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)

In this paper, we present several extensions of epistemic logic with update operators modelling public information change. Next to the well-known public announcement operators, we also study public substitution operators. We prove many of the results regarding expressivity and completeness using so-called reduction axioms. We develop a general method for using reduction axioms and apply it to the logics at hand.

In this paper we investigate a logic for modelling individual and collective acceptances that is called acceptance logic. The logic has formulae of the form $A_{Gx} \phi $ reading 'if the agents in the set of agents G identify themselves with institution x then they together accept that φ'. We extend acceptance logic by two kinds of dynamic modal operators. The first kind are public announcements of the form x!ψ, meaning that the agents learn that ψ is the case in (...) context x. Formulae of the form [x!ψ]φ mean that φ is the case after every possible occurrence of the event x!ψ. Semantically, public announcements diminish the space of possible worlds accepted by agents and sets of agents. The announcement of ψ in context x makes all ¬ψ-Worlds inaccessible to the agents in such context. In this logic, if the set of accessible worlds of G in context x is empty, then the agents in G are not functioning as members of x, they do not identify themselves with x. In such a situation the agents in G may have the possibility to join x. To model this we introduce here a second kind of dynamic modal operator of acceptance shifting of the form G:x↑ψ. The latter means that the agents in G shift (change) their acceptances in order to accept ψ in context x. Semantically, they make ψ-worlds accessible to G in the context x, which means that, after such operation, G is functioning as member of x (unless there are no ψ-worlds). We show that the resulting logic has a complete axiomatization in terms of reduction axioms for both dynamic operators. In the paper we also show how the logic of acceptance and its dynamic extension can be used to model some interesting aspects of judgement aggregation. In particular, we apply our logic of acceptance to a classical scenario in judgment aggregation, the so-called 'doctrinal paradox' or 'discursive dilemma' (Pettit, Philosophical Issues 11: 268-299, 2001; Kornhauser and Sager, Yale Law Journal 96: 82-117, 1986). (shrink)

While dynamic epistemic logics with common knowledge have been extensively studied, dynamic epistemic logics with distributed knowledge have so far received far less attention. In this paper we study extensions of public announcement logic ( $\mathcal{PAL }$ ) with distributed knowledge, in particular their expressivity, axiomatisations and complexity. $\mathcal{PAL }$ extended only with distributed knowledge is not more expressive than standard epistemic logic with distributed knowledge. Our focus is therefore on $\mathcal{PACD }$ , the result of adding both common and (...) distributed knowledge to $\mathcal{PAL }$ , which is more expressive than each of its component logics. We introduce an axiomatisation of $\mathcal{PACD }$ , which is not surprising: it is the combination of well-known axioms. The completeness proof, however, is not trivial, and requires novel combinations and extensions of techniques for dealing with $S5$ knowledge, distributed knowledge, common knowledge and public announcements at the same time. We furthermore show that $\mathcal{PACD }$ is decidable, more precisely that it is $\textsc {exptime}$ -complete. This result also carries over to $\mathcal{S 5\mathcal CD }$ with common and distributed knowledge operators for all coalitions (and not only the grand coalition). Finally, we propose a notion of a trans-bisimulation to generalise certain results and give deeper insight into the proofs. (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)

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)

In this paper, illocutionary acts of commanding will be differentiated from perlocutionary acts that affect preferences of addressees in a new dynamic logic which combines the preference upgrade introduced in DEUL (dynamic epistemic upgrade logic) by van Benthem and Liu with the deontic update introduced in ECL II (eliminative command logic II) by Yamada. The resulting logic will incorporate J. L. Austin’s distinction between illocutionary acts as acts having mere conventional effects and perlocutionary acts as acts having real effects upon (...) attitudes and actions of agents, and help us understand why saying so can make it so in explicit performative utterances. We will also discuss how acts of commanding give rise to so-called “deontic dilemmas” and how we can accommodate most deontic dilemmas without triggering so-called “deontic explosion”. (shrink)

Current dynamic epistemic logics often become cumbersome and opaque when common knowledge is added for groups of agents. Still, postconditions regarding common knowledge express the essence of what communication achieves. We present some methods that yield so-called reduction axioms for common knowledge. We investigate the expressive power of public announcement logic with relativized common knowledge, and present reduction axioms that give a detailed account of the dynamics of common knowledge in some major communication types.

We look at two fundamental logical processes, often intertwined in planning and problem solving: inference and update. Inference is an internal process with which we uncover what is implicit in the information we already have. Update, on the other hand, is produced by external communication, usually in the form of announcements and in general in the form of observations, giving us information that might not have been available (even implicitly) before. Both processes have received attention from the logic community, usually (...) separately. In this work, we develop a logical language that allows us to describe them together. We present syntax, semantics and a complete axiom system; we discuss similarities and differences with other approaches and mention how the work can be extended. (shrink)

This paper is divided in five sections. Section 11.1 sketches the history of the distinction between speech act with negative content and negated speech act, and gives a general dynamic interpretation for negated speech act. “Downdate semantics” for AGM contraction is introduced in Section 11.2. Relying on semantically interpreted contraction, Section 11.3 develops the dynamic semantics for constative and directive speech acts, and their external negations. The expressive completeness for the formal variants of natural language utterances, none of which is (...) a retraction, has been proved in Section 11.4. The last section gives a laconic answer to the question posed in the title of the paper. (shrink)