The logic of ‘being informed’ gives a formal analysis of a cognitive state that does not coincide with either belief, or knowledge. To Floridi, who first proposed the formal analysis, the latter is supported by the fact that unlike knowledge or belief, being informed is a factive, but not a reflective state. This paper takes a closer look at the formal analysis itself, provides a pure and an applied semantics for the logic of being informed, and tries to find out (...) to what extent the formal analysis can contribute to an information-based epistemology. (shrink)

Cognitive states as well as cognitive commodities play central though distinct roles in our epistemological theories. By being attentive to how a difference in their roles affects our way of referring to them, we can undoubtedly accrue our understanding of the structure and functioning of our main epistemological theories. In this paper we propose an analysis of the dichotomy between states and commodities in terms of the method of abstraction, and more specifically by means of infomorphisms between different ways to (...) classify states of information, information-bases, and evidential situations. (shrink)

One of the basic principles of the general definition of information is its rejection of dataless information, which is reflected in its endorsement of an ontological neutrality. In general, this principles states that “there can be no information without physical implementation” (Floridi (2005)). Though this is standardly considered a commonsensical assumption, many questions arise with regard to its generalised application. In this paper a combined logic for data and information is elaborated, and specifically used to investigate the consequences of restricted (...) and unrestricted data-implementation-principles. (shrink)

As Vincent Hendricks remarks early on in this book, the formal and mainstream traditions of epistemic theorising have mostly evolved independently of each other. This initial impression is confirmed by a comparison of the main problems and methods practitioners in each tradition are concerned with. Mainstream epistemol- ogy engages in a dialectical game of proposing and challenging definitions of knowledge. Formal epistemologists proceed differently, as they design a wide variety of axiomatic and model-theoretic methods whose consequences they investigate independently of (...) the need of giving counterexample-free definitions of knowledge. Or at least, this is a common way to explain where both disciplines stand in the larger landscape of epistemic theorising, and why interactions between them remain scarce. The main ambition of this book is to show that the distinction between formal and mainstream approaches should not preclude a fruitful interaction, and that it only takes the right outlook on their respective practices to disclose plenty of room for interaction. (shrink)

In this paper we address the problem of combining a logic with nonmonotonic modal logic. In particular we study the intuitionistic case. We start from a formal analysis of the notion of intuitionistic consistency via the sequent calculus. The epistemic operator M is interpreted as the consistency operator of intuitionistic logic by introducing intuitionistic stable sets. On the basis of a bimodal structure we also provide a semantics for intuitionistic stable sets.

The paper provides a framework for representing belief-contravening hypotheses in games of perfect information. The resulting t-extended information structures are used to encode the notion that a player has the disposition to behave rationally at a node. We show that there are models where the condition of all players possessing this disposition at all nodes (under their control) is both a necessary and a sufficient for them to play the backward induction solution in centipede games. To obtain this result, we (...) do not need to assume that rationality is commonly known (as is done in [Aumann (1995)]) or commonly hypothesized by the players (as done in [Samet (1996)]). The proposed model is compared with the account of hypothetical knowledge presented by Samet in [Samet (1996)] and with other possible strategies for extending information structures with conditional propositions. (shrink)

Representing an epistemic situation involving several agents obviously depends on the modeling point of view one takes. We start by identifying the types of modeling points of view which are logically possible. We call the one traditionally followed by epistemic logic the perfect external approach, because there the modeler is assumed to be an omniscient and external observer of the epistemic situation. In the rest of the paper we focus on what we call the internal approach, where the modeler is (...) one of the agents involved in the situation. For this approach we propose and axiomatize a logical formalism based on epistemic logic. This leads us to formalize some intuitions about the internal approach and about its connections with the external ones. Finally, we show that our internal logic is decidable and PSPACE-complete. (shrink)

Epistemic logic is one of the most exciting areas in medieval philosophy. Neglected almost entirely after the end of the Middle Ages, it has been rediscovered by philosophers of the twentieth century. Epistemic Logic in the Later Middle Ages provides the first comprehensive study of the subject. Ivan Boh explores the contrast between epistemic and alethic conceptions of consequence, the general epistemic rules of consequence, the search for conditions of knowing contingent propositions, the problems of substitutivity in intentional contexts, the (...) considerations of epistemic/doxastic iterated modalities, and the problems of composite and divided senses in authors ranging from Abelard to Frachantian. Boh concludes with a comparison between medieval endeavors and the epistemic logic of our own times. Written in a clear and readable style with minimal symbolic apparatus, this book employs modern symbolism and conceptual frameworks, and complements the studies of the syntacticand semantic dimensions of medieval logic. (shrink)

The paradox of knowability is a logical result suggesting that, necessarily, if all truths are knowable in principle then all truths are in fact known. The contrapositive of the result says, necessarily, if in fact there is an unknown truth, then there is a truth that couldn't possibly be known. More specifically, if p is a truth that is never known then it is unknowable that p is a truth that is never known. The proof has been used to argue (...) against versions of anti-realism committed to the thesis that all truths are knowable. For clearly there are unknown truths; individually and collectively we are non-omniscient. So, by the main result, it is false that all truths are knowable. The result has also been used to draw more general lessons about the limits of human knowledge. Still others have taken the proof to be fallacious, since it collapses an apparently moderate brand of anti-realism into an obviously implausible and naive idealism. (shrink)

Does a factive conception of knowability figure in ordinary use? There is some reason to think so. ‘Knowable’ and related terms such as ‘discoverable’, ‘observable’, and ‘verifiable’ all seem to operate factively in ordinary discourse. Consider the following example, a dialog between colleagues A and B: A: We could be discovered. B: Discovered doing what? A: Someone might discover that we're having an affair. B: But we are not having an affair! A: I didn’t say that we were. A’s remarks (...) sound contradictory. In this context the factivity of ‘someone might discover that’ explains this fact. So there is some reason to believe that knowability and related modalities are factive in ordinary use. For factive treatments of knowability in the context of epistemic theories of truth, compare Tennant (2000: 829) and Wright (2001: 59-60, n. 17). (shrink)

This paper contains a formal treatment of the system of quantified epistemic logic sketched in Appendix II of Carlson (1983). Section 1 defines the syntax and recapitulates the model set rules and principles of the Appendix system. Section 2 defines a possible worlds semantics for this system, and shows that the Appendix system is complete with respect to this semantics. Section 3 extends the system by an explicit truth operatorT it is true that and considers quantification over nonexistent individuals. Section (...) 4 formalizes the idea of variable identity criteria typical of Hintikkian epistemic logic. (shrink)

This paper analyzes the logical form of valuing. I argue that valuing a concept or property is a universal statement qua logical form, that valuing an object is an existential statement qua logical form, and, furthermore, that a correct analysis of the logical form of valuing contains doxastic operators. I show that these ingredients give rise to an interesting interplay between uniform and ununiform quantification, on the one hand, and de dicto and de re beliefs, on the other. I apply (...) this analysis to the value of political freedom. The received view is that the value of freedom lies in the value of the specific things one is free to do. But Ian Carter has recently shown that freedom has irreducible, "non-specific" value, too. I show that underlying the debate between the proponents of the received view and their critics is a disagreement about logical form: ununiform de dicto beliefs about freedom as a concept, for the received view, and uniform half-de dicto-half-de re beliefs about freedom as an object, for its critics. (shrink)

Using epistemic logic, we provide a non-probabilistic way to formalise payoff uncertainty, that is, statements such as ‘player i has approximate knowledge about the utility functions of player j.’ We show that on the basis of this formalisation common knowledge of payoff uncertainty and rationality (in the sense of excluding weakly dominated strategies, due to Dekel and Fudenberg (1990)) characterises a new solution concept we have called ‘mixed iterated strict weak dominance.’.

This paper contributes to an increasing literature strengthening the connection between epistemic logic and epistemology (Van Benthem, Hendricks). I give a survey of the most important applications of epistemic logic in epistemology. I show how it is used in the history of philosophy (Steiner's reconstruction of Descartes' sceptical argument), in solutions to Moore's paradox (Hintikka), in discussions about the relation between knowledge and belief (Lenzen) and in an alleged refutation of verificationism (Fitch) and I examine an early argument about the (...) (im)possibility of epistemic logic (Hocutt). Subsequently, I deal with interpretive questions about epistemic logic that, although implicitly, already appeared in the first section. I contend that a conception of epistemic logic as a theory of knowledge assertions is incoherent, and I argue that it does not make sense to adopt a normative interpretation of epistemic logic. Finally, I show ways to extend epistemic logic with other branches of philosophical logic so as to make it useful for some epistemological questions. Conditional logics and logics of public announcement are used to understand causal theories of knowledge and versions of reliabilism. Temporal logic helps understand some dynamic aspects of knowledge as well as the verificationist thesis. (shrink)

We develop a logical system that captures two different interpretations of what extensive games model, and we apply this to a long-standing debate in game theory between those who defend the claim that common knowledge of rationality leads to backward induction or subgame perfect (Nash) equilibria and those who reject this claim. We show that a defense of the claim à la Aumann (1995) rests on a conception of extensive game playing as a one-shot event in combination with a principle (...) of rationality that is incompatible with it, while a rejection of the claim à la Reny (1988) assumes a temporally extended, many-moment interpretation of extensive games in combination with implausible belief revision policies. In addition, the logical system provides an original inductive and implicit axiomatization of rationality in extensive games based on relations of dominance rather than the usual direct axiomatization of rationality as maximization of expected utility. (shrink)

Formal learning theory constitutes an attempt to describe and explain the phenomenon of learning, in particular of language acquisition. The considerations in this domain are also applicable in philosophy of science, where it can be interpreted as a description of the process of scientific inquiry. The theory focuses on various properties of the process of hypothesis change over time. Treating conjectures as informational states, we link the process of conjecture-change to epistemic update. We reconstruct and analyze the temporal aspect of (...) learning in the context of dynamic and temporal logics of epistemic change. We first introduce the basic formal notions of learning theory and basic epistemic logic. We provide a translation of the components of learning scenarios into the domain of epistemic logic. Then, we propose a characterization of finite identifiability in an epistemic temporal language. In the end we discuss consequences and possible extensions of our work. (shrink)

In this paper we compare different models of vagueness viewed as a specific form of subjective uncertainty in situations of imperfect discrimination. Our focus is on the logic of the operator “clearly” and on the problem of higher-order vagueness. We first examine the consequences of the notion of intransitivity of indiscriminability for higher-order vagueness, and compare several accounts of vagueness as inexact or imprecise knowledge, namely Williamson’s margin for error semantics, Halpern’s two-dimensional semantics, and the system we call Centered semantics. (...) We then propose a semantics of degrees of clarity, inspired from the signal detection theory model, and outline a view of higher-order vagueness in which the notions of subjective clarity and unclarity are handled asymmetrically at higher orders, namely such that the clarity of clarity is compatible with the unclarity of unclarity. (shrink)

Compositional verification aims at managing the complexity of theverification process by exploiting compositionality of the systemarchitecture. In this paper we explore the use of a temporal epistemiclogic to formalize the process of verification of compositionalmulti-agent systems. The specification of a system, its properties andtheir proofs are of a compositional nature, and are formalized within acompositional temporal logic: Temporal Multi-Epistemic Logic. It isshown that compositional proofs are valid under certain conditions.Moreover, the possibility of incorporating default persistence ofinformation in a system, is (...) explored. A completion operation on aspecific type of temporal theories, temporal completion, is introducedto be able to use classical proof techniques in verification withrespect to non-classical semantics covering default persistence. (shrink)

When reasoning about complex domains, where information available is usually only partial, nonmonotonic reasoning can be an important tool. One of the formalisms introduced in this area is Reiter's Default Logic (1980). A characteristic of this formalism is that the applicability of default (inference) rules can only be verified in the future of the reasoning process. We describe an interpretation of default logic in temporal epistemic logic which makes this characteristic explicit. It is shown that this interpretation yields a semantics (...) for default logic based on temporal epistemic models. A comparison between the various semantics for default logic will show the differences and similarities of these approaches and ours. (shrink)

Several justification logics have been created, starting with the logic LP, [1]. These can be thought of as explicit versions of modal logics, or of logics of knowledge or belief, in which the unanalyzed necessity (knowledge, belief) operator has been replaced with a family of explicit justification terms. We begin by sketching the basics of justification logics and their relations with modal logics. Then we move to new material. Modal logics come in various strengths. For their corresponding justification logics, differing (...) strength is reflected in different vocabularies. What we show here is that for justification logics corresponding to modal logics extending T, various familiar extensions are actually conservative with respect to each other. Our method of proof is very simple, and general enough to handle several justification logics not directly corresponding to distinct modal logics. Our methods do not, however, allow us to prove comparable results for justification logics corresponding to modal logics that do not extend T. That is, we are able to handle explicit logics of knowledge, but not explicit logics of belief. This remains open. (shrink)

We examine the paradox of the surprise examination using dynamic epistemic logic. This logic contains means of expressing epistemic facts as well as the effects of learning new facts, and is therefore a natural framework for representing the puzzle. We discuss a number of different interpretations of the puzzle in this context, and show how the failure of principle of success, that states that sentences, when learned, remain to be true and come to be believed, plays a central role in (...) understanding the puzzle. (shrink)

This paper discusses the possibility of modelling inductive inference (Gold 1967) in dynamic epistemic logic (see e.g. van Ditmarsch et al. 2007). The general purpose is to propose a semantic basis for designing a modal logic for learning in the limit. First, we analyze a variety of epistemological notions involved in identification in the limit and match it with traditional epistemic and doxastic logic approaches. Then, we provide a comparison of learning by erasing (Lange et al. 1996) and iterated epistemic (...) update (Baltag and Moss 2004) as analyzed in dynamic epistemic logic. We show that finite identification can be modelled in dynamic epistemic logic, and that the elimination process of learning by erasing can be seen as iterated belief-revision modelled in dynamic doxastic logic. Finally, we propose viewing hypothesis spaces as temporal frames and discuss possible advantages of that perspective. (shrink)

We study a generalization of the Muddy Children puzzle by allowing public announcements with arbitrary generalized quantifiers. We propose a new concise logical modeling of the puzzle based on the number triangle representation of quantifi ers. Our general aim is to discuss the possibility of epistemic modeling that is cut for specifi c informational dynamics. Moreover, we show that the puzzle is solvable for any number of agents if and only if the quanti fier in the announcement is positively active (...) (satis es a form of variety). (shrink)

In a penetrating investigation of the relationship between belief and quantitative degrees of confidence (or degrees of belief) Richard Foley (1992) suggests the following thesis: ... it is epistemically rational for us to believe a proposition just in case it is epistemically rational for us to have a sufficiently high degree of confidence in it, sufficiently high to make our attitude towards it one of belief. Foley goes on to suggest that rational belief may be just rational degree of confidence (...) above some threshold level that the agent deems sufficient for belief. He finds hints of this view in Locke’s discussion of probability and degrees of assent, so he calls it the Lockean Thesis.1 The Lockean Thesis has important implications for the logic of belief. Most prominently, it implies that even a logically ideal agent whose degrees of confidence satisfy the axioms of probability theory may quite rationally believe each of a large body of propositions that are jointly inconsistent. For example, an agent may legitimately believe that on each given occasion her well-maintained car will start, but nevertheless believe that she will eventually encounter a.. (shrink)

John Locke proposed a straightforward relationship between qualitative and quantitative doxastic notions: belief corresponds to a sufficiently high degree of confidence. Richard Foley has further developed this Lockean thesis and applied it to an analysis of the preface and lottery paradoxes. Following Foley's lead, we exploit various versions of these paradoxes to chart a precise relationship between belief and probabilistic degrees of confidence. The resolutions of these paradoxes emphasize distinct but complementary features of coherent belief. These features suggest principles that (...) tie together qualitative and quantitative doxastic notions. We show how these principles may be employed to construct a quantitative model - in terms of degrees of confidence - of an agent's qualitative doxastic state. This analysis fleshes out the Lockean thesis and provides the foundation for a logic of belief that is responsive to the logic of degrees of confidence. (shrink)

Epistemic logic is the logic of knowledge and belief. It provides insight into the properties of individual knowers, has provided a means to model complicated scenarios involving groups of knowers and has improved our understanding of the dynamics of inquiry.

This book provides a valuable look at the work of up and coming epistemologists. The topics covered range from the central issues of mainstream epistemology to the more formal issues in epistemic logic and confirmation theory. This book should be read by anyone interested in seeing where epistemology is currently focused and where it is heading. - Stewart Cohen , Arizona State University..

Epistemic logic begins with the recognition that our everyday talk about knowing and believing has some systematic features that we can track and re‡ect upon. Epistemic logicians have studied and extended these glints of systematic structure in fascinating and important ways since the early 1960s. However, for one reason or another, mainstream epistemologists have shown little interest. It is striking to contrast the marginal role of epistemic logic in contemporary epistemology with the centrality of modal logic for metaphysicians. This article (...) is intended to help in correcting this oversight by presenting some important developments in epistemic logic and suggesting ways to understand their applicability to traditional epistemological problems. Obviously, by itself, tweaking the formal apparatus of epistemic logic does not solve traditional epistemological problems. Epistemic logic can help us to navigate through problems in a systematic fashion by unpacking the logic of the problematic concepts, it can also lead us to recognize problems that we had not anticipated. This is basically analogous to the role that modal logic has played in contemporary metaphysics. (shrink)

The following analysis shows how developments in epistemic logic can play a nontrivial role in cognitive neuroscience. We argue that the striking correspondence between two modes of identification, as distinguished in the epistemic context, and two cognitive systems distinguished by neuroscientific investigation of the visual system (the "where" and "what" systems) is not coincidental, and that it can play a clarificatory role at the most fundamental levels of neuroscientific theory.

van Bentham et al. (Merging frameworks for interaction: DEL and ETL, 2007) provides a framework for generating the models of Epistemic Temporal Logic ( ETL : Fagin et al., Reasoning about knowledge, 1995; Parikh and Ramanujam, Journal of Logic, Language, and Information, 2003) from the models of Dynamic Epistemic Logic ( DEL : Baltag et al., in: Gilboa (ed.) Tark 1998, 1998; Gerbrandy, Bisimulations on Planet Kripke, 1999). We consider the logic TDEL on the merged semantic framework, and its extension (...) with the labeled past-operator “ P ϵ ” (“The event ϵ has happened before which. . .”). To axiomatize the extension, we introduce a method for transforming a given model into a normal form in a suitable sense. These logics suggest further applications of DEL in the theory of agency, the theory of learning, etc. (shrink)

Various theories try to give accounts of how measures of this confidence do or ought to behave, both as far as the internal mental consistency of the agent as ...

Kaplan says that monsters violate Principle 2 of his theory. Principle 2 is that indexicals, pure and demonstrative alike, are directly referential. In providing this explanation of there being no monsters, Kaplan feels his theory has an advantage over double-indexing theories like Kamp’s or Segerberg’s (or Stalnaker’s), which either embrace monsters or avoid them only by ad hoc stipulation, in the sharp conceptual distinction it draws between circumstances of evaluation and contexts of utterance. We shall argue that Kaplan’s prohibition is (...) also essentially stipulative, and that it is too general. The main difference between ourselves and Kaplan is that the basic carriers of a truth-value is a sentence-in-a-context; our account is utterance-based. (shrink)

For deductive reasoning to be justified, it must be guaranteed to preserve truth from premises to conclusion; and for it to be useful to us, it must be capable of informing us of something. How can we capture this notion of information content, whilst respecting the fact that the content of the premises, if true, already secures the truth of the conclusion? This is the problem I address here. I begin by considering and rejecting several accounts of informational content. I (...) then develop an account on which informational contents are indeterminate in their membership. This allows there to be cases in which it is indeterminate whether a given deduction is informative. Nevertheless, on the picture I present, there are determinate cases of informative (and determinate cases of uninformative) inferences. I argue that the model I offer is the best way for an account of content to respect the meaning of the logical constants and the inference rules associated with them without collapsing into a classical picture of content, unable to account for informative deductive inferences. (shrink)

The logical omniscience problem, whereby standard models of epistemic logic treat an agent as believing all consequences of its beliefs and knowing whatever follows from what else it knows, has received plenty of attention in the literature. But many attempted solutions focus on a fairly narrow specification of the problem: avoiding the closure of belief or knowledge, rather than showing how the proposed logic is of philosophical interest or of use in computer science or artificial intelligence. Sentential epistemic logics, as (...) opposed to traditional possible worlds approaches, do not suffer from the problems of logical omniscience but are often thought to lack interesting epistemic properties. In this paper, I focus on the case of rule-based agents, which play a key role in contemporary AI research but have been neglected in the logical literature. I develop a framework for modelling monotonic, nonmonotonic and introspective rule-based reasoners which have limited cognitive resources and prove that the resulting models have a number of interesting properties. An axiomatization of the resulting logic is given, together with completeness, decidability and complexity results. (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.

Information is often modelled as a set of relevant possibilities, treated as logically possible worlds. However, this has the unintuitive consequence that the logical consequences of an agent's information cannot be informative for that agent. There are many scenarios in which such consequences are clearly informative for the agent in question. Attempts to weaken the logic underlying each possible world are misguided. Instead, I provide a genuinely psychological notion of epistemic possibility and show how it can be captured in a (...) formal model, which I call a fan. I then show how to use fans to build formal models of being informed, as well as knowledge, belief and information update. (shrink)

One of the fundamental properties inclassical equational reasoning isLeibniz's principle of substitution. Unfortunately, this propertydoes not hold instandard epistemic logic. Furthermore,Herbrand's lifting theorem which isessential to thecompleteness ofresolution andParamodulation in theclassical first order logic (FOL), turns out to be invalid in standard epistemic logic. In particular, unlike classical logic, there is no skolemization normal form for standard epistemic logic. To solve these problems, we introduce anintensional epistemic logic, based on avariation of Kripke's possible-worlds semantics that need not have a constant (...) domain. We show how a weaker notion of substitution through indexed terms can retain the Herbrand theorem. We prove how the logic can yield a satisfibility preserving skolemization form. In particular, we present an intensional principle for unifing indexed terms. Finally, we describe asound andcomplete inference system for a Horn subset of the logic withequality, based onepistemic SLD-resolution. (shrink)

This paper deals with the problem of verification of game-like structures by means of symbolic model checking. Alternating-time Temporal Epistemic Logic (ATEL) is used for expressing properties of multi-agent systems represented by alternating epistemic temporal systems as well as concurrent epistemic game structures. Unbounded model checking (a SAT based technique) is applied for the first time to verification of ATEL. An example is given to show an application of the technique.

In this paper I combine the dynamic epistemic logic ofGerbrandy (1999) with the probabilistic logic of Fagin and Halpern (1994). The resultis a new probabilistic dynamic epistemic logic, a logic for reasoning aboutprobability, information, and information change that takes higher orderinformation into account. Probabilistic epistemic models are defined, and away to build them for applications is given. Semantics and a proof systemis presented and a number of examples are discussed, including the MontyHall Dilemma.

A first-order logic of belief with identity is proposed, primarily to give an account of possible de re contradictory beliefs, which sometimes occur as consequences of de dicto non-contradictory beliefs. A model has two separate, though interconnected domains: the domain of objects and the domain of appearances. The satisfaction of atomic formulas is defined by a particular S-accessibility relation between worlds. Identity is non-classical, and is conceived as an equivalence relation having the classical identity relation as a subset. A tableau (...) system with labels, signs, and suffixes is defined, extending the basic language $\mathscr{L}_{\mathbf{QB}}$ by quasiformulas (to express the denotations of predicates). The proposed logical system is paraconsistent since $\phi \wedge \neg\phi$ does not ``explode'' with arbitrary syntactic consequences. (shrink)

We show how some model-theoretical devices (local reasoning, modes of presentation, an additional accessibility relation) can be combined in first-order modal logic to formalize the consequence relation that includes de dicto and de re contradictory beliefs. Instead of special ``sense objects'', appearances of objects in an agent's belief are introduced and presented as ordered pairs consisting of an object and an individual constant. A non-classical identity relation is applied. A relation S on the set of possible worlds is introduced, which (...) models possible distortions in an agent's picture of a (real) world. The application of such models in deontic logic is illustrated by a characteristic example. , , , , , , , ,. (shrink)

We investigate the research programme of dynamic doxastic logic (DDL) and analyze its underlying methodology. The Ramsey test for conditionals is used to characterize the logical and philosophical differences between two paradigmatic systems, AGM and KGM, which we develop and compare axiomatically and semantically. The importance of Gärdenfors’s impossibility result on the Ramsey test is highlighted by a comparison with Arrow’s impossibility result on social choice. We end with an outlook on the prospects and the future of DDL.

This paper addresses the problem of upgrading functional information to knowledge. Functional information is defined as syntactically well-formed, meaningful and collectively opaque data. Its use in the formal epistemology of information theories is crucial to solve the debate on the veridical nature of information, and it represents the companion notion to standard strongly semantic information, defined as well-formed, meaningful and true data. The formal framework, on which the definitions are based, uses a contextual version of the verificationist principle of truth (...) in order to connect functional to semantic information, avoiding Gettierization and decoupling from true informational contents. The upgrade operation from functional information uses the machinery of epistemic modalities in order to add data localization and accessibility as its main properties. We show in this way the conceptual worthiness of this notion for issues in contemporary epistemology debates, such as the explanation of knowledge process acquisition from information retrieval systems, and open data repositories. (shrink)

Various conceptual approaches to the notion of information can currently be traced in the literature in logic and formal epistemology. A main issue of disagreement is the attribution of truthfulness to informational data, the so called Veridicality Thesis (Floridi 2005). The notion of Epistemic Constructive Information (Primiero 2007) is one of those rejecting VT. The present paper develops a formal framework for ECI. It extends on the basic approach of Artemov’s logic of proofs (Artemov 1994), representing an epistemic logic based (...) on dependent justifications, where the definition of information relies on a strict distinction from factual truth. The definition obtained by comparison with a Normal Modal Logic translates a constructive logic for “becoming informed”: its distinction from the logic of “being informed”—which internalizes truthfulness—is essential to a general evaluation of information with respect to truth. The formal disentanglement of these two logics, and the description of the modal version of the former as a weaker embedding into the latter, allows for a proper understanding of the Veridicality Thesis with respect to epistemic states defined in terms of information. (shrink)

This paper introduces a multi-modal polymorphic type theory to model epistemic processes characterized by trust, defined as a second-order relation affecting the communication process between sources and a receiver. In this language, a set of senders is expressed by a modal prioritized context, whereas the receiver is formulated in terms of a contextually derived modal judgement. Introduction and elimination rules for modalities are based on the polymorphism of terms in the language. This leads to a multi-modal non-homogeneous version of a (...) type theory, in which we show the embedding of the modal operators into standard group knowledge operators. (shrink)

Abstract: I argue that the solution to the Red Hat Problem, a puzzle derived from interactive epistemic logic, requires S5. Interactive epis- temic logic is set out in formal terms, and an attempt to solve the red hat puzzle is made in K, K, and K, each of which fails, showing that a stronger system, K is required.

We present a direct reduction of dynamic epistemic logic in the spirit of [4] to propositional dynamic logic (PDL) [17, 18] by program transformation. The program transformation approach associates with every update action a transformation on PDL programs. These transformations are then employed in reduction axioms for the update actions. It follows that the logic of public announcement, the logic of group announcements, the logic of secret message passing, and so on, can all be viewed as subsystems of PDL. Moreover, (...) the program transformation approach can be used to generate the appropriate reduction axioms for these logics. Our direct reduction of dynamic epistemic logic to PDL was inspired by the reduction of dynamic epistemic logic to automata PDL of [13]. Our approach shows how the detour through automata can be avoided. (shrink)

Some systems of modal logic, such as S5, which are often used as epistemic logics with the ‘necessity’ operator read as ‘the agent knows that’, are problematic as general epistemic logics for agents whose computational capacity does not exceed that of a Turing machine because they impose unwarranted constraints on the agent’s theory of non-epistemic aspects of the world, for example by requiring the theory to be decidable rather than merely recursively axiomatizable. To generalize this idea, two constraints on an (...) epistemic logic are formulated: r.e. conservativeness, that any recursively enumerable theory R in the sublanguage without the epistemic operator is conservatively extended by some recursively enumerable theory in the language with the epistemic operator which is permitted by the logic to be the agent’s overall theory; the weaker requirement of r.e. quasi-conservativeness is similar except for applying only when R is consistent. The logic S5 is not even r.e. quasiconservative; this result is generalized to many other modal logics. However, it is also proved that the modal logics S4, Grz and KDE are r.e. quasi-conservative and that K4, KE and the provability logic GLS are r.e. conservative. Finally, r.e. conservativeness and r.e. quasiconservativeness are compared with related non-computational constraints. (shrink)