We provide a Kripke semantics for a STIT logic with the "next" operator. As the atemporal group STIT is undecidable and unaxiomatizable, we are interested in strict fragments of atemporal group STIT. First we prove that the satisfiability problem of a formula of the fragment made up of individual coalitions plus the grand coalition is also NEXPTIME-complete. We then generalize this result to a fragment where coalitions are in a given lattice. We also prove that if we restrict the language (...) to nested coalitions the satisfiability problem is NP-complete if the number of agents is fixed and PSPACE-complete if the number of agents is variable. Finally we embed individual STIT with the "next" operator into a fragment of atemporal group STIT. (shrink)

We introduce and study a PDL-style logic for reasoning about protocols, or plans, under imperfect information. Our paper touches on a number of issues surrounding the relationship between an agent’s abilities, available choices, and information in an interactive situation. The main question we address is under what circumstances can the agent commit to a protocol or plan, and what can she achieve by doing so?

In this paper, we give an alternative semantics to the non-normal logic of knowing how proposed by Fervari et al., based on a class of Kripke neighborhood models with both the epistemic relations and neighborhood structures. This alternative semantics is inspired by the same quantifier alternation pattern of ∃∀\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\exists \forall $$\end{document} in the semantics of the know-how modality and the neighborhood semantics for the standard modality. We show that this new semantics (...) is equivalent to the original Kripke semantics in terms of the validities. A key result is a representation theorem showing that the more abstract Kripke neighborhood models can be represented by the concrete Kripke models with action transitions modulo the valid formulas. We prove the completeness of the logic for the neighborhood semantics. The neighborhood semantics can be adapted to other variants of logics of knowing how. It provides us a powerful technical tool to study these logics while preserving the basic semantic intuition. (shrink)

In this paper, we propose a dynamic epistemic framework to capture the knowledge evolution in multi-agent systems where agents are not able to observe. We formalize multi-agent conformant planning with group knowledge, and reduce planning problems to model checking problems. We prove that multi-agent conformant planning with group knowledge is Pspace -complete on the size of dynamic epistemic models. We also consider the alternative Kripke semantics, and show that for each Kripke model with perfect recall and no miracles, there is (...) an equivalent dynamic epistemic model and vice versa. (shrink)

We present a variant of ATL with incomplete information which includes the distributed knowledge operators corresponding to synchronous action and perfect recall. The cooperation modalities assume the use the distributed knowledge of coalitions and accordingly refer to perfect recall incomplete information strategies. We propose a model-checking algorithm for the logic. It is based on techniques for games with imperfect information and partially observable objectives, and involves deciding emptiness for automata on infinite trees. We also propose an axiomatic system and prove (...) its completeness for a rather expressive subset. As for the constructs left outside this completely axiomatised subset, we present axioms by which they can be defined in the subset on the class of models in which every state has finitely many successors and give a complete axiomatisation for a “flat” subset of the logic with these constructs included. (shrink)

Dynamic epistemic logic describes the possible information-changing actions available to individual agents, and their knowledge pre-and post conditions. For example, public announcement logic describes actions in the form of public, truthful announcements. However, little research so far has considered describing and analysing rational choice between such actions, i.e., predicting what rational self-interested agents actually will or should do. Since the outcome of information exchange ultimately depends on the actions chosen by all the agents in the system, and assuming that agents (...) have preferences over such outcomes, this is a game theoretic scenario. This is, in our opinion, an interesting general research direction, combining logic and game theory in the study of rational information exchange. In this article we take some first steps in this direction: we consider the case where available actions are public announcements, and where each agent has a (typically epistemic) goal formula that she would like to become true. What will each agent announce? The truth of the goal formula also depends on the announcements made by other agents. We analyse such public announcement games. (shrink)

We study the logic of strategic ability of coalitions of agents with bounded memory by introducing Alternating-time Temporal Logic with Bounded Memory (ATLBM), a variant of Alternating-time Temporal Logic (ATL). ATLBM accounts for two main consequences of the assumption that agents have bounded memory. First, an agent can only remember a strategy that specifies actions in a bounded number of different circumstances. While the ATL-formula means that coalition C has a joint strategy which will make φ true forever, the ATLBM-formula (...) means that C has a joint strategy which for each agent in C specifies what to do in no more than n different circumstances and which will make φ true forever. Second, an agent has bounded recall—a strategy can only take the last m states of the system into account. We use the logic to study the interaction between strategic ability, bounded number of decisions, bounded recall and incomplete information. We discuss the logical properties and expressiveness of ATLBM, and its relationship to ATL. We show that ATLBM can express properties of strategic ability under bounded memory which cannot be expressed in ATL. (shrink)

This paper explores the analysis of ability, where ability is to be understood in the epistemic sense—in contrast to what might be called a causal sense. There are plenty of cases where an agent is able to perform an action that guarantees a given result even though she does not know which of her actions guarantees that result. Such an agent possesses the causal ability but lacks the epistemic ability. The standard analysis of such epistemic abilities relies on the notion (...) of action types—as opposed to action tokens—and then posits that an agent has the epistemic ability to do something if and only if there is an action type available to her that she knows guarantees it. We show that these action types are not needed: we present a formalism without action types that can simulate analyzes of epistemic ability that rely on action types. Our formalism is a standard epistemic extension of the theory of “seeing to it that”, which arose from a modal tradition in the logic of action. (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)

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 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)