Appellate opinions were evaluated on variables related to expert admissibility to assess the effects of Daubert v. Merrell Dow Pharmaceuticals, Inc. in criminal cases. Analysis reveals changes in appellate courts’ consideration of Frye v. United States, the 4 Daubert criteria, and several Federal Rules of Evidence. The importance of Frye and the general acceptance criterion decreased over time,...

We study admissibility of inference rules and unification with parameters in transitive modal logics (extensions of K4), in particular we generalize various results on parameterfree admissibility and unification to the setting with parameters. Specifically, we give a characterization of projective formulas generalizing Ghilardi’s characterization in the parameter-free case, leading to new proof...

The concept of ‘fully permissible sets’ is defined by an algorithm that eliminates strategy subsets. It is characterized as choice sets when there is common certain belief of the event that each player prefer one strategy to another if and only if the former weakly dominates the latter on the set of all opponent strategies or on the union of the choice sets that are deemed possible for the oppo...

Brandenburger et al. (2008) establish epistemic foundations for rationality and common assumption of rationality (RCAR), where rationality includes admissibility, using lexicographic type structures. Their negative result that RCAR is empty whenever the type structure is complete and continuous suggests that iterated admissibility (IA) requires players to have prior knowledge about each other, ...

Using admissibility for a computable model theory for uncountable structures

A well-known problem in intuitionistic logic is the existence of valid but not derivable rules. This problem seems to be related with some constructive features of intuitionism (disjunction and existence property) but appear also in modal logics. We study here a particular case of this phenomenon, admissible rules in propositional calculus. G.E.Mints in [Mi 72] give sufficients conditions for a...

Deduction modulo is a framework in which theories are integrated into proof systems such as natural deduction or sequent calculus by presenting them using rewriting rules. When only terms are rewritten, cut admissibility in those systems is equivalent to the confluence of the rewriting system, as shown by Dowek, RTA 2003, LNCS 2706. This is no longer true when considering rewriting rules involv...

For any finite and consistent first-order theory, we can find a presentation as a rewriting system that enjoys cut admissibility. Since proofs are rarely built without context, it is essential to develop methods that are adapted to search for proofs in theories. For instance, SMT provers provide efficient tools. Nevertheless, they are restricted to some particular theories, such as linear arith...

We analyse the notion of iterated admissibility, i.e., avoidance of weakly dominated strategies, as a solution concept for extensive games of infinite horizon. This concept is known to provide a valuable criterion for selecting among multiple equilibria and to yield sharp predictions in finite games. However, generalisations to the infinite are inherently problematic, due to unbounded dominance...

Sufficient conditions for the finite and infinite-time admissibility of an observation operator are given. It is shown that the estimates of Weiss are close to being sufficient. If the semigroup is surjective, then the estimate is sufficient.