Between Facts and Norms: Contributions to a Discourse Theory of Law and Democracy

What is modal logic

THE distinguished author of “Why the Mind has a Body” is one of the most original and fearless philosophers of the school which labels itself “Critical Realism.” The present short volume, though it is written with all the freshness and vigour we associate with his work, is frankly disappointing. This is because, instead of stating his theory and advancing his argument from his own point of view, he develops it by means of a rather tedious criticism of Mr. Bradley, Mr. Russell, M. Bergson, and other philosophers. His own theory rests, he tells us, on two assumptions: first, that there is a world; second, that there is a self. Nature, he is convinced, is really what it appears to be, and the self is an outgrowth of nature, though in some of its manifestations rising above it. It seems to us that the primary difficulty of such assumptions is that they conflict with physical science and are irreconcilable with the scientific concepts of nature and self. In philosophy, assumptions in the premises have a curious knack of turning up in the conclusion so that no real progress can be made, but they are otherwise harmless enough. Scientific reality is a question of real metaphysical interest at the present time, but it finds no place in this theory, which is mainly concerned with the question of sense-data.A Theory of Knowledge.Charles AugustusStrongBy. Pp. xii+103. (London, Bombay and Sydney: Constable and Co., Ltd., 1923.) 6s. net.

Theory of Knowledge

This book develops a new view of logic as a theory of information-driven agency and intelligent interaction between many agents - with conversation, argumentation and games as guiding examples. It provides one uniform account of dynamic logics for acts of inference, observation, questions and communication, that can handle both update of knowledge and revision of beliefs. It then extends the dynamic style of analysis to include changing preferences and goals, temporal processes, group action and strategic interaction in games. Throughout, the book develops a mathematical theory unifying all these systems, and positioning them at the interface of logic, philosophy, computer science and game theory. A series of further chapters explores repercussions of the 'dynamic stance' for these areas, as well as cognitive science.

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Logical Dynamics of Information and Interaction

Knowledge in Flux

Classical epistemic logic describes implicit knowledge of agents about facts and knowledge of other agents based on semantic information. The latter is produced by acts of observation or communication that are described well by dynamic epistemic logics. What these logics do not describe, however, is how significant information is also produced by acts of inference—and key axioms of the system merely postulate “deductive closure”. In this paper, we take the view that all information is produced by acts, and hence we also need a dynamic logic of inference steps showing what effort on the part of the agent makes a conclusion explicit knowledge. Strong omniscience properties of agents should be seen not as static idealizations, but as the result of dynamic processes that agents engage in. This raises two questions: (a) how to define suitable information states of agents and matching notions of explicit knowledge, (b) how to define natural processes over these states that generate new explicit knowledge. To this end, we use a static base from the existing awareness literature, extending it into a dynamic system that includes traditional acts of observation, but also adding and dropping formulas from the current ‘awareness’ set. We give a completeness theorem, and we show how this dynamics updates explicit knowledge. Then we extend our approach to multi-agent scenarios where awareness changes may happen privately. Finally, we mention further directions and related approaches. Our contribution can be seen as a ‘dynamification’ of existing awareness logics.

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The dynamics of awareness

Today, logic is taught to a much broader academic audience than just the traditional target group of mathematicians and philosophers. Logic in Action provides modern open courseware, in the form of a freely accessible animated e-book, as an extensive teaching tool for this growing student population. The project stresses the methodological merits of logic for a wide range of interdisciplinary sciences.

Logic in action

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, seman- tics and a complete axiom system; we discuss similarities and differences with other approaches and mention how the work can be extended.

Inference and update

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.

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Dynamic Epistemic Logic for Implicit and Explicit Beliefs

By moving from a suggestive example, the paper analyzes how information flows among agents involved in a deliberation. By deliberating, agents become aware of details, draw the attention of the group to some issues, perform inferences and announce what they know. The proposed framework--which builds on the paradigm of dynamic logic-- captures how, during a deliberation, information results from stepwise multi-agent interaction.

Fernando R. Velázquez-Quesada

Papers

The dynamics of awareness

Logic in action

Inference and update

Dynamic Epistemic Logic for Implicit and Explicit Beliefs

Twelve angry men: a study on the fine-grain of announcements