## Abstract We show that a coherent theory of partially ordered connectives can be developed along the same line as partially ordered quantification. We estimate the expressive power of various partially ordered connectives and use methods like Ehrenfeucht games and infinitary logic to get various
POTMiner: mining ordered, unordered, and partially-ordered trees
✍ Scribed by Aída Jiménez; Fernando Berzal; Juan-Carlos Cubero
- Publisher
- Springer-Verlag
- Year
- 2009
- Tongue
- English
- Weight
- 946 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0219-1377
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
We use a known combinatorial argument to prove that among all ordered trees the ratio of the total number of vertices to leaves is two. We introduce a new combinatorial bijection on the set of these trees that shows why this must be so. Ordered trees are then enumerated by number of leaves, total pa
This is to be read "For every x there is a y and for every u there is a v (depending only on u) such that y ( x , y, u , w) ." The precise meaning of this can be given in terms of SKOLEM functions; the above formula is semantically equivalent to the second-order formula Such partially-ordered quant
of non-crossing partitions.
## Abstract Connections between partially ordered connectives and Henkin quantifiers are considered. It is proved that the logic with all partially ordered connectives and the logic with all Henkin quantifiers coincide. This implies that the hierarchy of partially ordered connectives is strongly hi