We construct logical languages which allow one to represent a variety of possible types of changes affecting the information states of agents in a multi-agent setting. We formalize these changes by defining a notion of epistemic program. The languages are two-sorted sets that contain not only sentences but also actions or programs. This is as in dynamic logic, and indeed our languages are not significantly more complicated than dynamic logics. But the semantics is more complicated. In general, the semantics of (...) an epistemic program is what we call aprogram model. This is a Kripke model of ‘actions’,representing the agents' uncertainty about the current action in a similar way that Kripke models of ‘states’ are commonly used in epistemic logic to represent the agents' uncertainty about the current state of the system. Program models induce changes affecting agents' information, which we represent as changes of the state model, called epistemic updates. Formally, an update consists of two operations: the first is called the update map, and it takes every state model to another state model, called the updated model; the second gives, for each input state model, a transition relation between the states of that model and the states of the updated model. Each variety of epistemic actions, such as public announcements or completely private announcements to groups, gives what we call an action signature, and then each family of action signatures gives a logical language. The construction of these languages is the main topic of this paper. We also mention the systems that capture the valid sentences of our logics. But we defer to a separate paper the completeness proof. (shrink)

We describe a general logical framework, Justification Logic, for reasoning about epistemic justification. Justification Logic is based on classical propositional logic augmented by justification assertions t: F that read t is a justification for F. Justification Logic absorbs basic principles originating from both mainstream epistemology and the mathematical theory of proofs. It contributes to the studies of the well-known Justified True Belief vs. Knowledge problem. We state a general Correspondence Theorem showing that behind each epistemic modal logic, there is a (...) robust system of justifications. This renders a new, evidence-based foundation for epistemic logic. As a case study, we offer a resolution of the GoldmanRed Barns in Justification Logic. Furthermore, we formalize the well-known Gettier example and reveal hidden assumptions and redundancies in Gettier’s reasoning. (shrink)

This paper adds evidence structure to standard models of belief, in the form of families of sets of worlds. We show how these more fine-grained models support natural actions of “evidence management”, ranging from update with external new information to internal rearrangement. We show how this perspective leads to new richer languages for existing neighborhood semantics for modal logic. Our main results are relative completeness theorems for the resulting dynamic logic of evidence.

Epistemic logic with its possible worlds semantic model is a powerful framework that allows us to represent an agent’s information not only about propositional facts, but also about her own information. Nevertheless, agents represented in this framework are logically omniscient: their information is closed under logical consequence. This property, useful in some applications, is an unrealistic idealisation in some others. Many proposals to solve this problem focus on weakening the properties of the agent’s information, but some authors have argued that (...) solutions of this kind are not completely adequate because they do not look at the heart of the matter: the actions that allow the agent to reach such omniscient state. Recent works have explored how acts of observation, inference, consideration and forgetting affect an agent’s implicit and explicit knowledge; the present work focuses on acts that affect an agent’s implicit and explicit beliefs. It starts by proposing a framework in which these two notions can be represented, and then it looks into their dynamics, first by reviewing the existing notion of belief revision, and then by introducing a rich framework for representing diverse forms of inference that involve both knowledge and beliefs. (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)

In the most popular logics combining knowledge and awareness, it is not possible to express statements about knowledge of unawareness such as “Ann knows that Bill is aware of something Ann is not aware of”—without using a stronger statement such as “Ann knows that Bill is aware of \(p\) and Ann is not aware of \(p\) ”, for some particular \(p\) . In Halpern and Rêgo (Proceedings of KR 2006; Games Econ Behav 67(2):503–525, 2009b) Halpern and Rêgo introduced a logic (...) in which such statements about knowledge of unawareness can be expressed. The logic extends the traditional framework with quantification over formulae, and is thus very expressive. As a consequence, it is not decidable. In this paper we introduce a decidable logic which can be used to reason about certain types of unawareness. Our logic extends the traditional framework with an operator expressing full awareness, i.e., the fact that an agent is aware of everything, and another operator expressing relative awareness, the fact that one agent is aware of everything another agent is aware of. The logic is less expressive than Halpern’s and Rêgo’s logic. It is, however, expressive enough to express all of the motivating examples in Halpern and Rêgo (Proceedings of KR 2006; Games Econ Behav 67(2):503–525, 2009b). In addition to proving that the logic is decidable and that its satisfiability problem is PSPACE-complete, we present an axiomatisation which we show is sound and complete. (shrink)