What is modal logic

The appendix to the chapter on dynamics supplements the chapter with an overview of dynamic epistemic logic: a branch of logic mainly developed in the decade after the first edition of this handbook was published. Dynamic epistemic logic is an extension of epistemic logic (the logic of knowledge), which focusses on information change, such as communication, usually involving more than one agent. The information of the agents includes information about each other's information, socalled higher-order information. The appendix consists of three parts. In the first part an example scenario is presented which can be captured by dynamic epistemic logic. The second part is a historical overview of the main approaches in dynamic epistemic logic is presented. The last part is a look towards the future which attempts to connect ideas from dynamic approaches to language with dynamic epistemic logic.

Dynamic Epistemic Logic (Update of Chapter 12)

We provide a retrospective of 25 years of the International Conference on AI and Law, which was first held in 1987. Fifty papers have been selected from the thirteen conferences and each of them is described in a short subsection individually written by one of the 24 authors. These subsections attempt to place the paper discussed in the context of the development of AI and Law, while often offering some personal reactions and reflections. As a whole, the subsections build into a history of the last quarter century of the field, and provide some insights into where it has come from, where it is now, and where it might go.

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A history of AI and Law in 50 papers: 25 years of the international conference on AI and Law

The vision of a Smart Electric Grid relies critically on substantial advances in intelligent decentralized control mechanisms. We propose a novel class of autonomous broker agents for retail electricity trading that can operate in a wide range of Smart Electricity Markets, and that are capable of deriving long-term, profit-maximizing policies. Our brokers use Reinforcement Learning with function approximation, they can accommodate arbitrary economic signals from their environments, and they learn efficiently over the large state spaces resulting from these signals. We show how feature selection and regularization can be leveraged to automatically optimize brokers for particular market conditions, and demonstrate the performance of our design in extensive experiments using real-world energy market data.

https://link.springer.com/content/pdf/10.1007%2Fs10994-013-5340-0.pdf

A reinforcement learning approach to autonomous decision-making in smart electricity markets

(b) ‡(KP & KyKP) AE ‡(KP & yKP) in the modal logic T, and so (c) ‡(KP & yKP) AE ^ in the minimal modal logic for ‡. Thus, a contradiction has been derived from the assumption P & yKP, and we have shown overall that P implies KP, making truth and knowledge equivalent. Proposed remedies for the paradox fall mainly into two kinds (cf. Brogaard and Salerno 2002; Wansing 2002). Some weaken the logic in the argument still further. This is like turning down the volume on your radio so as not to hear the bad news. You will not hear much good news either. Other remedies leave the logic untouched, but weaken the verification principle itself. This is like censoring the news: you hear things loud and clear, but they may not be so interesting. The proposal made below falls into the latter category, but using a different perspective from mere tinkering with proof rules or premises. We will emphasize positive reasons why VT can, and sometimes should, fail having to do with the ways in which we learn new information.

What One May Come to Know

Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence (IJCAI-11)

https://pure.rug.nl/ws/files/9749152/ARTINT2699.pdf

On the succinctness of some modal logics

Fitch showed that not every true proposition can be known in due time; in other words, that not every proposition is knowable. Moore showed that certain propositions cannot be consistently believed. A more recent dynamic phrasing of Moore-sentences is that not all propositions are known after their announcement, i.e., not every proposition is successful. Fitch's and Moore's results are related, as they equally apply to standard notions of knowledge and belief (S 5 and KD45, respec- tively). If we interpret 'successful' as 'known after its announcement' and 'knowable' as 'known after some announcement', successful implies knowable. Knowable does not imply successful: there is a proposition j that is not known after its announcement but there is another announcement after which j is known. We show that all propositions are knowable in the more general sense that for each proposition, it can become known or its negation can become known. We can get to know whether it is true: (Kj ⁄ K¬j). This result comes at a price. We cannot get to know whether the proposition was true. This restricts the philosophical relevance of interpreting 'knowable' as 'known after an announcement'.

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Everything is Knowable - How to Get to Know Whether a Proposition is True

The last decade has been witness to a rapid growth of interest in logics intended to support reasoning about the interactions between knowledge and action Typically, logics combining dynamic and epistemic components contain ontic actions (which change the state of the world, eg, switching a light on) or epistemic actions (which affect the information possessed by agents, eg, making an announcement) We introduce a new logic for reasoning about the interaction between knowledge and action, in which each agent in a system is assumed to perceive some subset of the overall set of Boolean variables in the system; these variables give rise to epistemic indistinguishability relations, in that two states are considered indistinguishable to an agent if all the variables visible to that agent have the same value in both states In the dynamic component of the logic, we introduce actions r(p, i) and c(p, i): the effect of r(p, i) is to reveal variable p to agent i; the effect of c(p, i) is to conceal p from i By using these dynamic operators, we can represent and reason about how the knowledge of agents changes when parts of their environment are concealed from them, or by revealing parts of their environment to them Our main technical result is a sound and complete axiomatisation for our logic

/pdf/a-logic-of-revelation-and-concealment-m3dgw8ayfu.pdf

A logic of revelation and concealment

Proving that one language is more succinct than another becomes harder when the underlying semantics is stronger. We propose to use Formula-Size Games (as put forward by Adler and Immerman, 2003), games that are played on two sets of models, and that directly link the length of play with the size of the formula. Using FSGs, we prove three succinctness results for m-dimensional modal logic: (1) In system Km, a notion of 'everybody knows' makes the resulting language exponentially more succinct for m > 1 (2) In S5m, the same language becomes more succinct for m > 3 and (3) Public Announcement Logic is exponentially more succinct than S5m, if m > 3. The latter settles an open problem raised by Lutz, 2006.

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Petar Iliev

Papers

Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence (IJCAI-11)

On the succinctness of some modal logics

Everything is Knowable - How to Get to Know Whether a Proposition is True

A logic of revelation and concealment

Succinctness of epistemic languages