Format

Presentations will be in 10 one-hour slots, papers available on website beforehand, we all read the material beforehand, actual presentation half an hour + half an hour discussion. In addition to the above, some presentations will be on current research by Stanford people.

Negotiation about topics and slots is still in progress. Your teacher will be a consultant before your presentation + your discussion manager. I will also fill any remaining slots.

Date	Topic	Reading
4/30	Opening session: Johan gave an overview of the program of "logical dynamics", based on his new book on logic of agency and intelligent interaction.
5/7	GAMES Alistair, Game equivalence Johan, Game solution procedures (brief synopsis)	Alistair's Handout (pdf) Alistair's Notes (pdf)
5/14	BEYOND INFORMATION Eric, From Belief Revision to Intention Revision Tomohiro, Taking Processes Seriously: Dynamic Epistemic Logics with Protocols (brief synopsis)	Eric's handout will be provided at the meeting. Merging Frameworks for Interaction (JPL article) (pdf) Tomohiro's Thesis (pdf) Article in progress (with Eric) (pdf)
5/21	DIALOGUE Thomas, Questions Jesse, Dialogue logics (brief synopsis)	Jesse's Handout (pdf)
5/28	PROOF DYNAMICS Alexei, Inference, omniscience, and update Josh and Darko, Three global applications of complex systems in philosophy: logic, language, and metaethics (brief synopsis)	Alexei's Handout (pdf)
6/4	TRUST Wes, Testimonial dynamics Johan, Concluding Remarks (brief synopsis)	Wes' Handout (pdf)

Week 2: Logic and Games

Alistair gave a presentation on game equivalence: handout obtainable via tokyodrifter@gmail.com.

A few additional notes from Johan (the whole session was eventually devoted  to discussing game equivalences):

* There seem to be four main approaches to defining an invariance relation between structures:

   (a) direct structure analogy (isomorphism, bisimulation, like in geometry or process theories),
   (b) via assigning 'normal forms',
   (c) via a sequence of small intuitive transformations, and closing off (like in mathematical knot theory),
   (d) having the same theory in some language expressing the relevant properties (maybe the 'logic way').

All are probably equivalent at some abstract level, but it is of interest to see how they relate in special cases.

* Normal form hierarchy for games: same strategic form, same set-theoretic form, same power sets?

In the latter case, my 2002 paper 'Extensive Games as Process Models' (Journal of Logic, Language and Information 11, 289–313) showed how power equivalence can also be described from the viewpoint of a matching modal language with 'forcing modalities', and a direct structure analogy: 'power bisimulation'. Bonanno's set-theoretic form, discussed by Alistair, seems a richer temporal forcing structure, that would match with a language with forcing modalities that can be stacked in a meaningful way.

* One way of approaching the general equivalence issue: do not start abstractly, but look at a concrete community using games, say logicians, and ask which equivalence notion they are implicitly using. My claim: most 'logic games' are based on (very coarse) power equivalence - whether that is a good thing or not. But of course, other equivalence may make sense for other purposes.

* Then comes additional structure as in Alistair's 'causal-epistemic games', where assumptions about agents inhabiting these games become crucial.

   (a) Add preferences: when are 'inhabited games' containing players equivalent, when we make assumptions about these players of rationality, trembling-hand performance, etc.?
   (b) Add knowledge,
   (c) Add belief?

The issue seems to be how to formulate intuitions about equivalence given the game structure plus the agent types. Maybe start with simple scenarios, separating out special cases: which games are equivalent for memory-restricted agents, for absent-minded agents, etc.? Or should we not start at the structural level at all, but rather with the optimal language for the reasoning that we want to capture about these scenarios?

* A few points about understanding the 'extra structure' that we need, in between bare games and baroque type spaces. The term 'knowledge' often equivocates here between knowledge about the future of the game (this makes sense even in otherwise 'perfect information' games), and knowledge based on partial observation, as in imperfect information games. Also, beliefs might be about available actions, but also about which action a player will take, even though others are available. Ideas about attractive notions of 'game equivalence' will again depend
very much on specifying what is meant.

* Would the chosen equivalence levels support good game theory, say, theorems generalizing classical ones by Nash, von Neuman?

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Week 3: Beyond Information

Synopsis of Eric's Presentation

While there is an extensive literature developing logical models to reason about informational attitudes (eg., belief, knowledge, certainty) in a dynamic environment, other mental states have received much less attention. (A notable exception here is work on logics of preferences and preference change). However, this is changing with recent articles developing a theory of intention revision (see two recent articles: Towards a theory of intention revision by van der Hoek, Jamroga and Wooldridge and A logic of intention and attempt by Lorini and Herzig. These papers take as a starting point logical frameworks derived from Cohen and Levesque's seminal paper aimed at formalizing Bratman's planning theory of intention. We (Thomas, Yoav and myself) develop a logic for reasoning about an agent's belief and intentions and how they may change over time. In the process we will reexamine a number of foundational issues surrounding so-called BDI-logics. See a recent paper by Yoav for a non-technical introduction to some of the key ideas that will drive our analysis.

Synopsis of Tomohiro's Presentation

See Tomohiro's dissertation.

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Week 4: Dialogue

Thomas introduced recent work on inquisitive semantics including new work by Johan and Stefan on modeling questions in DEL. Jesse gave an overview of some of the literature on dialogues.

Synopsis of Thomas' Presentation
In this session we looked at two recent logics of questions: Inquisitive Logic, a current project of J. Groenendijk and students; and forthcoming work by J. van Benthem and S. Minica incorporating questions into Dynamic Epistemic Logic. At the end of the talk, we gestured toward a way of combining the two frameworks, namely by labeling the dynamic modalities with formulas of inquisitive logic, thereby including a wide range of "issue raising" and "resolving" operations, but keeping the underlying epistemic logic classical.
See here for a recent paper explaining Groenendijk's inquisitive semantics.

Synopsis of Jesse's Presentation
Conversations, debates, and dialogues are a natural target for study using the tools and methods of logical dynamics. One formalization of dialogues, due to Lorenzen, is one of the earliest examples of game- theoretic semantics. The field seems to have enjoyed little attention after the fundamental work of Lorenzen and his student Lorenz, but these days it appears to be enjoying a small renaissaince in various quarters (such as in France under the direction of S. Rahman, and as a project in the LogICCC framework now underway in the Nethlands, Germany, and Portugal). Lorenzen's original motivations were essentially connected with intuitionistic logic, and one can get that impression quickly when looking at how the so-called particle rules (which govern how the players can attack or defend statements based on their logical form) and the procedural rules (which govern overall how the dialogue game is to be played) permit the Opponent to win when the Proponent lays down an instance of the double negation law or the principle of the excluded middle. Indeed, theorems about Lorenzen dialogues show how Proponent has a winning strategy in the dialogue game for a formula A iff A is intuitionistically valid; one has analogous theorems for various logics (provided, of course, that the rules of the dialogue game are modified in a suitable way). Further directions for research involve extensions to the dialogues so that knowledge and belief are explicitly part of the discussion, using dialogues as a way to understand mathematically rigorous argumentation and formal prof checking, and as a tool for possibly analyzing zero-knowledge proofs.

Synopsis of Audrey's Presentation
Fitch's Paradox of knowability presents a problem to the Verificationist Thesis that every truth is knowable. More specifically, when we take an instance of a Moore sentence such as "p is true, but you don't know it", and substitute it into the schema, we find ourselves with the absurd result that if p is true, then it is known. Some work by van Benthem has already explored the connections between this paradox and Dynamic Epistemic Logic (DEL), concentrating on the manner in which truths come to be known. Some recent extensions of DEL which incorporate past temporal operators have discussed the extent to which such a formalism can express propositions about learning, and about what is learned by the announcement of a formula. Applying these insights to Fitch's Paradox allows us to see the value of a temporal solution to the paradox, where such a solution has been considered in the literature, but rejected.

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Week 5: Proof Dynamics

Synopsis of Alexei's Presentation

See the handout and the two papers discussed: Merging observation and access in dynamic logic by Johan van Benthem and Inference and update by Fernando Velázquez-Quesada

Three global applications of complex systems in philosophy: logic, language, and metaethics
Josh Shepherd and Darko Sarenac "Robur gregi in lupo, robur lupo in grege."


In this talk, we explore some of the consequences of viewing ourselves as complex dynamical systems. We argue that taken seriously the "dynamic turn," as Johan van Benthem has called it, really enables us to see some old and difficult philosophical problems in a genuinely new light. Problems that seem marred with unpleasant dichotomies under the standard static philosophical lens, we will claim, open up to a full range of exciting new questions once examined under the keen light of the dynamical lens.

We first look at natural language and the role it is best seen as playing in the cooperative behavior of a group of dynamical systems. We will argue that utterances are coupled with their receivers or interpreters and the proper way of understanding them is in the light of this coupled relationship. The signaler is ‘tuned’ into and by this coupling she possesses not just the capacity to use language in an abstract setting, but also – and perhaps fundamentally – possesses a subtle social ability of predicting the way in which an utterance will affect an audience in a given situation. Thus, in a sense the role of language is to produce dynamical coupling in a group, that is, to turn a group into a single cooperating dynamical system.

Without denying the importance of the years of static research, this approach raises a new set of questions about language and language use. We simply claim that the picture is not complete until the temporal, spatial, and resource bounded properties of language are fully understood. As humans, we often say things the way we do because the mode we use is the most efficient and most direct in the given context. Language use is expensive, we will argue, and we are not only acutely trained to communicate messages successfully, but we are also trained to communicate them with minimal use of resources and time. To achieve this, we freely use all the spatial structure accessible to all agents involved.

This view of language seems to have direct consequences to logic research. It emphasizes efficiency, spatial connectedness of utterances, and perhaps most importantly, time. All of these properties have been explored logically, of course. What we propose is a systematic treatment and classification of logics with respect to such properties. Such a systematic view opens up further avenues of research.

Finally, we suggest that looking at moral agents and moral communities as complex dynamical systems affords a new perspective on certain metaethical issues. More specifically, we argue that a dynamics approach usefully addresses concerns and problems arising from the debate between moral particularists and generalists. Particularists emphasize the role of context and claim that moral principles cannot fully codify the moral domain; generalists complain that particularism renders the normative landscape shapeless. We think that a dynamics approach – which adds, predictably, the dimensions of time, space, environmental parameters, and an emphasis that agents are coupled with their environments to the problem space – can help explain the role of context, and thus the failure of traditional moral principles, as well as provide the normative landscape with some structure. Drawing on the dynamic approach to language sketched earlier, we argue that one upshot of a dynamics approach to ethics might be a fuller explanation of the role of moral discourse in moral development and problem solving. One question which we seek to treat is: how does moral language interact with moral behavioral patterns? We are optimistic that a dynamics approach can shed light on moral agents’ abilities to recognize interesting social patterns, and we would like to understand how such pattern recognition enables the further evolution of complex social and moral behaviors. Further, we seek to apply some tools of dynamic systems theory to models of cooperation, in order to study the relationship between and problems arising from individualistic moral goals and those moral goals which require cooperation, interaction, altruism, and so on. This move obviously makes the space more complex and one needs to be careful in choosing the appropriate variables to capture the cooperative dynamics, its advantages, and optimal implementations.

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Week 6: Trust & Concluding Remarks

Thomas introduced recent work on inquisitive semantics including new work by Johan and Stefan on modeling questions in DEL. Jesse gave an overview of some of the literature on dialogues.

Synopsis of Wes' Presentation

See the draft of a working paper by Wes.

Concluding Remarks (Johan)
We made quite some progress in one month, and many comments by colleagues at the workshop and its aftermath were really helpful: http://ai.stanford.edu/~epacuit/lmh-spr09/programme.html

• PAL, though well-researched, still has that open question about decidability or axiomatizablitiy of the set of its schematic validities. These are the principles that are 'generically' valid.
• Logics of inference (Alexei): could we also do them more directly using ideas about proof structure, such as Artemov's LP operations?
• Dynamic logics of questions: suddenly we have two approaches, classical explicit DEL-style, and implicit intuitionistic 'inquisitive semantics'. Thomas had ideas about merging them: let's see.
• Beliefs: one somewhat urgent open problem, how to do reduction axioms for common belief that form in groups?
• Intentions: let's wait to hear from Eric, Thomas, and Yoav.
• Mid-term scenarios 1: games. Tomohiro and Jesse are looking at combinations of dialogue games and DEL observations.
• Mid-term scenarios 2: Wes' testimonial logic is another case. Lots of new questions (e.g., how to axiomatize trust defined in terms of conditional beliefs), and might be applicable to concrete legal scenarios. Crichton's paradox, "Trust nobody"
• Long-term scenarios 1: like Tomohiro's protocols. I plan to write a little pilot paper with Kelly on how epistemic-doxastic temporal logic might serve as a sort of qualitative approximation to formal learning theory in its full algorithmic guise. We'll see.
• Long-term scenarios 2: how dynamic logics of local updates interface with dynamical systems analysis of long-term behavior, as in evolutionary game theory. (Darko Sarenac, Brian Skyrms)
• New areas/challenges to logics of rational agency that have been suggested by George Smith, Sol and others: case studies in Law, History of Science, (Philosophy of) Mathematics.

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Specific Reading Material

We will be adding papers on concrete topics as we proceed.

Background Reading Material

Below is some additional reading material related to some of the topics we will discuss in this workshop.

Further Links

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Consider going to LORI-II Chongqing, the second Chinese conference on Logic, Rationality and Interaction, October 2009, where the Chinese community in this area will meet with their counterparts worldwide!