Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Executable Set Theory and Arithmetic Encodings in Prolog   The paper is organized as a self-contained literate Prolog program that
implements elements of an executable finite set theory with focus on
combinatorial generation and arithmetic encodings. The complete Prolog code is
available at http://logic.csci.unt.edu/tarau/research/2008/pHFS.zip . First,
ranking and unranking functions for some "mathematically elegant" data types in
the universe of Hereditarily Finite Sets with Urelements are provided,
resulting in arithmetic encodings for powersets, hypergraphs, ordinals and
choice functions. After implementing a digraph representation of Hereditarily
Finite Sets we define {\em decoration functions} that can recover well-founded
sets from encodings of their associated acyclic digraphs. We conclude with an
encoding of arbitrary digraphs and discuss a concept of duality induced by the
set membership relation. In the process, we uncover the surprising possibility
of internally sharing isomorphic objects, independently of their language level
types and meanings.

25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc