Kathrin Konczak

NoMoRe: A System for Non-Monotonic Reasoning under Answer Set Semantics

NoMoRe implements answer set semantics for normal logic programs. It realizes a novel paradigm to compute answer sets by computing a-colorings (non-standard graph colorings with two colors) of the block graph (a labeled digraph) associated with a given program P (see [5] for details). Intuitively, an a-coloring reflects the set of generating rules for an answer set, which means that noMoRe is rule-based and not atom-based like most of the other known systems. Since the core system was designed for propositional programs only, we have integrated lparse [8] as a grounder in order to deal with variables. Furthermore, we have included an interface to the graph drawing tool DaVinci [6] for visualization of block graphs. This allows for a structural analysis of programs.

NoMoRe: Non-monotonic Reasoning with Logic Programs

The non-monotonic reasoning system noMoRe [2] implements answer set semantics for normal logic programs. It realizes a novel, rule-based paradigm to compute answer sets by computing non-standard graph colorings of the block graph associated with a given logic program (see [8],[9],[6] for details). These non-standard graph colorings are called a-colorings or application-colorings since they reflect the set of generating rules (applied rules) for an answer set. Hence noMoRe is rule-based and not atom-based like most of the other known systems. In the recent release of noMoRe we have added backward propagation of partial a-colorings and a technique called jumping in order to ensure full (backward) propagation [6]. Both techniques improve the search space pruning of noMoRe. Furthermore, we have extended the syntax by integrity, weight and cardinality constraints [11],[5]1.

Graphs and Colorings for Answer Set Programming: Abridged Report

We investigate rule dependency graphs and their colorings for characterizing the computation of answer sets of logic programs. We start from a characterization of answer sets in terms of totally colored dependency graphs. To a turn, we develop a series of operational characterizations of answer sets in terms of operators on partial colorings. In analogy to the notion of a derivation in proof theory, our operational characterizations are expressed as (non-deterministically formed) sequences of colorings, turning an uncolored graph into a totally colored one. This results in an operational framework in which different combinations of operators result in different formal properties. Among others, we identify the basic strategy employed by the noMoRe system and justify its algorithmic approach. Also, we distinguish Fitting’s and well-founded semantics.

More on noMoRe

This paper focuses on the efficient computation of answer sets for normal logic programs. It concentrates on a recently proposed rule-based method (implemented in the noMoRe system) for computing answer sets. We show how noMoRe and its underlying method can be improved tremendously by extending the computation of deterministic consequences. With these changes noMoRe is able to deal with more challenging problem classes.

Graphs and colorings for answer set programming

We investigate the usage of rule dependency graphs and their colorings for characterizing and computing answer sets of logic programs. This approach provides us with insights into the interplay between rules when inducing answer sets. We start with different characterizations of answer sets in terms of totally colored dependency graphs that differ in graph-theoretical aspects. We then develop a series of operational characterizations of answer sets in terms of operators on partial colorings. In analogy to the notion of a derivation in proof theory, our operational characterizations are expressed as (non-deterministically formed) sequences of colorings, turning an uncolored graph into a totally colored one. In this way, we obtain an operational framework in which different combinations of operators result in different formal properties. Among others, we identify the basic strategy employed by the noMoRe system and justify its algorithmic approach. Furthermore, we distinguish operations corresponding to Fittings operator as well as to well-founded semantics.

nomore : a system for computing preferred answer sets

The integration of preferences into Answer Set Programming (ASP) constitutes an important practical device for distinguishing certain preferred answer sets from non-preferred ones. Up to now, the preference semantics we are considering in this system description were incorporated into answer set solvers either by meta-interpretation [3] or by pre-compilation front-ends [2]; therefore, such kinds of preferences were never integrated into the core existing ASP solvers.

Abduction and preferences in linguistics

We associate optimality theory with abduction and preference handling. We present linguistic problems that appear in the study of dialects as new application of abduction and preference handling. Differences in German dialects originate from different rankings of linguistic constraints which determine the well-formedness of expressions within a language. We introduce a framework for analyzing differences in German dialects by abduction of preferences. More precisely, we will take the perspective of a linguist and reconstruct dialectal variation as abduction problem: Given an observation that a sentence is found as grammatically correct, abduct the underlying constraint ranking. For this, we give a new definition for the determination of optimal candidates for total orders with indifferences. Additionally, we give an encoding for the diagnosis front-end of the DLV system.

NoMoRe: A System for Non-monotonic Reasoning with Logic Programs under Answer Set Semantics

The noMoRe system (first prototype) implements answer set semantics for propositional normal logic programs. It uses an alternative implementation paradigm to compute answer sets by computing non-standard graph colorings of labeled directed graphs associated with logic programs. Therefore noMoRe is an interesting experimental tool for scientists working with logic programs on a theoretical or practical basis. Furthermore, we have included a tool for visualization of those graphs corresponding to programs.