicit information needs based on the recognition of the current situation. (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)

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)

According to evidentialism, what is epistemically rational to believe is determined by evidence alone. So, assuming that prejudiced beliefs are irrational, evidentialism entails that they must not be properly based on the evidence. Recently, philosophers have been interested in cases of beliefs that seem to undermine evidentialism: these are beliefs that seem both prejudiced (and, thus, irrational) and properly based on the evidence (and, thus, rational). In these cases, a believer has strong statistical evidence that most members of a social (...) group have some property and then comes to believe that an individual member of that social group will likely have that property. For example, a server at a restaurant has statistical evidence that most Black diners tip less than average and then comes to believe that a particular Black diner will likely tip less than average. The goal of this paper is to defend evidentialism from the challenge posed to it by beliefs like the server’s by developing a plausible evidentialist account that explains away these conflicting intuitions. (shrink)

We propose in this paper a new family of belief merging operators, that is based on a game between sources : until a coherent set of sources is reached, at each round a contest is organized to find out the weakest sources, then those sources has to concede. This idea leads to numerous new interesting operators and opens new perspectives for belief merging. Some existing operators are also recovered as particular cases. Those operators can be seen as a (...) special case of Booth's Belief Negotiation Models [BOO 02], but the achieved restriction forms a consistent family of merging operators that worths to be studied on its own. (shrink)

This paper proposes a minimal logic of fine-grained information dynamics via belief bases. The framework is shown to be able to accommodate explicit belief, implicit belief, awareness of and awareness that, where awareness of agents is not treated as a tacit premise. A sound and complete axiomatization of static logic is established, upon which a series of dynamic operations are defined. It is argued that these dynamics adapt different scenarios. Our logic is minimal because to each (...) agent we only attach two databases, from which a variety of epistemic attitudes are generated. (shrink)

This paper proposes a notion of ambiguity aversion and characterizes it in the context of biseparable preferences, which include many popular ambiguity models in the literature. The defined properties suggest that ambiguity aversion is characterized by the properties of its capacity. This formalizes a sharp distinction between ambiguity and risk aversion, where risk aversion is characterized by the properties of its utility index and its probability weighting function.

Perception is commonly regarded by philosophers as being the only basis of empirical knowledge. I challenge this assumption by investigating how we come to have beliefs about the emotional experiences of ourselves and others, and how we come to have beliefs about the emotional properties of inanimate objects, such as the belief that the church is somber. Before presenting my account of this type of belief formation, I argue that the observation that someone is in a particular emotional (...) state, or the observation that an inanimate object displays an emotional property, should not be subsumed under the rubric of perception. I argue that this subsumption oversimplifies the nature of such observations and leaves too many interesting and important philosophical questions unanswered. In addition to suggesting how these sorts of beliefs are formed, I argue that philosophers should endeavor to include them in their discussions of knowledge, and I examine how three contemporary accounts of knowledge can be expanded to accommodate such beliefs in the capacity of knowledge claims. (shrink)

This work considers the formalisation of the merging process of stratified belief bases, where beliefs are stored in different layers or strata. Their strata are ranked, following a total order, employing the value the agent using the belief base assigns to these beliefs. The agent uses an argumentation mechanism to reason from the belief base and obtain the final inferences. We present two ways of merging stratified belief bases: the first is defined by merging (...) two strata without belief preservation, and the second by merging two strata with belief preservation. For these operators, as layers merge, it is possible that some information has to be deleted from the stratum to maintain consistency. The latter merge operator will be defined as performing their actions so that information removed from the stratum is preserved after the merging by moving it to a stratum containing information perceived as having a lower value and where those beliefs may trigger a new revision, possibly starting a cascading effect. (shrink)

We look at the problem of revising fuzzy belief bases, i.e., belief base revision in which both formulas in the base as well as revision-input formulas can come attached with varying degrees. Working within a very general framework for fuzzy logic which is able to capture certain types of uncertainty calculi as well as truth-functional fuzzy logics, we show how the idea of rational change from “crisp” base revision, as embodied by the idea of partial meet (base) (...) revision, can be faithfully extended to revising fuzzy belief bases. We present and axiomatise an operation of partial meet fuzzy base revision and illustrate how the operation works in several important special instances of the framework. We also axiomatise the related operation of partial meet fuzzy base contraction. (shrink)

This manuscript presents a topological argumentation framework for modelling notions of evidence-based (i.e., justified) belief. Our framework relies on so-called topological evidence models to represent the pieces of evidence that an agent has at her disposal, and it uses abstract argumentation theory to select the pieces of evidence that the agent will use to define her beliefs. The tools from abstract argumentation theory allow us to model agents who make decisions in the presence of contradictory information. Thanks to this, (...) it is possible to define two new notions of beliefs, grounded beliefs and fully grounded beliefs. These notions are discussed in this paper, analysed and compared with the existing notion of topological justified belief. This comparison revolves around three main issues: closure under conjunction introduction, the level of consistency and their logical strength. (shrink)

In this article we explore multiple change operators, i.e., operators in which the epistemic input is a set of sentences instead of a single sentence. We propose two types of change: prioritized change, in which the input set is fully accepted, and symmetric change, where both the epistemic state and the epistemic input are equally treated. In both kinds of operators we propose a set of postulates and we present different constructions: kernel changes and partial meet changes.

It is a platitude that belief is subject to a standard of correctness: a belief is correct if and only if it is true. But not all standards of correctness are authoritative or binding. Some standards of correctness may be arbitrary, unjustified or outrightly wrong. Given this, one challenge to proponents of the truth norm of belief, is to answer what Korsgaard (1996) calls ‘the normative question’. Is the truth norm of belief authoritative or binding regarding (...) what one ought to or may believe? If so, what grounds its authority? The aim of this paper is to offer a novel answer to the grounding challenge on a reason-based normative framework. I develop and defend a practice-based account of the truth norm, according to which, the authority of the truth norm of belief is grounded in what I call the T-practice, a justified social practice that functions to facilitate knowledge production, maintenance, and social cooperation. (shrink)

Knowledge-based programs (KBPs) are a powerful notion for expressing action policies in which branching conditions refer to implicit knowledge and call for a deliberation task at execution time. However, branching conditions in KBPs cannot refer to possibly erroneous beliefs or to graded belief, such as “if my belief that φ holds is high then do some action α else perform some sensing action β”.

Two studies are reported which demonstrate that analytic responding on everyday reasoning problems can be increased and bias eliminated after training on the law of large numbers. Critical thinking problems involving belief-consistent, neutral, and inconsistent conclusions were presented. Belief bias was eliminated when a written justification of argument strength was elicited. However, belief-based responding was still evident when evaluations of the arguments were elicited using rating scales. This finding demonstrates a dissociation between analytic and belief-based responding (...) as a function of response format. In Experiment 2 an instructional condition designed to foster decontextualised reasoning was included but was ineffective in reducing the degree to which judgements were biased by beliefs. It was concluded that training which makes available the analytic strategies necessary to evaluate a problem has the potential to facilitate performance only if the requested response triggers conscious deliberation of the evidence. (shrink)

Two studies are reported which demonstrate that analytic responding on everyday reasoning problems can be increased and bias eliminated after training on the law of large numbers. Critical thinking problems involving belief-consistent, neutral, and inconsistent conclusions were presented. Belief bias was eliminated when a written justification of argument strength was elicited. However, belief-based responding was still evident when evaluations of the arguments were elicited using rating scales. This finding demonstrates a dissociation between analytic and belief-based responding (...) as a function of response format. In Experiment 2 an instructional condition designed to foster decontextualised reasoning was included but was ineffective in reducing the degree to which judgements were biased by beliefs. It was concluded that training which makes available the analytic strategies necessary to evaluate a problem has the potential to facilitate performance only if the requested response triggers conscious deliberation of the evidence. (shrink)

Global forest loss is highest in the tropical region, an area with high biological biodiversity. As some of these forests are part of indigenous forest management, it is important to pay attention to such management, its values and practices for better conservation. This paper focuses on sacred freshwater swamp forests of the Western Ghats, India, and with it a faith-based approach to nature conservation. Drawing on fieldwork and focus groups, we present the rituals and rules that structure the governance of (...) sacred swamps. We also discuss in depth the ecological, socio-cultural and economic valuation of these freshwater swamps by various local groups. In this way, we show overlaps and differences of valuation among different groups. In the context of a secular state with a diversity of faith groups and migration dynamics, we propose that faith-based governance of sacred swamps can benefit from the emphasis of faith-independent, 'accessible' ecological, socio-cultural and economic values to foster a dialogue around sacred swamps and their place for livelihoods and nature conservation. (shrink)

The aggregation of individual judgments on logically interconnected propositions into a collective decision on the same propositions is called judgment aggregation. Literature in social choice and political theory has claimed that judgment aggregation raises serious concerns. For example, consider a set of premises and a conclusion where the latter is logically equivalent to the former. When majority voting is applied to some propositions (the premises) it may give a different outcome than majority voting applied to another set of propositions (the (...) conclusion). This problem is known as the discursive dilemma (or paradox). The discursive dilemma is a serious problem since it is not clear whether a collective outcome exists in these cases, and if it does, what it is like. Moreover, the two suggested escape-routes from the paradox—the so-called premise-based procedure and the conclusion-based procedure—are not, as I will show, satisfactory methods for group decision-making. In this paper I introduce a new aggregation procedure inspired by an operator defined in artificial intelligence in order to merge belief bases. The result is that we do not need to worry about paradoxical outcomes, since these arise only when inconsistent collective judgments are not ruled out from the set of possible solutions. (shrink)

In this paper, finite-time tracking problem of nonholonomic mobile robots for a moving target is considered. First of all, polar coordinates are used to characterize the distance and azimuth between the moving target and the robot. Then, based on the distance and azimuth transported from the sensor installed on the robot, a finite-time tracking control law is designed for the nonholonomic mobile robot by the switching control method. Rigorous proof shows that the tracking error converges to zero in (...) a finite time. Numerical simulation demonstrates the effectiveness of the proposed control method. (shrink)

Past research has identified a number of asymmetries based on moral judgments. Beliefs about what a person values, whether a person is happy, whether a person has shown weakness of will, and whether a person deserves praise or blame seem to depend critically on whether participants themselves find the agent's behavior to be morally good or bad. To date, however, the origins of these asymmetries remain unknown. The present studies examine whether beliefs about an agent's “true self” explain these observed (...) asymmetries based on moral judgment. Using the identical materials from previous studies in this area, a series of five experiments indicate that people show a general tendency to conclude that deep inside every individual there is a “true self” calling him or her to behave in ways that are morally virtuous. In turn, this belief causes people to hold different intuitions about what the agent values, whether the agent is happy, whether he or she has shown weakness of will, and whether he or she deserves praise or blame. These results not only help to answer important questions about how people attribute various mental states to others; they also contribute to important theoretical debates regarding how moral values may shape our beliefs about phenomena that, on the surface, appear to be decidedly non-moral in nature. (shrink)