Multiple Conclusion Rules in Logics with the Disjunction Property

We prove that for the intermediate logics with the disjunction property any basis of admissible rules can be reduced to a basis of admissible m-rules (multiple-conclusion rules), and every basis of admissible m-rules can be reduced to a basis of admissible rules. These results can be generalized to a broad class of logics including positive logic and its extensions, Johansson logic, normal extensions of S4, n-transitive logics and intuitionistic modal logics

On unification and admissible rules in Gabbay-de Jongh logics

In this paper we study the admissible rules of intermediate logics with the disjunction property. We establish some general results on extension of models and sets of formulas, and eventually specialize to provide a a basis for the admissible rules of the Gabbay-de Jongh logics and to show that that logic has finitary unification type

The depth of intuitionistic cut free proofs

Abstract We prove a quadratic upper bound for the depth of cut free proofs in propositional intuitionistic logic formalized with Gentzen's sequent calculus. We discuss bounds on the necessary number of reuses of left implication rules. We exhibit an example showing that this quadratic bound is optimal. As a corollary, this gives a new proof that propositional validity for intuitionistic logic is in PSPACE

Towards sustainable kinetic resolution, a combination of bio-catalysis, flow chemistry and bio-based solvents

The esterification of 2-phenylpropionic acid was investigated as a model system for enzyme catalysed (CALB, Novozyme 435) reactions in bio-based solvents. A multi-parameter correlation taking into account solvent parameters was developed to explain experimental observations. A continuous flow process using p-cymene as the solvent was operated over several weeks, thus combining a sustainable solvent and flow chemistry for kinetic resolution

Inference Rules in Nelson’s Logics, Admissibility and Weak Admissibility

© 2015, Springer Basel. Our paper aims to investigate inference rules for Nelson’s logics and to discuss possible ways to determine admissibility of inference rules in such logics. We will use the technique offered originally for intuitionistic logic and paraconsistent minimal Johannson’s logic. However, the adaptation is not an easy and evident task since Nelson’s logics do not enjoy replacement of equivalences rule. Therefore we consider and compare standard admissibility and weak admissibility. Our paper founds algorithms for recognizing weak admissibility and admissibility itself – for restricted cases, to show the problems arising in the course of study