The unification problem in a logical system L can be defined in the following way: given a formula φ(x1, . . . , xα), determine whether there exists formulas ψ1, . . ., ψα such that φ(ψ1, . . . , ψα) is in L. The research on unification for modal logics was originally motivated by the admissibility problem for rules of inference: given a rule of inference φ1(x1, . . . , xα), . . . , φm(x1, . . ...

Inspired by the Curry-Howard correspondence, we study normalisation procedures in the depth-bounded intuitionistic sequent calculus of Hudelmaier (1988) for the implicational case, thus strengthening existing approaches to Cut-admissibility. We decorate proofs with proofterms and introduce various term-reduction systems representing proof transformations. In contrast to previous papers which ga...

Multiple path multistage interconnection networks as compared to their parental one path cube-type networks provide better permutation capability and offer such important property as fault-tolerance. In this paper an approach for investigation permuting ability of R-path Omega networks is proposed. The analysis as concerned to arbitrary permutations is done with the help of number theory method...

It is shown that the right shift semigroup on L(R+) does not satisfy the weighted Weiss conjecture for α ∈ (0, 1). In other words, αadmissibility of scalar valued observation operators cannot always be characterised by a simple resolvent growth condition. This result is in contrast to the unweighted case, where 0-admissibility can be characterised by a simple growth bound. The result is proved ...

We consider a financial market with one riskless and one risky asset. The super-replication theorem states that there is no duality gap in the problem of super-replicating a contingent claim under transaction costs and the associated dual problem. We give two versions of this theorem. The first theorem relates a numéraire-based admissibility condition in the primal problem to the notion of a lo...

Partial type theories allow reasoning about recursively-defined computations using fixed-point induction. However, fixed-point induction is only sound for admissible types and not all types are admissible in sufficiently expressive dependent type theories. Previous solutions have either introduced explicit admissibility conditions on the use of fixed points, or limited the underlying type theor...

Brandenburger, Friedenberg, and Keisler [Econometrica 76 (2008), 307352] show that rationality and common assumption of rationality (RCAR) is impossible in a complete and continuous type structure. We show, by inroducing an alternative notion of “weak assumption”, that rationality and common weak assumption of rationality (RCWAR) is possible in a complete and continuous type structure. This pos...