A proposition is noncontingent, if it is necessarily true or it is necessarily false. In an epistemic context, ‘a proposition is noncontingent’ means that you know whether the proposition is true. In this paper, we study contingency logic with the noncontingency operator? but without the necessity operator 2. This logic is not a normal modal logic, because?→ is not valid. Contingency logic cannot define many usual frame properties, and its expressive power is weaker than that of basic modal logic over (...) classes of models without reflexivity. These features make axiomatizing contingency logics nontrivial, especially for the axiomatization over symmetric frames. In this paper, we axiomatize contingency logics over various frame classes using a novel method other than the methods provided in the literature, based on the ‘almost-definability’ schema AD proposed in our previous work. We also present extensions of contingency logic with dynamic operators. Finally, we compare our work to the related work in the fields of contingency logic and ignorance logic, where the two research communities have similar results but are apparently unaware of each other’s work. One goal of our paper is to bridge this gap. (shrink)

In this paper, we investigate the use of event models for automated planning. Event models are the action defining structures used to define a semantics for dynamic epistemic logic. Using event models, two issues in planning can be addressed: Partial observability of the environment and knowledge. In planning, partial observability gives rise to an uncertainty about the world. For single-agent domains, this uncertainty can come from incomplete knowledge of the starting situation and from the nondeterminism of actions. In multi-agent domains, (...) an additional uncertainty arises from the fact that other agents can act in the world, causing changes that are not instigated by the agent itself. For an agent to successfully construct and execute plans in an uncertain environment, the most widely used formalism in the literature on automated planning is “belief states”: sets of different alternatives for the current state of the world. Epistemic logic is a significantly more expressive and theoretically better founded method for representing knowledge and ignorance about the world. Further, epistemic logic allows for planning according to the knowledge (and iterated knowledge) of other agents, allowing the specification of a more complex class of planning domains, than those simply concerned with simple facts about the world. We show how to model multi-agent planning problems using Kripke-models for representing world states, and event models for representing actions. Our mechanism makes use of slight modifications to these concepts, in order to model the internal view of agents, rather than that of an external observer. We define a type of planning domain called epistemic planning domains, a generalisation of classical planning domains, and show how epistemic planning can successfully deal with partial observability, nondeterminism, knowledge and multiple agents. Finally, we show epistemic planning to be decidable in the single-agent case, but only semi-decidable in the multi-agent case. (shrink)

We model the forgetting of propositional variables in a modal logical context where agents become ignorant and are aware of each others’ or their own resulting ignorance. The resulting logic is sound and complete. It can be compared to variable-forgetting as abstraction from information, wherein agents become unaware of certain variables: by employing elementary results for bisimulation, it follows that beliefs not involving the forgotten atom(s) remain true.

We model the forgetting of propositional variables in a modal logical context where agents become ignorant and are aware of each others’ or their own resulting ignorance. The resulting logic is sound and complete. It can be compared to variable-forgetting as abstraction from information, wherein agents become unaware of certain variables: by employing elementary results for bisimulation, it follows that beliefs not involving the forgotten atom(s) remain true.

In public announcement logic it is assumed that all agents pay attention to the announcement. Weaker observational conditions can be modelled in action model logic. In this work, we propose a version of public announcement logic wherein it is encoded in the states of the epistemic model which agents pay attention to the announcement. This logic is called attention-based announcement logic. We give an axiomatization of the logic and prove that complexity of satisfiability is the same as that of public (...) announcement logic, and therefore lower than that of action model logic. An attention-based announcement can also be described as an action model. We extend our logic by integrating attention change. Finally, we add the notion of common belief to the language, we exploit this to formalize the concept of joint attention, that has been widely discussed in the philosophical and cognitive science literature, and we provide a corresponding axiomatization. This axiomatization also employs the auxiliary notion of attention-based relativized common belief. (shrink)

We analyze a recent trend in epistemic logic which consists in studying construction of knowledge from the agents’ observational abilities. It is based on the intuition that an agent’s knowledge comes from three possible sources: her observations, communication with other agents, and inference. The approaches mainly focus on the former two and suppose that the object of observations are propositional variables and that agents learn from public announcements. This allows to model knowledge in a more compact and intuitive way than (...) with Hintikka’s semantics. However, the semantics that one can find in the literature come with some counter-intuitive validities such as common knowledge of visibilities or the knowledge operator distributing over disjunctions. We propose a solution of each of these two issues and illustrate them with well-known toy examples of epistemic logic. (shrink)

In public announcement logic it is assumed that all agents pay attention to the announcement. Weaker observational conditions can be modelled in action model logic. In this work, we propose a version of public announcement logic wherein it is encoded in the states of the epistemic model which agents pay attention to the announcement. This logic is called attention-based announcement logic. We give an axiomatization of the logic and prove that complexity of satisfiability is the same as that of public (...) announcement logic, and therefore lower than that of action model logic. An attention-based announcement can also be described as an action model. We extend our logic by integrating attention change. Finally, we add the notion of common belief to the language, we exploit this to formalize the concept of joint attention, that has been widely discussed in the philosophical and cognitive science literature, and we provide a corresponding axiomatization. This axiomatization also employs the auxiliary notion of attention-based relativized common belief. (shrink)

This chapter provides a brief introduction to propositional epistemic logic and its applications to epistemology. No previous exposure to epistemic logic is assumed. Epistemic-logical topics discussed include the language and semantics of basic epistemic logic, multi-agent epistemic logic, combined epistemic-doxastic logic, and a glimpse of dynamic epistemic logic. Epistemological topics discussed include Moore-paradoxical phenomena, the surprise exam paradox, logical omniscience and epistemic closure, formalized theories of knowledge, debates about higher-order knowledge, and issues of knowability raised by Fitch’s paradox. The references (...) and recommended readings provide gateways for further exploration. (shrink)