Implicit diagnosticity in an information-buying task. How do we use the information that we bring with us to a problem?

Past research suggests that people may make use of diagnosticity information when explicit data regarding P(D | H) and P(D | ? H) are given to them. However, people fall victim to pseudodiagnosticity biases and ignore P(D | ? H) when such data must be actively sought. This series of four experiments utilized judgment problems in which subjects have knowledge of P(D | ? H) but must recognize the relevance of that knowledge for the judgment at hand. It was hypothesized that subjects who genuinely understood the role of P(D | ? H) in hypothesis testing would respond to this manipulation of implicit diagnosticity by exhibiting greater confidence and lesser information buying when given evidence of relatively high diagnosticity. In the first three studies, subjects attempted to judge the guilt or innocence of suspects in several fictional crimes. In the fourth experiment, subjects attempted to judge the club membership status of students at their own university. Greater amounts of information were bought when the only available information was of low diagnosticity. Subjects also expressed greater confidence in judgments made using highly diagnostic information. However, within the legal scenario, sensitivity to diagnosticity was dependent upon the implication of the cues received. Results are discussed with respect to Bayesian probability, expected value theory, and a confidence criterion model of information purchasing.     

Sharvy’s Lucy and Benjamin Puzzle

Sharvy’s puzzle concerns a situation in which common knowledge of two parties is obtained by repeated observation each of the other, no fixed point being reached in finite time. Can a fixed point be reached?     

Common knowledge of payoff uncertainty in games

Using epistemic logic, we provide a non-probabilistic way to formalise payoff uncertainty, that is, statements such as ‘player i has approximate knowledge about the utility functions of player j.’ We show that on the basis of this formalisation common knowledge of payoff uncertainty and rationality (in the sense of excluding weakly dominated strategies, due to Dekel and Fudenberg (1990)) characterises a new solution concept we have called ‘mixed iterated strict weak dominance.’     

Democratic Answers to Complex Questions – An Epistemic Perspective

This paper addresses a problem for theories of epistemic democracy. In a decision on a complex issue which can be decomposed into several parts, a collective can use different voting procedures: Either its members vote on each sub-question and the answers that gain majority support are used as premises for the conclusion on the main issue (premise based-procedure, pbp), or the vote is conducted on the main issue itself (conclusion-based procedure, cbp). The two procedures can lead to different results. We investigate which of these procedures is better as a truth-tracker, assuming that there exists a true answer to be reached. On the basis of the Condorcet jury theorem, we show that the pbp is universally superior if the objective is to reach truth for the right reasons. If one instead is after truth for whatever reasons, right or wrong, there will be cases in which the cbp is more reliable, even though, for the most part, the pbp still is to be preferred.     

Algebraization, Parametrized Local Deduction Theorem and Interpolation for Substructural Logics over FL

Substructural logics have received a lot of attention in recent years from the communities of both logic and algebra. We discuss the algebraization of substructural logics over the full Lambek calculus and their connections to residuated lattices, and establish a weak form of the deduction theorem that is known as parametrized local deduction theorem. Finally, we study certain interpolation properties and explain how they imply the amalgamation property for certain varieties of residuated lattices. Dedicated to the memory of Willem Johannes Blok     

Loosely Guarded Fragment of First-Order Logic has the Finite Model Property

We show that the loosely guarded and packed fragments of first-order logic have the finite model property. We use a construction of Herwig and Hrushovski. We point out some consequences in temporal predicate logic and algebraic logic.