Schedule

Improvised.

Logic aims at truth, or more accurately, at deriving some truths from other truths. But why are we interested in truth in the first place? Surely one reason is that relying on truth makes it easier to make better choices.

One could think of Game theory as a tool which bridges the gap between logic and rationality.

Decision theory - or single agent game theory tells us when to make the best choice in a game of us against nature. But nature has no desire to further or frustrate our efforts. Things change when there are other agents involved. Then the best thing for us to do will depend on what they do. And they will think the same. Issues like common knowledge and rationalizability will then arise.

Also, each of us carries with us an envelope of beliefs, just as a tortoise carries its shell. Working with others, even when we have compatible ends, requires reconciling out respective shells.

"How different is she from me?" That will depend on whether we are choosing a movie to go to or whether we are choosing whether to vote Democrat or Republican. This insight makes it possible to define a logical distance between two people, in areas in which they can collaborate, and other areas where they will see each other as opponents if not as enemies. The resulting metric space, or collection of metric spaces can be a subject of mathematical investigation.

You are a triage nurse placing patients in a queue. You are packing

objects in bins and having decided which bin to choose for some object and you are attempting to minimize the number of bins, your are a martingale betting on a sequence wishing to win innite capital. You are in an online situation, and the kinds of combinatorial structures you must deal with can be thought of as online structures. Algorithmics for such structures are increasingly important, especially as data becomes so large that only a fragment of, for example, graphs representing data can be visible in the execution of an algorithm. Such algorithms and structures have a striking similarity to classical computability, particularly computable analysis.

I will report on some recent work giving general frameworks for algo-

rithmics on online structures. Currently there are many algorithms and no theortical basis for this area. Tractability of questions highlight the need

for approriate parameterizations such as early work [3, 4], and algorithmic

structure of the presentations such as in upcoming work of Askes [1].

[Abstract with references]

In 2003 Zia Movahed pointed to a passage of Avicenna, written probably in 1022, which Movahed claimed anticipated the modal formula of Barcan (that `For every $x$ necessarily $\phi$' entails `Necessarily for every $x$ $\phi$'), and its converse. Since 2003, examination of early logical writings of Avicenna has clarified how he understood entailments between modal sentences, using his own new temporal language to provide a kind of semantics. In the light of that, Movahed's claim for the Barcan formula needs some tidying up but is basically correct. But by his semantics Avicenna should not have claimed the converse Barcan formula and probably didn't claim it.

We describe the glorious history of Foundations, examine the less glorious present, and discuss the uncertain future, what it may be and what we would like it to be.

BIO:

Yuri Gurevich is Professor Emeritus at the University of Michigan. The last 20 years of his career he was a Principal Researcher at Microsoft.

Gurevich is a Guggenheim, ACM, EATCS, and AAAS Fellow, a foreign member of Academia Europaea, and Dr. Honoris Causa of a Belgian and a Russian universities.

The TPTP World is a well established infrastructure that supports research, development,

and deployment of Automated Theorem Proving (ATP) systems. This paper provides

an overview of the logic languages of the TPTP World, from classical first-order form,

through typed first-order form, up to typed higher-order form, and beyond to non-classical

forms. The logic languages are described in a non-technical way, and are illustrated with

examples using the TPTP language.

Since the early days of artificial intelligence, many logics have been explored as tools for knowledge representation and reasoning. Drawing on my own and others' research I will illustrate potential applications of logic, with a target of reasoning with nested beliefs in human-machine interaction scenarios.

(Joint work with Rolf Hennicker and Alexander Knapp) Epistemic logic is a classical tool for reasoning about knowledge in many applications. In this work we apply epistemic logic to ensemble computing, i.e. to distributed systems in which groups of computing entities collaborate to reach common goals. We introduce so-called epistemic ensembles that use shared knowledge for collaboration between agents. Collaboration is achieved by announcements of knowledge from one agent to others. For specifying epistemic ensemble behaviours we use formulas of dynamic epistemic logic with compound actions. Our semantics relies on an epistemic notion of ensemble transition systems as behavioural models. These transition systems describe control flow over epistemic states for expressing knowledge-based collaboration of agents. This is in contrast to dynamic epistemic logic where no control information can be captured. Specifications are implemented by epistemic processes that are composed in parallel to form ensemble realisations. We give a formal operational semantics of these processes, show that it is invariant under bisimulation, and provide a notion of correct realisation of an ensemble requirement specification. We illustrate our approach by examples.

Conditional statements are arguably central to reasoning, both in mathematical and philosophical logic. Yet their meanings show a wide range from informational entailment to proof rules, and from classical to nonmonotonic varieties. This history is far from over, and in this talk, I will discuss two more perspectives. One is that of conditionals as describing effects of dynamic actions of information update, which leads to new results about their role in dynamic-epistemic logics. A further perspective (arising from geometrizing update universes of information states) is one of conditionals as spatial operators, giving rise to new modal logics of spatial structures. In summary, following the thread of what conditionality means can take us all across logic.