Negation and Implication in Quasi-Nelson Logic

Quasi-Nelson logic is a recently-introduced generalization of Nelson’s constructive logic with strong negation to a non-involutive setting. In the present paper we axiomatize the negation-implication fragment of quasi-Nelson logic (QNI-logic), which constitutes in a sense the algebraizable core of quasi-Nelson logic. We introduce a finite Hilbert-style calculus for QNI-logic, showing completeness and algebraizability with respect to the variety of QNI-algebras. Members of the latter class, also introduced and investigated in a recent paper, are precisely the negation-implication subreducts of quasi-Nelson algebras. Relying on our completeness result, we also show how the negation-implication fragments of intuitionistic logic and Nelson’s constructive logic may both be obtained as schematic extensions of QNI-logic.

Revisiting Explicit Negation in Answer Set Programming

A common feature in Answer Set Programming is the use of a second negation, stronger than default negation and sometimes called explicit, strong or classical negation. This explicit negation is normally used in front of atoms, rather than allowing its use as a regular operator. In this paper we consider the arbitrary combination of explicit negation with nested expressions, as those defined by Lifschitz, Tang and Turner. We extend the concept of reduct for this new syntax and then prove that it can be captured by an extension of Equilibrium Logic with this second negation. We study some properties of this variant and compare to the already known combination of Equilibrium Logic with Nelson’s strong negation.

BELNAP–DUNN MODAL LOGICS: TRUTH CONSTANTS VS. TRUTH VALUES

We shall be concerned with the modal logic BK—which is based on the Belnap–Dunn four-valued matrix, and can be viewed as being obtained from the least normal modal logic K by adding ‘strong negation’. Though all four values ‘truth’, ‘falsity’, ‘neither’ and ‘both’ are employed in its Kripke semantics, only the first two are expressible as terms. We show that expanding the original language of BK to include constants for ‘neither’ or/and ‘both’ leads to quite unexpected results. To be more precise, adding one of these constants has the effect of eliminating the respective value at the level of BK-extensions. In particular, if one adds both of these, then the corresponding lattice of extensions turns out to be isomorphic to that of ordinary normal modal logics.

Evaluation software for effects produced by MOOC in mediums with different linguistically levels

MOOC appearance has produced, in a first phase, more discussions than contributions. Despite pessimistic opinions or those catastrophic foreseeing the end of the classic education by accepting MOOC, the authors consider that, as it is happening in all situations when a field is reformed, instead of criticism or catastrophic predictions, an assessment should be simply made. MOOC will not be better or worse if it is discussed and dissected but can be tested in action, perfected by results, or abandoned if it has no prospects. Without testing, no decision is valid. A similarity between the MOOC appearance and the appearance of the idea of flying machines heavier than air can be made. In the flight case, the first reaction was a strong negation (including at Academies level) and only performing the first independent flight with an apparatus heavier than air has shifted orientation from denial to contributions. So, practical tests clarified the battle between ideas. The authors of this article encourage the idea of testing–assessment and, therefore, imagined and proposed one software for quickly assess whether MOOC produces changes in knowledge, by simply transferring courses from ‘face-to-face’ environment into the virtual one. Among the methods of statistical analysis for student behavioral changes was chosen the Keppel method. It underpins the assessment method of this work being approached using both the version with one variable and also with three variables. It is intended that this attempts to pave the way for other series of rapid assessment regarding MOOC effects (using other statistical methods). We believe, that this is the only approach that can lead either to improve the system or to renunciation.