Completeness for the Classical Antecedent Fragment of Inquisitive First-Order Logic

Inquisitive first order logic "Equation missing" is an extension of first order classical logic, introducing questions and studying the logical relations between questions and quantifiers. It is not known whether "Equation missing" is recursively axiomatizable, even though an axiomatization has been found for fragments of the logic (Ciardelli, 2016). In this paper we define the $$\mathsf {ClAnt}$$ ClAnt —classical antecedent—fragment, together with an axiomatization and a proof of its strong completeness. This result extends the ones presented in the literature and introduces a new approach to study the axiomatization problem for fragments of the logic.

Generalized Majority Voter Design Method for N-Modular Redundant Systems Used in Mission- and Safety-Critical Applications

Mission- and safety-critical circuits and systems employ redundancy in their designs to overcome any faults or failures of constituent circuits and systems during the normal operation. In this aspect, the N-modular redundancy (NMR) is widely used. An NMR system is comprised of N identical systems, the corresponding outputs of which are majority voted to generate the system outputs. To perform majority voting, a majority voter is required, and the sizes of majority voters tend to vary depending on an NMR system. Majority voters corresponding to NMR systems are physically realized by enumerating the majority input clauses corresponding to an NMR system and then synthesizing the majority logic equation. The issue is that the number of majority input clauses corresponding to an NMR system is governed by a mathematical combination, the complexity of which increases substantially with increases in the level of redundancy. In this context, the design of a majority voter of any size corresponding to an NMR specification based on a new, generalized design approach is described. The proposed approach is inherently hierarchical and progressive since any NMR majority voter can be constructed from an (N − 2)MR majority voter along with additional logic corresponding to the two extra inputs. Further, the proposed approach paves the way for simultaneous production of the NMR system outputs corresponding to different degrees of redundancy, which is not intrinsic to the existing methods. This feature is additionally useful for any sharing of common logic with diverse degrees of redundancy in appropriate portions of an NMR implementation.