Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algebraic Answer Set Programming   Non-monotonic reasoning is an essential part of human intelligence
prominently formalized in artificial intelligence research via answer set
programming. In this paper, we introduce the sequential composition of answer
set programs. We show that the notion of composition gives rise to a family of
finite program algebras, baptized {\em ASP algebras} in this paper.
Interestingly, we can derive algebraic formulas for the syntactic
representation of the well-known Faber-Leone-Pfeifer- and Gelfond-Lifschitz
reducts. On the semantic side, we show that the immediate consequence operator
of a program can be represented via composition, which allows us to compute the
least model semantics of Horn programs without any explicit reference to
operators. As a result, we can characterize answer sets algebraically, which
bridges the conceptual gap between the syntax and semantics of an answer set
program in a mathematically satisfactory way, and which provides an algebraic
characterization of strong and uniform equivalence. Moreover, it gives rise to
an algebraic meta-calculus for answer set programs. In a broader sense, this
paper is a further step towards an algebra of logic programs first envisioned
by Richard A. O'Keefe in 1985 and in the future we plan to lift the methods of
this paper to wider classes of programs, most importantly to higher-order and
disjunctive programs and extensions thereof.

28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
2
The categories of this paper are: math
24
The categories of this paper are: dg-ga