Proper epistemic knowledge bases (PEKBs) are syntactic knowledge bases that use multi-agent epistemic logic to represent nested multi-agent knowledge and belief. PEKBs have certain syntactic restrictions that lead to desirable computational properties; primarily, a PEKB is a conjunction of modal literals, and therefore contains no disjunction. Sound entailment can be checked in polynomial time,...

Weitzman’s [13] search model requires that, conditional on stopping, theagent only takes boxes which have already been inspected. We relax thisassumption and allow the agent to take any uninspected box without in-specting its contents when stopping. Thus, each uninspected box is nowa potential outside option. This introduces a new trade-off: every timethe agent inspects a bo...

The traditional view of skill acquisition is that it can be explained by a gradual transition from behavior based on declarative rules in the form of examples and instructions towards general knowledge represented by procedural rules. This view is challenged by Logan’s instance theory, which specifies that skill acquisition can be explained by the accumulation of examples or instances of the sk...

Predicate detection is an important problem in testing and debugging distributed programs. Cooper and Marzullo introduced two modalities possibly and definitely as a solution to this problem. Given a predicate p, a computation satisfies possibly : p if p is true for some global state in the computation. A computation satisfies definitely : p if all paths from the initial to the final global sta...

In Bird 2001 I argued that a law that might seem to many to be contingent is in fact necessary. In short the argument is this. Given the existence of salt and water, Coulomb’s law of electrostatic attraction is sufficient to make the former dissolve in the latter. So any possible world in which salt failed to dissolve in water would be one in which Coulomb’s law is false. However, it is also th...

It has been well argued that correlation does not imply causation. Is the converse true: does non-correlation imply non-causation, or more plainly, does causation imply correlation? Here we argue that this is a useful intuition of the semantic essence of the faithfulness assumption of causal graphs. Although the statement is intuitively reasonable, it is not categorically true (but it is true w...

For a simple model of a stock, whose stock price is a geometric Brownian motion in which the drift rate changes back and forth between positive and negative values, optimal selling times are computed. An infinite optimal selling time meaning you should just hold the stock.