Periodicity of Negation

Periodicity of Negation

In the context of a distributive lattice we a) specify the sort of mappings that could be generally called ‘negations’ and b) study their behavior under iteration. We show that there are periodic and nonperiodic ones. Natural periodic negations exist with periods 2, 3 and 4 and pace 2, as well as natural non-periodic ones, arising from the interaction of interior and quasi interior mappings wit...

Periodicity and Almost-periodicity

Negation and Double-Negation of Chinese Oppositeness

Oppositeness refers to the paradigmatic relationship of two words holding the contrast meanings. The fact that linguistic opposite differs from logical contrast has been discussed in theories, but has not been tested in practice. In this paper, we investigate three main subtypes of Chinese oppositeness, via using logical tests of negation and double-negation. Result shows that purely logical te...

Negation Without Negation in Probabilistic Logic Programming

Probabilistic logic programs without negation can have cycles (with a preference for false), but cannot represent all conditional distributions. Probabilistic logic programs with negation can represent arbitrary conditional probabilities, but with cycles they create logical inconsistencies. We show how allowing negative noise probabilities allows us to represent arbitrary conditional probabilit...

Poincaré Duality and Periodicity, Ii. James Periodicity

Let K be a connected finite complex. This paper studies the problem of whether one can attach a cell to some iterated suspension ΣK so that the resulting space satisfies Poincaré duality. When this is possible, we say that ΣK is a spine. We introduce the notion of quadratic self duality and show that if K is quadratically self dual, then ΣK is a spine whenever j is a suitable power of two. The ...