Prioritized bases, i.e., weakly ordered sets of sentences, have been used for specifying an agent’s ‘basic’ or ‘explicit’ beliefs, or alternatively for compactly encoding an agent’s belief state without the claim that the elements of a base are in any sense basic. This paper focuses on the second interpretation and shows how a shifting of priorities in prioritized bases can be used for a simple, constructive and intuitive way of representing a large variety of methods for the change of belief (...) states—methods that have usually been characterized semantically by a system-of-spheres modeling. Among the methods represented are ‘radical’, ‘conservative’ and ‘moderate’ revision, ‘revision by comparison’ in its raising and lowering variants, as well as various constructions for belief expansion and contraction. Importantly, none of these methods makes any use of numbers. (shrink)

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

We 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)

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

In this paper we compare Leitgeb’s stability theory of belief and Spohn’s ranking-theoretic account of belief. We discuss the two theories as solutions to the lottery paradox. To compare the two theories, we introduce a novel translation between ranking functions and probability functions. We draw some crucial consequences from this translation, in particular a new probabilistic belief notion. Based on this, we explore the logical relation between the two belief theories, showing that models of Leitgeb’s theory correspond to certain models (...) of Spohn’s theory. The reverse is not true. Finally, we discuss how these results raise new questions in belief theory. In particular, we raise the question whether stability is rightly thought of as a property pertaining to belief. (shrink)

In this commentary on Rotts paper Stability, Strength and Sensitivity: Converting Belief into Knowledge, I discuss two problems of the stability theory of knowledge which are pointed out by Rott. I conclude that these problems offer no reason for rejecting the stability theory, but might be grounds for deviating from the standard AGM account of belief revision which Rott presupposes.

This paper proposes a logical framework for representing static and dynamic properties of different kinds of individual and collective attitudes. A complete axiomatization as well as a decidability result for the logic are given. The logic is applied to game theory by providing a formal analysis of the epistemic conditions of iterated deletion of weakly dominated strategies (IDWDS), or iterated weak dominance for short. The main difference between the analysis of the epistemic conditions of iterated weak dominance given in this (...) paper and other analysis is that we use a semi-qualitative approach to uncertainty based on the notion of plausibility first introduced by Spohn, whereas other analysis are based on a quantitative representation of uncertainty in terms of probabilities. (shrink)

We offer a general framework for theorizing about the structure of knowledge and belief in terms of the comparative normality of situations compatible with one’s evidence. The guiding idea is that, if a possibility is sufficiently less normal than one’s actual situation, then one can know that that possibility does not obtain. This explains how people can have inductive knowledge that goes beyond what is strictly entailed by their evidence. We motivate the framework by showing how it illuminates knowledge about (...) the future, knowledge of lawful regularities, knowledge about parameters measured using imperfect instruments, the connection between knowledge, belief, and probability, and the dynamics of knowledge and belief in response to new evidence. (shrink)

If updating with E has the same result across all epistemically possible worlds, then the agent has no uncertainty as to the behavior of the update, and we may call it a transparent update. If an agent is uncertain about the behavior of an update, we may call it opaque. In order to model the uncertainty an agent has about the result of an update, the same update must behave differently across different possible worlds. In this paper, I study opaque (...) updates using a simple system of dynamic epistemic logic suitably modified for that purpose. The paper highlights the connection between opaque updates and the dynamic-epistemic principles Perfect-Recall and No-Miracles. I argue that opaque updates are central to contemporary discussions in epistemology, in particular to externalist theories of knowledge and to the related problem of epistemic bootstrapping, or easy knowledge. Opaque updates allow us to explicitly investigate a dynamic form of uncertainty, using simple and precise logical tools. (shrink)

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

We propose a new model for forming and revising beliefs about unknown probabilities. To go beyond what is known with certainty and represent the agent’s beliefs about probability, we consider a plausibility map, associating to each possible distribution a plausibility ranking. Beliefs are defined as in Belief Revision Theory, in terms of truth in the most plausible worlds. We consider two forms of conditioning or belief update, corresponding to the acquisition of two types of information: learning observable evidence obtained by (...) repeated sampling from the unknown distribution; and learning higher-order information about the distribution. The first changes only the plausibility map, but leaves the given set of possible distributions essentially unchanged; the second rules out some distributions, thus shrinking the set of possibilities, without changing their plausibility ordering.. We look at stability of beliefs under either of these types of learning, defining two related notions, as well as a measure of the verisimilitude of a given plausibility model. We prove a number of convergence results, showing how our agent’s beliefs track the true probability after repeated sampling, and how she eventually gains in a sense knowledge of that true probability. Finally, we sketch the contours of a dynamic doxastic logic for statistical learning. (shrink)

Stalnaker, 169–199 2006) introduced a combined epistemic-doxastic logic that can formally express a strong concept of belief, a concept of belief as ‘subjective certainty’. In this paper, we provide a topological semantics for belief, in particular, for Stalnaker’s notion of belief defined as ‘epistemic possibility of knowledge’, in terms of the closure of the interior operator on extremally disconnected spaces. This semantics extends the standard topological interpretation of knowledge with a new topological semantics for belief. We prove that the belief (...) logic KD45 is sound and complete with respect to the class of extremally disconnected spaces and we compare our approach to a different topological setting in which belief is interpreted in terms of the derived set operator. We also study belief revision as well as belief dynamics by providing a topological semantics for conditional belief and belief update modalities, respectively. Our setting based on extremally disconnected spaces, however, encounters problems when extended with dynamic updates. We then propose a solution consisting in interpreting belief in a similar way based on hereditarily extremally disconnected spaces, and axiomatize the belief logic of hereditarily extremally disconnected spaces. Finally, we provide a complete axiomatization of the logic of conditional belief and knowledge, as well as a complete axiomatization of the corresponding dynamic logic. (shrink)

The relation of scepticism to infallibilism and fallibilism is a contested issue. In this paper I argue that Cartesian sceptical arguments, i.e. sceptical arguments resting on sceptical scenarios, are neither tied to infallibilism nor collapse into fallibilism. I interpret the distinction between scepticism and fallibilism as a scope distinction. According to fallibilism, each belief could be false, but according to scepticism all beliefs could be false at the same time. However, to put this distinction to work sceptical scenarios have to (...) be understood as ignorance-possibilities, not as error-possibilities. To show that scepticism is not tied to infallibilism I reject the principle of unrestricted relevance according to which any error- or ignorance-possibility whatsoever is relevant. Instead I argue that the sceptic should distinguish between local and global ignorance-possibilities. Global ignorance-possibilities are relevant even though not all ignorance-possibilities are relevant. The result is a refined version of the Cartesian sceptical argument that avoids two traps other versions do not avoid. (shrink)

The problem of philosophical skepticism relates to the difficulty involved in underwriting the claim that we know anything of spatio-temporal reality. It is often claimed, in fact, that proper philosophical scrutiny reveals quite the opposite from what common sense suggests. Knowledge of external reality is thought to be even quite obviously denied to us as a result of the alleged fact that we all fail to know that certain skeptical scenarios do not obtain. A skeptical scenario is one in which (...) we have neurological occurrences just like any normal situation in which we actually perceive spatio-temporal objects, but where we are deceived in some sense as a result of the manipulation of our brains from some outside source. In this work I attempt to address the problem of philosophical skepticism by claiming that most of us are able to come to know plenty about external reality, since we can come to realize that a certain philosophical theory of perception is correct. The theory I have in mind is what I call a non-cognitive theory of perception. According to this view, perceptual experience is defined by continuous, sensitive behavioral interaction with spatio-temporal objects of the appropriate size, shape, hardness, speed, etc. Knowing that this theory of perception is correct is equivalent to knowing that we know plenty about external reality. This is ultimately because by knowing that a non-cognitive theory of perception is true, we know that any skeptical scenario must fail to obtain. The structure of the work proceeds by first discussing the significance of the problem of philosophical skepticism in some detail. Chapter 1 lays out how the problem does indeed forcefully arise if it is conceded that we fail to know that the skeptical scenarios fail to obtain. Chapter 2 develops the sort of view of our epistemological situation that falls out of accepting without qualification that the problem exists. Chapter 3 examines and criticizes certain popular responses to the skeptical problem. The main goal of these first three preliminary chapters is to indicate that once it is admitted that we fail to know that the skeptical scenarios fail to obtain, the problem of philosophical skepticism forcefully presents itself. Chapter 4, however, attacks the idea that we fail to know that the skeptical scenarios fail to obtain. In this chapter I argue that this idea is wedded to the position that a certain theory of perception is correct. The theory in question is what I call a conjunctive theory of veridical experience. According to this view, normal experience of spatio-temporal objects occurs when a subject has a certain perceptual experience, and that experience also happens to match up with and/or be satisfied by what is really the case. Only when a theory of this sort is assumed, I argue, is the claim that we fail to know that the skeptical scenarios fail to obtain found to be obvious. In chapter 5 I argue that, in fact, a non-cognitive theory, rather than a conjunctive theory, is the correct view to maintain. In the final chapter 6 I develop the epistemological position that falls out of accepting a non-cognitive theory. (shrink)