Intermediate decision trees are the subtrees of the ful l (unpruned) decision tree generated in a breadth-first order An extensive empirical investigation evaluates the classification error of intermediate decision trees and compares their performance to ful l and pruned trees Em pirical results were generated using C4 5 with 66 databases from the UCI machine learning database repository Result...

We investigate the descriptive complexity of finite abelian groups. Using Ehrenfeucht-Fräıssé games we find upper and lower bounds on quantifier depth, quantifier alternations, and number of variables of a first-order sentence that distinguishes two finite abelian groups. Our main results are the following. Let G1 and G2 be a pair of non-isomorphic finite abelian groups, and let m be a number t...

We study a natural hierarchy in first-order logic, namely the quantifier structure hierarchy, which gives a systematic classification of first-order formulas based on structural quantifier resource. We define a variant of Ehrenfeucht-Fräıssé games that characterizes quantifier classes and use it to prove that this hierarchy is strict over finite structures, using strategy compositions. Moreover...

The lattice E of c.e. sets is a popular object of study in Computability Theory [So87]. A principal fact about this lattice is the undecidability of its first-order theory Th(E). Moreover, Th(E) is known [HN98] to be m-equivalent to the first-order arithmetic Th(N) where N := (ω; +,×). The lattice E may be considered as the lattice of effectively open subsets of the discrete topological space ω...

Let v(F ) denote the number of vertices in a fixed connected pattern graph F . We show an infinite family of patterns F such that the existence of a subgraph isomorphic to F is expressible by a first-order sentence of quantifier depth 23 v(F ) + 1, assuming that the host graph is sufficiently large and connected. On the other hand, this is impossible for any F with using less than 2 3 v(F ) − 2...

Descriptive Experience Sampling (DES) is a method for exploring inner experience. DES subjects carry a random beeper in natural environments; when the beep sounds, they capture their inner experience, jot down notes about it, and report it to an investigator in a subsequent expositional interview. DES is a fundamentally idiographic method, describing faithfully the pristine inner experiences of...