Partial Up and Down Logic

Partial Up and Down Logic

Partial Up and Down

This paper presents logics for reasoning about extension and reduction of partial information states. This enterprise amounts to non-persistent variations of certain constructive logics, in particular the so-called logic of constructible falsity of Nelson 1949]. We provide simple semantics, sequential calculi, completeness and decidability proofs. The most simple logical means for knowledge rep...

Judging up and down.

In Experiment I subjects were asked to judge whether an arrow was pointing up or pointing down at various heights inside a surrounding rectangle. They were faster on an arrow pointing up the higher it was in the rectangle, and they were faster on an arrow pointing down the lower it was in the rectangle. Experiments 2, 3, and 4 were designed to test sources for this"congruity effect." The intrus...

Up-and-down designs

Consecutive Up-down Patterns in Up-down Permutations

In this paper, we study the distribution of the number of consecutive pattern matches of the five up-down permutations of length four, 1324, 2314, 2413, 1432, and 3412, in the set of up-down permutations. We show that for any such τ , the generating function for the distribution of the number of consecutive pattern matches of τ in the set of up-down permutations can be expressed in terms of wha...