This paper is a critique of version three of Joonmo Kim’s paper entitled “P 6= NP by Modus Tollens.” After summarizing Kim’s proof, we note that the logic that Kim uses is inconsistent, which provides evidence that the proof is invalid. To show this, we will consider two reasonable interpretations of Kim’s definitions, and show that “P 6= NP” does not seem to follow in an obvious way using any ...

According to a higher order reasoning account, inferential reasoning processes underpin the widely observed cue competition effect of blocking in causal learning. The inference required for blocking has been described as modus tollens (if p then q, not q therefore not p). Young children are known to have difficulties with this type of inference, but research with adults suggests that this infer...

Deductive reasoning is traditionally viewed as a unitary process involving either rule-based or visuo-spatial mechanisms. However, there is a disagreement in the neuroimaging literature on whether the data support one alternative over the other. Here we test the hypothesis that discrepancies in the literature result from the reasoning materials themselves. Using functional magnetic resonance im...

In 1936 Cohen & Marrian isolated from human pregnancy urine an amorphous water-soluble substance containing about 50% of combined oestriol. From its elementary composition and properties this substance appeared to consist largely of an oestriol monoglucuronide. Subsequently (Cohen, Marrian & Odell, 1936) this substance yielded a crystalline sodium salt, which, on the basis of its elementary com...

In the title compound, C(30)H(41)NO(6), the three six-membered rings adopt chair conformations and the stereochemistry of the A/B and B/C ring junctions are trans. The five-membered ring D adopts an envelope conformation, with the methyl-ene C atom as the flap. The title compound was synthesized via esterification, Tollens reaction, 1,5-hydride shift from the natural tetracyclic diterpenoid iso...

Uncertain entailment is a methodology for calculating the truth value of an uncertain formula via the maximum uncertainty principle when the truth values of other uncertain formulas are given. In order to find the truth value of additional formula, this paper will introduce an entailment model. As applications of uncertain entailment, this paper will also discuss modus ponens, modus tollens, an...

In this study, electrophysiological correlates of belief-laden reasoning were investigated. As subjects, trained participants were required to draw a logical conclusion after being exposed to 4 conditional arguments: the inhibitory content of modus tollens (ICMT), facilitatory content of modus tollens (FCMT), inhibitory content of denial of the antecedent (ICDA) and facilitatory content of deni...