Reasoning About Knowledge is the first book to provide a general discussion of approaches to reasoning about knowledge and its applications to distributed ...

This paper introduces a two-dimensional modal logic to reason about knowledge in asynchronous multi-agent message-passing systems. We present a new theoretical definition for concurrent knowledge in order to describe the kind of knowledge typical in such asynchronous environments. To define concurrent knowledge, we propose the closed sub-product of modal logics: a two-dimensional formal semantics where one dimension corresponds to asynchronous runs, the other corresponds to consistent cuts and the concurrent knowledge is defined as the (...) transitive closure over the product of the former dimensions. We axiomatize the presented logic issuing proofs of soundness and completeness with respect to the class of closed sub-product of modal frames. (shrink)

In this paper, the Carneades argumentation system is extended to represent a procedural view of inquiry in which evidence is marshalled to support or defeat claims to knowledge. The model is a sequence of moves in a collaborative group inquiry in which parties take turns making assertions about what is known or not known, putting forward evidence to support them, and subjecting these moves to criticisms. It is shown how this model of evaluating evidence in an inquiry is (...) based on a defeasible logic using forms of argument that admit exceptions. It is contended that reasoning from absence of knowledge is as important to inquiry as positive reasoning from evidence to knowledge. The philosophical conflict between this view of reasoning about knowledge and the true-belief-plus view is explored by airing objections and replies on both sides. (shrink)

We extend Moss and Parikh’s bi-modal system for knowledge and effort by means of hybrid logic. In this way, some additional concepts from topology related to knowledge can be captured. We prove the soundness and completeness as well as the decidability of the extended system. Special emphasis will be placed on algebras.

In the most popular logics combining knowledge and awareness, it is not possible to express statements about knowledge of unawareness such as “Ann knows that Bill is aware of something Ann is not aware of”—without using a stronger statement such as “Ann knows that Bill is aware of \(p\) and Ann is not aware of \(p\) ”, for some particular \(p\) . In Halpern and Rêgo (Proceedings of KR 2006; Games Econ Behav 67(2):503–525, 2009b) Halpern and Rêgo (...) introduced a logic in which such statements about knowledge of unawareness can be expressed. The logic extends the traditional framework with quantification over formulae, and is thus very expressive. As a consequence, it is not decidable. In this paper we introduce a decidable logic which can be used to reason about certain types of unawareness. Our logic extends the traditional framework with an operator expressing full awareness, i.e., the fact that an agent is aware of everything, and another operator expressing relative awareness, the fact that one agent is aware of everything another agent is aware of. The logic is less expressive than Halpern’s and Rêgo’s logic. It is, however, expressive enough to express all of the motivating examples in Halpern and Rêgo (Proceedings of KR 2006; Games Econ Behav 67(2):503–525, 2009b). In addition to proving that the logic is decidable and that its satisfiability problem is PSPACE-complete, we present an axiomatisation which we show is sound and complete. (shrink)

We present a representation for reasoning and planning with an incomplete state description (open-world) called PSIPLAN-S. The presented formalism has several properties critical for application domains with a large degree of incompleteness in the state description, particularly, in domains with a large or unknown set of all objects. The formalism offers (1) considerably expressive state and goal description language, that includes limited universal quantification, (2) representation of sensing actions and knowledge goals, (3) a correct and complete state update (...) procedure, and (4) complete reasoning within a substantial subset of the language. The approach is illustrated by examples from a working system. (shrink)

In this paper we propose a new semantics, based on the notion of a "contextual model", that makes it possible to express and compare — within a unique formal framework — different views on the roles of various notions of context in knowledge ascriptions. We use it to provide a logical analysis of such positions as skeptical and moderate invariantism, contextualism, and subject-sensitive invariantism. A dynamic formalism is also proposed that offers new insights into a classical skeptical puzzle.

In this paper non-normal worlds semantics is presented as a basic, general, and unifying approach to epistemic logic. The semantical framework of non-normal worlds is compared to the model theories of several logics for knowledge and belief that were recently developed in Artificial Intelligence (AI). It is shown that every model for implicit and explicit belief (Levesque), for awareness, general awareness, and local reasoning (Fagin and Halpern), and for awareness and principles (van der Hoek and Meyer) induces a (...) non-normal worlds model validating precisely the same formulas (of the language in question). (shrink)

Twenty-seven semi-guided conversations between lecturers and Spanish-speaking undergraduate students were recorded at five different universities in Europe where English is the medium of instruction. Examination of the metaphorical language used in these conversations revealed that SIGHT plays an important role in academic mentoring in English. Lecturers often frame their advice to undergraduate students in terms of what has been called “UNDERSTANDING IS SEEING,” on the face of it a somewhat unsurprising finding. If one takes it that the correlation between mental (...) and visual activity is somehow “primary” then this way of reasoning about learning and knowledge should be common ground in conversations between English- and Spanish-speaking interlocutors. However, we found no such alignment between the two groups of participants in an academic setting. The Spanish speakers not only used words and terms associated with vision significantly less frequently t.. (shrink)

Sound and complete axiomatizations are provided for a number of different logics involving modalities for the knowledge of multiple agents and operators for branching time, extending previous work of Halpern, van der Meyden and Vardi [to appear, SIAM Journal on Computing] for logics of knowledge and linear time. The paper considers the system constraints of synchrony, perfect recall and unique initial states, which give rise to interaction axioms. The language is based on the temporal logic CTL*, interpreted with (...) respect to a version of the bundle semantics. (shrink)

We study the problem of embedding Halpern and Moses's modal logic of minimal knowledge states into two families of modal formalism for nonmonotonic reasoning, McDermott and Doyle's nonmonotonic modal logics and ground nonmonotonic modal logics. First, we prove that Halpern and Moses's logic can be embedded into all ground logics; moreover, the translation employed allows for establishing a lower bound (3p) for the problem of skeptical reasoning in all ground logics. Then, we show a translation of Halpern (...) and Moses's logic into a significant subset of McDermott and Doyle's formalisms. Such a translation both indicates the ability of Halpern and Moses's logic of expressing minimal knowledge states in a more compact way than McDermott and Doyle's logics, and allows for a comparison of the epistemological properties of such nonmonotonic modal formalisms. (shrink)

When we experience the world – see, hear, feel, taste, or smell things – we gain all sorts of knowledge about the things around us. And this knowledge figures heavily in our reasoning about the world – about what to think and do in response to it. But what is the nature of this knowledge? On one commonly held view, all knowledge is constituted by beliefs in propositions. But in this paper I (...) argue against this view. I argue that some knowledge is constituted, not by beliefs in propositions, but by awareness of properties and objects. To make my case, I focus on the role of visual perception in reasoning. I start by introducing a principle about the relationship between knowledge and reasoning, which says that to learn something new by reasoning, one must know the bases of one’s reasoning. Then I argue that in some cases of genuine, knowledge-conferring reasoning, the bases of our reasoning are not propositions that we believe; rather, they’re properties or objects that we see. Thus, I conclude that some such knowledge is non-propositional and is rather what some call “knowledge of things”. (shrink)

We address the way verb-based and rule-content knowledge are combined in understanding institutional deontics. Study 1 showed that the institutional regulations used in our studies were readily categorised into one of two content groups: rights or duties. Participants perceived rights as benefiting the addressees identified by the rule, whereas they perceived duties as benefiting the collective that imposed the rule. Studies 2, 3, and 4 showed that rule content had clear effects on perceptions of violations and relevance of cases (...) for explaining the rule, even when controlling for deontic verb, phrasing of the action permitted by a right, or the formality of the deontic verb. These effects are incompatible with a simple pragmatic disambiguation approach to pragmatic modulation, as they often induce permissibility judgments that contradict the core semantic meanings of the deontic verbs. Other ways of reconciling verb meaning with rule content should be considered in a fuller the.. (shrink)

In this paper we introduce Dynamic Epistemic Logic, which is alogic for reasoning about information change in a multi-agent system. Theinformation structures we use are based on non-well-founded sets, and canbe conceived as bisimulation classes of Kripke models. On these structures,we define a notion of information change that is inspired by UpdateSemantics (Veltman, 1996). We give a sound and complete axiomatization ofthe resulting logic, and we discuss applications to the puzzle of the dirtychildren, and to knowledge programs.

This chapter investigates Spinoza's conception of reason, focusing on (i) the difference between reason and the imagination, and (ii) the difference between reason and intuitive knowledge. The central interpretive debate this chapter considers is about the scope of rational cognition. Some commentators have argued that it is only possible to have rational cognition of properties that are universally shared, whereas intuitive knowledge may grasp the essences of particular individuals. Another prominent interpretation is that reason differs from intuition (...) only in virtue of its form or manner of apprehension, and not in virtue of the content or ideas it apprehends. However, authors on both sides of the debate have held that reason is incapable of grasping singular things. After summarizing the debate, this chapter presents an argument that Spinozan reason is not blind to particulars: it is (at least sometimes) capable of grasping the causal structure that characterizes an individual. (shrink)

In this paper, we first propose a simple formal language to specify types of agents in terms of necessary conditions for their announcements. Based on this language, types of agents are treated as ‘first-class citizens’ and studied extensively in various dynamic epistemic frameworks which are suitable for reasoning about knowledge and agent types via announcements and questions. To demonstrate our approach, we discuss various versions of Smullyan’s Knights and Knaves puzzles, including the Hardest Logic Puzzle Ever (HLPE) (...) proposed by Boolos (in Harv Rev Philos 6:62–65, 1996). In particular, we formalize HLPE and verify a classic solution to it. Moreover, we propose a spectrum of new puzzles based on HLPE by considering subjective (knowledge-based) agent types and relaxing the implicit epistemic assumptions in the original puzzle. The new puzzles are harder than the previously proposed ones in the literature, in the sense that they require deeper epistemic reasoning. Surprisingly, we also show that a version of HLPE in which the agents do not know the others’ types does not have a solution at all. Our formalism paves the way for studying these new puzzles using automatic model checking techniques. (shrink)

We present a bimodal logic suitable for formalizing reasoning about points and sets, and also states of the world and views about them. The most natural interpretation of the logic is in subset spaces , and we obtain complete axiomatizations for the sentences which hold in these interpretations. In addition, we axiomatize the validities of the smaller class of topological spaces in a system we call topologic . We also prove decidability for these two systems. Our results (...) on topologic relate early work of McKinsey on topological interpretations of S4 with recent work of Georgatos on topologic. Some of the results of this paper were presented at the 1992 conference on Theoretical Aspects of Reasoning about Knowledge. (shrink)

Inferences about spatial, temporal, and other relations are ubiquitous. This article presents a novel model-based theory of such reasoning. The theory depends on 5 principles. The structure of mental models is iconic as far as possible. The logical consequences of relations emerge from models constructed from the meanings of the relations and from knowledge. Individuals tend to construct only a single, typical model. They spontaneously develop their own strategies for relational reasoning. Regardless of strategy, the difficulty (...) of an inference depends on the process of integration of the information from separate premises, the number of entities that have to be integrated to form a model, and the depth of the relation. The article describes computer implementations of the theory and presents experimental results corroborating its main principle. (shrink)

Decades of research have focused on children's reasoning about math equivalence problems for both practical and theoretical insights. Not only are math equivalence problems foundational in arithmetic and algebra, they also represent a class of problems on which children's thinking is resistant to change. Feedback is one instructional tool that can serve as a key trigger of cognitive change. In this paper, we review all experimental studies on the effects of feedback on children's understanding of math equivalence. Meta-analytic (...) results indicate that feedback has positive effects for low-knowledge learners and negative effects for high-knowledge learners, and these effects are stronger for procedural outcomes than conceptual outcomes. Findings highlight the variable influences of feedback on math equivalence understanding and suggest that models of thinking and reasoning need to consider learner characteristics, learning outcomes, and learning materials, as well as the dynamic interactions among them. (shrink)

is used to give a formalization of Artemov’s knowledge based reasoning approach to game theory, (KBR), [ 4 , 5 ]. Epistemic states of players are represented explicitly and reasoned about formally. We give a detailed analysis of the Centipede game using both proof theoretic and semantic machinery. This helps make the case that PDL + E can be a useful basis for the logical investigation of game theory.

The communicative effect of a collective message from the Dutch former minister of finance Wouter Bos to inform all his contacts about his new email address is completely different from that of a set of individual messages to the same list. The talk will explain how differences of this kind can be modelled in epistemic logic (the logic of knowledge). A central notion here is common knowledge. We will explain the general framework for describing update effects of (...) messages as mappings on epistemic models (“knowledge models”), and we will give a sketch of some recent work in this area. (shrink)

We introduce a logic specifically designed to support reasoning about social choice functions. The logic includes operators to capture strategic ability, and operators to capture agent preferences. We establish a correspondence between formulae in the logic and properties of social choice functions, and show that the logic is expressively complete with respect to social choice functions, i.e., that every social choice function can be characterised as a formula of the logic. We prove that the logic is decidable, and (...) give a complete axiomatization. To demonstrate the value of the logic, we show in particular how it can be applied to the problem of determining whether a social choice function is strategy-proof. (shrink)

Background: Ethical problems are a universal phenomenon but rarely researched concerning patients dying from acute stroke. These patients often have a reduced consciousness from stroke onset and thereby lack ability to convey their needs and could be described as ‘incompetent’ decision makers regarding their own care. Objective: The aim of the study was to deepen the understanding of stroke team members’ reasoning about truth-telling in end-of-life care due to acute stroke. Research design: Qualitative study based on individual interviews (...) utilizing combined deductive and inductive content analysis. Participants and research context: A total of 15 stroke team members working in stroke units of two associated county hospitals in western Sweden participated. Ethical considerations: The study was approved by the Regional Ethics Review Board, Gothenburg, Sweden. Findings: The main findings were the team members’ dynamic movement between the categories ‘Truth above all’ and ‘Hide truth to protect’. Honesty was highly valued and considered as a reason for always telling the truth, with the argument of truth as common morality. However, the carers also argued for hiding the truth for different reasons such as not adding extra burden in the sorrow, awaiting a timely moment and not being a messenger of bad news. Withholding truth could both be seen as a way of protecting themselves from difficult conversations and to protect others. Discussion: The results indicate that there are various barriers for truthfulness. Interpreted from a virtue of ethics perspective, withholding of truth might also be seen as an expression of sound judgement to put the patient’s best interest first. Conclusion: The carers may need support in the form of supervision to be given space to reflect on their experience and thereby promote ethically justified care. Here, the multi-professional team can be of great value and contribute through inter-professional sharing of knowledge. (shrink)

According to the Doomsday Argument we have to rethink the probabilities we assign to a soon or not so soon extinction of mankind when we realize that we are living now, rather early in the history of mankind. Sleeping Beauty finds herself in a similar predicament: on learning the date of her first awakening, she is asked to re-evaluate the probabilities of her two possible future scenarios. In connection with Doom, I argue that it is wrong to assume that our (...) ordinary probability judgements do not already reflect our place in history: we justify the predictive use we make of the probabilities yielded by science by our knowledge of the fact that we live now, a certain time before the possible occurrence of the events the probabilities refer to. Our degrees of belief should change drastically when we forget the date—importantly, this follows without invoking the “Self Indication Assumption”. Subsequent conditionalization on information about which year it is cancels this probability shift again. The Doomsday Argument is about such probability shifts, but tells us nothing about the concrete values of the probabilities —for these, experience provides the only basis. Essentially the same analysis applies to the Sleeping Beauty problem. I argue that Sleeping Beauty “thirders” should be committed to thinking that the Doomsday Argument is ineffective; whereas “halfers” should agree that doom is imminent—but they are wrong. (shrink)

This paper addresses an argument offered by John Hawthorne against the propriety of an agent’s using propositions she does not know as premises in practical reasoning. I will argue that there are a number of potential structural confounds in Hawthorne’s use of his main example, a case of practical reasoning about a lottery. By drawing these confounds out more explicitly, we can get a better sense of how to make appropriate use of such examples in theorizing (...) class='Hi'>about norms, knowledge, and practical reasoning. I will conclude by suggesting a prescription for properly using lottery propositions to do the sort of work that Hawthorne wants from them. (shrink)

Is knowledge definable as justified true belief? We argue that one can legitimately answer positively or negatively, depending on whether or not one’s true belief is justified by what we call adequate reasons. To facilitate our argument we introduce a simple propositional logic of reason-based belief, and give an axiomatic characterization of the notion of adequacy for reasons. We show that this logic is sufficiently flexible to accommodate various useful features, including quantification over reasons. We use our framework to (...) contrast two notions of JTB: one internalist, the other externalist. We argue that Gettier cases essentially challenge the internalist notion but not the externalist one. Our approach commits us to a form of infallibilism about knowledge, but it also leaves us with a puzzle, namely whether knowledge involves the possession of only adequate reasons, or leaves room for some inadequate reasons. We favor the latter position, which reflects a milder and more realistic version of infallibilism. (shrink)

Here I pose a challenge to realism about knowledge, the view that facts about knowledge are non-trivially mind-independent, adapting an evolutionary debunking argument from metaethics. In brief: Our beliefs about knowledge are the products of innate knowledge-representing capacities with a deep and well documented evolutionary history, and, crucially, this history indicates that such capacities are indifferent to whether there are any mind-independent facts about knowledge. Instead, knowledge-representing capacities are likely just (...) a byproduct of processing limitations on primate cognition. This presents an explanatory challenge for the knowledge realist—How is it, then, that we nonetheless happen to have many true beliefs about knowledge? I’ll argue that, without abandoning the non-naturalism that characterizes much of contemporary epistemology, realism struggles to provide a compelling answer. In contrast, evolutionary anti-realism, the view advocated for here, meets the explanatory challenge head-on. Facts about knowledge are grounded in facts about what our innate knowledge-representing capacities classify as knowledge, so it’s no surprise that we have many true beliefs about knowledge. While none of this shows that realism about knowledge is false, these considerations give us ceteris paribus reason to prefer an anti-realist approach. (shrink)