The deformed double covering of E(2) group, denoted by Ẽκ(2), is obtained by contraction from the SUμ(2). The contraction procedure is then used for producing a new examples of differential calculi: 3D– left covariant calculus on both Ẽκ(2) and the deformed Euclidean group Eκ(2) and two different 4D–bicovariant calculi on Ẽκ(2) which correspond to the one 4D–bicovariant calculi on Eκ(2) describ...

Monoidal t-norm based logic MTL is the logic of left continuous t-norms. We introduce two analytic calculi for first-order MTL. These are obtained by lifting two sequent calculi for different fragments of this logic to the hypersequent level with subsequent addition of Avron’s communication rule. Our calculi enable to prove the mid(hyper)sequent theorem. As corollaries follow Herbrand’s theorem...

We present proof methods for the logics of nonmonotonic reasoning defined by Kraus, Lehmann and Magidor (KLM). We introduce tableaux calculi (called T S) for all KLM logics. We provide decision procedures for KLM logics based on these calculi, and we study their complexity. Finally, we describe KLMLean 2.0, a theorem prover implementing the calculi T S inspired by the “lean” methodology. KLMLea...

We propose a notion of focusing for nested sequent calculi for modal logics which brings down the complexity of proof search to that of the corresponding sequent calculi. The resulting systems are amenable to specifications in linear logic. Examples include modal logic K, a simply dependent bimodal logic and the standard non-normal modal logics. As byproduct we obtain the first nested sequent c...

A patient who was troubled by the persistent passage of prostatic calculi following transurethral prostatectomy is reported. The pathogenesis of these calculi is postulated.