A well-known open problem in epistemic logic is to give a syntactic characterization of the successful formulas. Semantically, a formula is successful if and only if for any pointed model where it is true, it remains true after deleting all points where the formula was false. The classic example of a formula that is not successful in this sense is the “Moore sentence” p ∧ ¬BOXp, read as “p is true but you do not know p.” Not only is the (...) Moore sentence unsuccessful, it is self-refuting, for it never remains true as described. We show that in logics of knowledge and belief for a single agent (extended by S5), Moorean phenomena are the source of all self-refutation; moreover, in logics for an introspective agent (extending KD45), Moorean phenomena are the source of all unsuccessfulness as well. This is a distinctive feature of such logics, for with a non-introspective agent or multiple agents, non-Moorean unsuccessful formulas appear. We also consider how successful and self-refuting formulas relate to the Cartesian and learnable formulas, which have been discussed in connection with Fitch’s “paradox of knowability.” We show that the Cartesian formulas are exactly the formulas that are not eventually self-refuting and that not all learnable formulas are successful. In an appendix, we give syntactic characterizations of the successful and the self-refuting formulas. (shrink)

Rational agents base their actions on information from observation, inference, introspection, or other sources. But this information comes in different kinds, and it is usually handled by different logical mechanisms. We discuss how to integrate external ‘updating information’ and internal ‘elucidating information’ into one system of dynamic epistemic logic, by distinguishing two basic informational actions: ‘bare seeing’ versus ‘conscious realization’.

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)

An introduction to philosophy of language since Frege, focusing on the 20th century.

Changing preferencesis a phenomenonoften invoked but rarely properlyaccounted for. Throughout the history of the social sciences, researchers have come against the possibility that their subjects’ preferenceswere affected by the phenomenato be explainedor by otherfactorsnot taken into accountin the explanation.Sporadically, attempts have been made to systematically investigate these in uences, but none of these seems to have had a lasting impact. Today we are still not much further with respect to preference change than we were at the middle of the last (...) century. This anthology hopes to provide a new impulse for research into this important subject. In particular, we have chosen two routes to amplify this impulse. First, we stress the use of modellingtechniquesfamiliar from economicsand decision theory. Instead of constructing complex, all-encompassing theories of preference change, the authors of this volume start with very simple, formal accounts of some possible and hopefully plausible mechanism of preference change. Eventually, these models may nd their way into larger, empirically adequate theories, but at this stage, we think that the most importantwork lies in building structure.Secondly,we stress the importance of interdisciplinary exchange. Only by drawing together experts from different elds can the complex empirical and theoretical issues in the modelling of preference change be adequately investigated. (shrink)

In their recently published book Nudge (2008) Richard H. Thaler and Cass R. Sunstein (T&S) defend a position labelled as ‘libertarian paternalism’. Their thinking appeals to both the right and the left of the political spectrum, as evidenced by the bedfellows they keep on either side of the Atlantic. In the US, they have advised Barack Obama, while, in the UK, they were welcomed with open arms by the David Cameron's camp (Chakrabortty 2008). I will consider the following questions. What (...) is Nudge? How is it different from social advertisement? Does Nudge induce genuine preference change? Does Nudge build moral character? Is there a moral difference between the use of Nudge as opposed to subliminal images to reach policy objectives? And what are the moral constraints on Nudge? (shrink)

This paper presents a logic combining Dynamic Epistemic Logic, a framework for reasoning about multi-agent communication, with a new multi-agent version of Justification Logic, a framework for reasoning about evidence and justification. This novel combination incorporates a new kind of multi-agent evidence elimination that cleanly meshes with the multi-agent communications from Dynamic Epistemic Logic, resulting in a system for reasoning about multi-agent communication and evidence elimination for groups of interacting rational agents.

In the last few years, preference logic and in particular, the dynamic logic of preference change, has suddenly become a live topic in my Amsterdam and Stanford environments. At the request of the editors, this article explains how this interest came about, and what is happening. I mainly present a story around some recent dissertations and supporting papers, which are found in the references. There is no pretense at complete coverage of preference logic (for that, see Hanson 2001) or even (...) of preference change (Hanson 1995). (shrink)

This book illustrates the program of Logical-Informational Dynamics. Rational agents exploit the information available in the world in delicate ways, adopt a wide range of epistemic attitudes, and in that process, constantly change the world itself. Logical-Informational Dynamics is about logical systems putting such activities at center stage, focusing on the events by which we acquire information and change attitudes. Its contributions show many current logics of information and change at work, often in multi-agent settings where social behavior is essential, (...) and often stressing Johan van Benthem's pioneering work in establishing this program. However, this is not a Festschrift, but a rich tapestry for a field with a wealth of strands of its own. The reader will see the state of the art in such topics as information update, belief change, preference, learning over time, and strategic interaction in games. Moreover, no tight boundary has been enforced, and some chapters add more general mathematical or philosophical foundations or links to current trends in computer science. The theme of this book lies at the interface of many disciplines. Logic is the main methodology, but the various chapters cross easily between mathematics, computer science, philosophy, linguistics, cognitive and social sciences, while also ranging from pure theory to empirical work. Accordingly, the authors of this book represent a wide variety of original thinkers from different research communities. And their interconnected themes challenge at the same time how we think of logic, philosophy and computation. Thus, very much in line with van Benthem's work over many decades, the volume shows how all these disciplines form a natural unity in the perspective of dynamic logicians (broadly conceived) exploring their new themes today. And at the same time, in doing so, it offers a broader conception of logic with a certain grandeur, moving its horizons beyond the traditional study of consequence relations. (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)

We formalize what it means to have permission to say something. We adapt the dynamic logic of permission by van der Meyden (J Log Comput 6(3):465–479, 1996 ) to the case where atomic actions are public truthful announcements. We also add a notion of obligation. Our logic is an extension of the logic of public announcements introduced by Plaza ( 1989 ) with dynamic modal operators for permission and for obligation. We axiomatize the logic and show that it is decidable.

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)

We take a logical approach to threshold models, used to study the diffusion of opinions, new technologies, infections, or behaviors in social networks. Threshold models consist of a network graph of agents connected by a social relationship and a threshold value which regulates the diffusion process. Agents adopt a new behavior/product/opinion when the proportion of their neighbors who have already adopted it meets the threshold. Under this diffusion policy, threshold models develop dynamically towards a guaranteed fixed point. We construct a (...) minimal dynamic propositional logic to describe the threshold dynamics and show that the logic is sound and complete. We then extend this framework with an epistemic dimension and investigate how information about more distant neighbors’ behavior allows agents to anticipate changes in behavior of their closer neighbors. Overall, our logical formalism captures the interplay between the epistemic and social dimensions in social networks. (shrink)

In this work, we present a multi-agent logic of knowledge and change of knowledge interpreted on topological structures. Our dynamics are of the so-called semi-private character where a group G of agents is informed of some piece of information \, while all the other agents observe that group G is informed, but are uncertain whether the information provided is \ or \. This article follows up on our prior work where the dynamics were public events. We provide a complete axiomatization (...) of our logic, and give two detailed examples of situations with agents learning information through semi-private announcements. (shrink)

We present Dynamic Epistemic Temporal Logic, a framework for reasoning about operations on multi-agent Kripke models that contain a designated temporal relation. These operations are natural extensions of the well-known “action models” from Dynamic Epistemic Logic. Our “temporal action models” may be used to define a number of informational actions that can modify the “objective” temporal structure of a model along with the agents’ basic and higher-order knowledge and beliefs about this structure, including their beliefs about the time. In essence, (...) this approach provides one way to extend the domain of action model-style operations from atemporal Kripke models to temporal Kripke models in a manner that allows actions to control the flow of time. We present a number of examples to illustrate the subtleties involved in interpreting the effects of our extended action models on temporal Kripke models. We also study preservation of important epistemic-temporal properties of temporal Kripke models under temporal action model-induced operations, provide complete axiomatizations for two theories of temporal action models, and connect our approach with previous work on time in DEL. (shrink)

Collective intentionality is one of the most fundamental notions in social ontology. However, it is often thought to refer to a capacity which does not presuppose the existence of any other social facts. This chapter critically examines this view from the perspective of one specific theory of collective intentionality, the theory of Margaret Gilbert. On the basis of Gilbert’s arguments, the chapter claims that collective intentionality is a highly contingent achievement of complex social practices and, thus, not a basic social (...) phenomenon. The argument proceeds in three steps. First, Gilbert’s thesis that certain kinds of collective intentionality presuppose joint normative commitments is introduced. Second, it is argued that, on this view, individual commitments can only constitute the relevant kinds of collective intentional states if there are socially shared “principles of membership” that connect the force of individual commitments to a shared content. Third, it is shown that strong collective intentionality depends on the practical acceptance of shared norms and on the establishment of authority relations through mutual recognition. (shrink)

We study a logic for reasoning about agents that pass messages according to a protocol. Protocols are specified extensionally, as sets of sequences of ?legal? actions assigned to each state in a Kripke model. Message-passing events that are licensed by the protocol are modeled as updates in the style of dynamic epistemic logic. We also consider changes to the protocol by introducing message-encoding modalities, corresponding to communications actions that lead to protocol extensions. While in our general framework, messages are arbitrary (...) objects, we also consider the case that the messages that are passed are sentences of the object language itself. We present complete calculi for our logics and clarify the relationship of our proposal to earlier work on public announcement logic. (shrink)

Belief revision from the point of view of doxastic logic. Logic Journal of the IGPL, 3(4), 535–553. Segerberg, K. (1995). Conditional action. In G. Crocco, L. Fariñas, & A. Herzig (Eds.), Conditionals: From philosophy to computer science, Studies ...

In this paper we show how recent concepts from Dynamic Logic, and in particular from Dynamic Epistemic logic, can be used to model and interpret quantum behavior. Our main thesis is that all the non-classical properties of quantum systems are explainable in terms of the non-classical flow of quantum information. We give a logical analysis of quantum measurements (formalized using modal operators) as triggers for quantum information flow, and we compare them with other logical operators previously used to model various (...) forms of classical information flow: the “test” operator from Dynamic Logic, the “announcement” operator from Dynamic Epistemic Logic and the “revision” operator from Belief Revision theory. The main points stressed in our investigation are the following: (1) The perspective and the techniques of “logical dynamics” are useful for understanding quantum information flow. (2) Quantum mechanics does not require any modification of the classical laws of “static” propositional logic, but only a non-classical dynamics of information. (3) The main such non-classical feature is that, in a quantum world, all information-gathering actions have some ontic side-effects. (4) This ontic impact can affect in its turn the flow of information, leading to non-classical epistemic side-effects (e.g. a type of non-monotonicity) and to states of “objectively imperfect information”. (5) Moreover, the ontic impact is non-local: an information-gathering action on one part of a quantum system can have ontic side-effects on other, far-away parts of the system. (shrink)

We used agent-based modelling to highlight the advantages and disadvantages of several management styles in biology, ranging from centralized to egalitarian ones. In egalitarian groups, all team members are connected with each other, while in centralized ones, they are only connected with the principal investigator. Our model incorporated time constraints, which negatively influenced weakly connected groups such as centralized ones. Moreover, our results show that egalitarian groups outperform others if the questions addressed are relatively simple or when the communication among (...) agents is limited. Complex epistemic spaces are explored best by centralized groups. They outperform other team structures because the individual members can develop their own ideas with less interference of the opinions of others. The optimal ratio between time spent on experimentation and dissemination varies between different organizational structures. Furthermore, if the evidence is shared only after a relevant degree of certainty is reached, all investigated groups epistemically profit. We discovered that the introduction of seminars to the model changes the epistemic performance in favour of weakly connected teams. Finally, the abilities of the principal investigator do not seem to outperform cognitive diversity, as group performances were not strongly influenced by the increase of her abilities. (shrink)

This study realizes belief/reliability change of a judge in a legal judgment by dynamic epistemic logic. A key feature of DEL is that possibilities in an agent’s belief can be represented by a Kripke model. This study addresses two difficulties in applying DEL to a legal case. First, since there are several methods for constructing a Kripke model, our question is how we can construct the model from a legal case. Second, since this study employs several dynamic operators, our question (...) is how we can decide which operators are to be applied for belief/reliability change of a judge. In order to solve these difficulties, we have implemented a computer system which provides two functions. First, the system can generate a Kripke model from a legal case. Second, the system provides an inconsistency solving algorithm which can automatically perform several operations in order to reduce the effort needed to decide which operators are to be applied. By our implementation, the above questions can be adequately solved. With our analysis method, six legal cases are analyzed to demonstrate our implementation. (shrink)

Over the past decades, logicians interested in rational agency and intelligent interaction studied major components of these phenomena, such as knowledge, belief, and preference. In recent years, standard ‘static’ logics describing information states of agents have been generalized to dynamic logics describing actions and events that produce information, revise beliefs, or change preferences, as explicit parts of the logical system. Van Ditmarsch, van der Hoek & Kooi 2007, Baltag, van Ditmarsch & Moss 2008, van Benthem, to appear A, are up-to-date (...) accounts of this dynamic trend (the present paper follows Chapter 9 of the latter book). But in reality, concrete rational agency contains all these dynamic processes entangled. A concrete setting for this entanglement are games – and this paper is a survey of their interfaces with logic, both static and dynamic. Games are intriguing also since their analysis brings together two major streams, or tribal communities: ‘hard’ mathematical logics of computation, and ‘soft’ philosophical logics of propositional attitudes. Of course, this hard/soft distinction is spurious, and there is no natural border line between the two sources: it is their congenial mixture that makes current theories of agency so lively. (shrink)

Scientists collect evidence in order to confirm or falsify scientific theories. Unfortunately, scientific evidence may sometimes be false or deceiving and as a consequence lead individuals to believe in a false theory. By interaction between scientists, such false beliefs may spread through the entire community. There is currently a debate about the effect of various network configurations on the epistemic reliability of scientific communities. To contribute to this debate from a logical perspective, this paper introduces an epistemic logical framework of (...) observation, interaction and belief revision in scientific communities. The presented sound and complete system provides the formal tools for qualitative analysis of the social dynamics of scientific inquiry. Furthermore, this paper includes detailed suggestions for future applications of the framework. (shrink)