Admissibility in Finitely Generated Quasivarieties

Checking the admissibility of quasiequations in a finitely generated (i.e., generated by a finite set of finite algebras) quasivariety Q amounts to checking validity in a suitable finite free algebra of the quasivariety, and is therefore decidable. However, since free algebras may be large even for small sets of small algebras and very few generators, this naive method for checking admissibility in Q is not computationally feasible. In this paper, algorithms are introduced that generate a minimal (with respect to a multiset well-ordering on their cardinalities) finite set of algebras such that the validity of a quasiequation in this set corresponds to admissibility of the quasiequation in Q. In particular, structural completeness (validity and admissibility coincide) and almost structural completeness (validity and admissibility coincide for quasiequations with unifiable premises) can be checked. The algorithms are illustrated with a selection of well-known finitely generated quasivarieties, and adapted to handle also admissibility of rules in finite-valued logics.

Phases of many flavors QCD: Lattice results

This note is based on our recent results on QCD with varying number of flavors of fundamental fermions. Topics include unusual, strong dynamics in the preconformal, confining phase, the physics of the conformal window and the role of ab-initio lattice simulations in establishing our current knowledge of the phases of many flavor QCD.

Canonical proof nets for classical logic

Proof nets provide abstract counterparts to sequent proofs modulo rule permutations; the idea being that if two proofs have the same underlying proof-net, they are in essence the same proof. Providing a convincing proof-net counterpart to proofs in the classical sequent calculus is thus an important step in understanding classical sequent calculus proofs. By convincing, we mean that (a) there should be a canonical function from sequent proofs to proof nets, (b) it should be possible to check the correctness of a net in polynomial time, (c) every correct net should be obtainable from a sequent calculus proof, and (d) there should be a cut-elimination procedure which preserves correctness. Previous attempts to give proof-net-like objects for propositional classical logic have failed at least one of the above conditions. In Richard McKinley (2010) [22], the author presented a calculus of proof nets (expansion nets) satisfying (a) and (b); the paper defined a sequent calculus corresponding to expansion nets but gave no explicit demonstration of (c). That sequent calculus, called LK∗ in this paper, is a novel one-sided sequent calculus with both additively and multiplicatively formulated disjunction rules. In this paper (a self-contained extended version of Richard McKinley (2010) [22]), we give a full proof of (c) for expansion nets with respect to LK∗, and in addition give a cut-elimination procedure internal to expansion nets – this makes expansion nets the first notion of proof-net for classical logic satisfying all four criteria.

Proof internalization in generalized Frege systems for classical logic

We present a general method for inserting proofs in Frege systems for classical logic that produces systems that can internalize their own proofs.

Censors for Boolean Description Logic

Protecting different kinds of information has become an important area of research. One aspect is to provide effective means to avoid that secrets can be deduced from the answers of legitimate queries. In the context of atomic propositional databases several methods have been developed to achieve this goal. However, in those databases it is not possible to formalize structural information. Also they are quite restrictive with respect to the specification of secrets. In this paper we extend those methods to match the much greater expressive power of Boolean description logics. In addition to the formal framework, we provide a discussion of various kinds of censors and establish different levels of security they can provide.

From Framework to Action: The DESIRE Approach to Combat Desertification

It has become increasingly clear that desertification can only be tackled through a multi-disciplinary approach that not only involves scientists but also stakeholders. In the DESIRE project such an approach was taken. As a first step, a conceptual framework was developed in which the factors and processes that may lead to land degradation and desertification were described. Many of these factors do not work independently, but can reinforce or weaken one another, and to illustrate these relationships sustainable management and policy feedback loops were included. This conceptual framework can be applied globally, but can also be made site-specific to take into account that each study site has a unique combination of bio-physical, socio-economic and political conditions. Once the conceptual framework was defined, a methodological framework was developed in which the methodological steps taken in the DESIRE approach were listed and their logic and sequence were explained. The last step was to develop a concrete working plan to put the project into action, involving stakeholders throughout the process. This series of steps, in full or in part, offers explicit guidance for other organizations or projects that aim to reduce land degradation and desertification.