In this paper, we present a modality-free pre-rough algebra. Łukasiewicz Moisil algebra and Wajsberg algebra are equivalent under a transformation. A similar type of equivalence exists in our proposed definition and standard definition of pre-rough algebra. We obtain a few modality-free algebras weaker than pre-rough algebra. Furthermore, it is also established that modality-free versions for other analogous structures weaker than pre-rough algebra do not exist. Both Hilbert-type axiomatization and sequent calculi for all proposed algebras are presented.

In the original publication of the article, errors in the production stages resulted in Vanessa Munro being listed as sole author.

Two types of logical consequence are compared: one, with respect to matrix and designated elements and the other with respect to ordering in a suitable algebraic structure. Particular emphasis is laid on algebraic structures in which there is no top-element relative to the ordering. The significance of this special condition is discussed. Sequent calculi for a number of such structures are developed. As a consequence it is re-established that the notion of truth as such, not to speak of tautologies, is (...) inessential in order to define validity of an argument. (shrink)

A new characterization of all the MV-algebras embedded in a CL-algebra has been presented. A new sequent calculus for Lukasiewicz ℵ0-valued logic is introduced. Some links between this calculus and the sequent calculus for multiplicative additive linear logic are established. It has been shown that Lukasiewicz ℵ0-valued logic can be embedded in a suitable extension of MALL.

There is a tendency to associate intelligence with speed. ‘Quick’ is a synonym for clever and suggests intellectual ability. ‘Slow’, by contrast, implies a want of intelligence, even stupidity. The slow child in the class is the one who is ‘behind’, the one who must ‘catch up’ with the others. This is symptomatic of a wider stress in our culture on getting things done quickly and ‘saving time’. It seems that fear of time running out often compels us into running (...) after it. Within philosophy however resources are available for challenging this perspective. (shrink)