History and research on proof by contradiction suggests is difficult for students in a number of ways. Students’ comprehension already-written proofs one such aspect that has received relatively little attention. Applying the cognitive lens Action-Process-Object-Schema (APOS) Theory to contradiction, we constructed tested model describes how student might construct concept ‘proof contradiction’...

A critical view of the alleged significance of Belnap four-valued logic for reasoning under inconsistent and incomplete information is provided. The difficulty lies in the confusion between truth-values and information states, when reasoning about Boolean propositions. So our critique is along the lines of previous debates on the relevance of many-valued logics and especially of the extension o...

In an article devoted to the Young Marx, I have already stressed the ambiguity of the idea of ‘inverting Hegel’. It seemed to me that strictly speaking this expression suited Feuerbach perfectly; the latter did, indeed, ‘turn speculative philosophy back on to its feet’, but the only result was to arrive with implacable logic at an idealist anthropology. But the expression cannot be applied to M...

In most existing systems that give expert advice, efforts are made to ensure that the rules in the knowledge base do not give rise to contradictions. This is partly to avoid confusing the user, and partly for fear that a logical system that generates even a single contradiction must collapse. We argue that not only can contradictions be tolerated, but they can even be useful. In a legal context...

We begin by motivating the use of paraconsistency and the detection of contradiction supported conclusions by recourse to examples. Next we overview WFSX p and present its embedding into WFS. We then address the problem of detecting contradiction support and relate it to WFSX p's intrinsic properties. Afterwards, we show how to implement two recent modal contradiction related constructs in the ...

We present a combined theoretical and experimental study of X-ray optical wave mixing. This class nonlinear phenomena combines the strengths spectroscopic techniques from domain, with high-resolution capabilities X-rays. In particular, sensitivity these can be exploited to selectively probe valence dynamics. Specifically, we focus on effect parametric down-conversion. description process, which...

Well Founded Semantics for logic programs extended with eXplicit negation (WFSX) is characterized by that, in any model, whenever :a (the explicit negation of a) holds, then a (the negation by default of a) also holds. When explicit negation is used contradiction may be present (e.g. a and :a both hold for some a) and thus no semantics is given to the program. We introduce here the notion of re...