Classical epistemic logic describes implicit knowledge of agents about facts and knowledge of other agents, based on semantic information. The latter is produced by acts of observation or communication, that are described well by dynamic epistemic logics. What these logics do not describe, however, is how significant information is also produced by acts of inference – and key axioms of the system merely postulate “deductive closure”. In this paper, we take the view that all information is produced by acts, and (...) hence we also need a dynamic logic of inference steps showing what effort on the part of the agent makes a conclusion explicit knowledge. Strong omniscience properties of agents should be seen not as static idealizations, but as the result of dynamic processes that agents engage in. This raises two questions: (a) how to define suitable information states of agents and matching notions of explicit knowledge, (b) how to define natural processes over these states that generate new explicit knowledge. To this end, we extend earlier epistemic “awareness models” into a dynamic system that includes acts of public observation, but also adding and dropping formulas from the currently ‘entertained’ set, we give a completeness theorem, and we show how this dynamics updates explicit knowledge. Similar ideas have been proposed before, but they were restricted to update with factual propositions; our new dynamic system applies to arbitrary formulas. We also extend our approach to multi-agent scenarios where awareness changes may happen privately. Finally, we mention further directions and related approaches. (shrink)

Logic has been a—disputed—ingredient in the emergence and development of the now very large field known as knowledge representation and reasoning. In this book (in progress), I select some central topics in this highly fruitful, albeit controversial, association (e.g., non-monotonic reasoning, implicit belief, logical omniscience, closed world assumption), identifying their sources and analyzing/explaining their elaboration in highly influential published work.

“There is no use in trying,” said Alice; “one can’t believe impossible things.” “I dare say you haven’t had much practice,” said the Queen. “When I was your age, I always did it for half an hour a day. Why, sometimes I’ve believed as many as six impossible things before breakfast”. Lewis Carroll, Through the Looking Glass. -/- It is a rather common view among philosophers that one cannot, properly speaking, be said to believe, conceive, imagine, hope for, or seek (...) what is impossible. -/- Some philosophers, for instance George Berkeley and the early Wittgenstein, thought that logically contradictory propositions lack cognitive meaning (informational content) and cannot, therefore, be thought or believed. Philosophers who do not go as far as Berkeley and Wittgenstein in denying that impossible propositions or states of affairs are thinkable, may still claim that it is impossible to rationally believe an impossible proposition. On a classical “Cartesian” view of belief, belief is a purely mental state of the agent holding true a proposition p that she “grasps” and is directly acquainted with. But if the agent is directly acquainted with an impossible proposition, then, presumably, she must know that it is impossible. But surely no rational agent can hold true a proposition that she knows is impossible. Hence, no rational agent can believe an impossible proposition. Thus it seems that on the Cartesian view of propositional attitudes as inner mental states in which proposition are immediately apprehended by the mind, it is impossible for a rational agent to believe, imagine or conceive an impossible proposition. -/- Ruth Barcan Marcus (1983) has suggested that a belief attribution is defeated once it is discovered that the proposition, or state of affairs that is believed is impossible. According to her intuition, just as knowledge implies truth, belief implies possibility. -/- It is commonplace that people claim to believe propositions that later turn out to be impossible. According to Barcan Marcus, the correct thing to say in such a situation is not: I once believed that A but I don’t believe it any longer since I have come to realize that it is impossible that A. What one should say is instead: It once appeared to me that I believed that A, but I did not, since it is impossible that A. Thus, Barcan Marcus defends what we might call Alice’s thesis: Necessarily, for any proposition p and any subject x, if x believes p, then p is possible. -/- Alice’s thesis that it is impossible to hold impossible beliefs, seems to come into conflict with our ordinary practices of attributing beliefs. Consider a mathematical example. Some mathematicians believe that CH (the continuum hypothesis) is true and others believe that it is false. But if CH is true, then it is necessarily true; and if it is false, then it is necessarily false. Regardless of whether CH is true or false, the conclusion seems to be that there are mathematicians who believe impossible propositions. -/- Examples of apparent beliefs in impossible propositions outside of mathematics are also easy to come by. Consider, for example, Kripke’s (1999) story of the Frenchman Pierre who without realizing it has two different names ‘London’ and ‘Londres’ for the same city, London. After having arrived in London, Pierre may assent to ‘Londres is beautiful and London is not beautiful’ without being in any way irrational. It seems reasonably to infer from this that Pierre believes that Londres is beautiful and London is not beautiful. But since ‘Londres’ and ‘London’ are rigid designators for the same city, it seems to follow from this that Pierre believes the inconsistent proposition that we may express as ‘London is both beautiful and not beautiful’. (shrink)

Models of collective deliberation often assume that the chief aim of a deliberative exchange is the sharing of information. In this paper, we argue that an equally important role of deliberation is to draw participants’ attention to pertinent questions, which can aid the assembly and processing of distributed information by drawing deliberators’ attention to new issues. The assumption of logical omniscience renders classical models of agents’ informational states unsuitable for modelling this role of deliberation. Building on recent insights from psychology, (...) linguistics and philosophy about the role of questions in speech and thought, we propose a different model in which beliefs are treated as answers directed at specific questions. Here, questions are formally represented as partitions of the space of possibilities and individuals’ information states as sets of questions and corresponding partial answers to them. The state of conversation is then characterised by individuals’ information together with the questions under discussion, which can be steered by various deliberative inputs. Using this model, deliberation is then shown to shape collective decisions in ways that classical models cannot capture, allowing for novel explanations of how group consensus is achieved. (shrink)

One of the open problems in the philosophy of information is whether there is an information logic (IL), different from epistemic (EL) and doxastic logic (DL), which formalises the relation “a is informed that p” (Iap) satisfactorily. In this paper, the problem is solved by arguing that the axiom schemata of the normal modal logic (NML) KTB (also known as B or Br or Brouwer’s system) are well suited to formalise the relation of “being informed”. After having shown that IL (...) can be constructed as an informational reading of KTB, four consequences of a KTB-based IL are explored: information overload; the veridicality thesis (Iap → p); the relation between IL and EL; and the Kp → Bp principle or entailment property, according to which knowledge implies belief. Although these issues are discussed later in the article, they are the motivations behind the development of IL. (shrink)

This chapter presents a new semantics for inductive empirical knowledge. The epistemic agent is represented concretely as a learner who processes new inputs through time and who forms new beliefs from those inputs by means of a concrete, computable learning program. The agent’s belief state is represented hyper-intensionally as a set of time-indexed sentences. Knowledge is interpreted as avoidance of error in the limit and as having converged to true belief from the present time onward. Familiar topics are re-examined within (...) the semantics, such as inductive skepticism, the logic of discovery, Duhem’s problem, the articulation of theories by auxiliary hypotheses, the role of serendipity in scientific knowledge, Fitch’s paradox, deductive closure of knowability, whether one can know inductively that one knows inductively, whether one can know inductively that one does not know inductively, and whether expert instruction can spread common inductive knowledge—as opposed to mere, true belief—through a community of gullible pupils. (shrink)

The relevance of any logical analysis lies in its ability to solve paradoxes and trace conceptual troubles back; with this respect, the task of epistemic logic is to handle paradoxes in connection with the concept of knowledge. Epistemic logic is currently introduced as the logical analysis of crucial concepts within epistemology, namely: knowledge, belief, truth, and justification. An alternative approach will be advanced here in order to enlighten such a discourse, as centred upon the word assertion and displayed in terms (...) of utterance. Insofar as epistemic modalities express some attitudes, the intentionality of discourse will be emphasized within an illocutionary modal logic. Two large views will range over the whole study: declarative and epistemic sentences have one and the same logic (assertion logic); the plurality of languages games doesn’t entail any logical pluralism. -/- La valeur d'une analyse logique réside dans sa capacité à résoudre des paradoxes et à comprendre l'origine de nos problèmes conceptuels ; à ce titre, le rôle d'une logique épistémique est de traiter des paradoxes liés au concept de connaissance. On présente généralement la logique épistémique comme une analyse logique de concepts centraux en épistémologie : connaissance, croyance, vérité, justification. Une autre approche sera proposée ici en vue de clarifier ce genre de discours, centrée sur la notion d'assertion et décrite en termes d'énonciation. Parce que les modalités épistémiques expriment des attitudes, c'est l'intentionnalité du discours qui sera mise en valeur dans le cadre d'une logique modale illocutoire. Deux thèses transversales parcourront l'ensemble du travail : les énoncés déclaratifs et épistémiques partagent la même logique (logique assertorique) ; la pluralité des jeux de langages n'implique pas un pluralisme logique. (shrink)

The impossibility theorem of Dekel, Lipman and Rustichini has been thought to demonstrate that standard state-space models cannot be used to represent unawareness. We first show that Dekel, Lipman and Rustichini do not establish this claim. We then distinguish three notions of awareness, and argue that although one of them may not be adequately modeled using standard state spaces, there is no reason to think that standard state spaces cannot provide models of the other two notions. In fact, standard space (...) models of these forms of awareness are attractively simple. They allow us to prove completeness and decidability results with ease, to carry over standard techniques from decision theory, and to add propositional quantifiers straightforwardly. (shrink)

Since its first appearance in 1966, the notion of a supervaluation has been regarded by many as a powerful tool for dealing with semantic gaps. Only recently, however, applications to semantic gluts have also been considered. In previous work I proposed a general framework exploiting the intrinsic gap/glut duality. Here I also examine an alternative account where gaps and gluts are treated on a par: although they reflect opposite situations, the semantic upshot is the same in both cases--the value of (...) some expressions is not uniquely defined. Other strategies for generalizing supervaluations are considered and some comparative facts are discussed. (shrink)

Syntactic logics do not suffer from the problems of logical omniscience but are often thought to lack interesting properties relating to epistemic notions. By focusing on the case of rule-based agents, I develop a framework for modelling resource-bounded agents and show that the resulting models have a number of interesting properties.