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Stateful STT-MRAM-Based Logic for Beyond–Von Neumann Computing
Published in Krzysztof Iniewski, Tomasz Brozek, Krzysztof Iniewski, Micro- and Nanoelectronics, 2017
Hiwa Mahmoudi, Thomas Windbacher, Viktor Sverdlov, Siegfried Selberherr
Material implication (IMP) is a fundamental two-input Boolean logic operation (s → t) that reads “s implies t” or “if s, then t” and is equivalent to “(NOT s) OR t” ((S¯+t)), as shown in Table 11.1. The operations IMP and NIMP (negated IMP) form a computationally complete logic basis in combination with any operation from the sets C and C′, respectively, for which C = {NOT, FALSE, XOR, NIMP} and C′ = {NOT, TRUE, XNOR, IMP}, and are therefore able to compute arbitrary Boolean functions.
A Creativity Support System Based on Causal Mapping
Published in Journal of Computer Information Systems, 2018
Interesting enough, even logic can be, to a certain extent, subjective. Most specifically, material implication [e.g., 73] can be difficult to interpret and to translate into current speech in theory formation, possibly introducing a degree of subjectivity in the expression of theories, due to its well-known paradoxes: whenever the antecedent is false, the conditional is true; whenever the consequent is true, the conditional is true. For this reason, the methodology followed in this article uses causal implication [10, 37]. In causal implication, all the propositions mean “causality sufficiency” as described by Burks [10]. This means that the antecedent may contain irrelevant conditions for the causal relationship to hold and still the proposition is correct. Henderson [37] exemplifies the difference between material and causal implications: the proposition “If my dog has a white tail it will die” is false in causal implication, but it is true in material implication, when the dog does not have a white tail.
Infectious and transparent emotivism
Published in Journal of Applied Non-Classical Logics, 2022
Notice that both transparent and non-transparent interpretations of SL-conditionals imply the paradoxes of material implication. That is, and ). On the other hand, WK-conditionals do not imply them. That is, and ). A WK-countermodel for the former is a valuation where and ; for the latter, it is a valuation where and .
From KLM-style conditionals to defeasible modalities, and back
Published in Journal of Applied Non-Classical Logics, 2018
Katarina Britz, Ivan Varzinczak
Furthermore, we have that both and . This stands in contrast with the conditional logics of Stalnaker (1968) and Lewis (1973), where the exigence of avoiding the paradoxes of material implication was one of the main motivations for their introduction. However, note that the following global variants of the paradoxes of material implication do hold in the KLM framework: