Conflict-driven ASP Solving with External Sources and Program Splits

Answer Set Programming (ASP) is a well-known problem solving approach based on nonmonotonic reasoning. HEX-programs extend ASP with external atoms for access to arbitrary external sources, which can also introduce constants that do not appear in the program (value invention). In order to determine the relevant constants during (pre-)grounding, external atoms must in general be evaluated under up to exponentially many possible inputs. While program splitting techniques allow for eliminating exhaustive pre-grounding, they prohibit effective conflict-driven solving. Thus, current techniques suffer either a grounding or a solving bottleneck. In this work we introduce a new technique for conflict-driven learning over multiple program components. To this end, we identify reasons for inconsistency of program components wrt. input from predecessor components and propagate them back. Experiments show a significant, potentially exponential speedup.

as Input Language for Answer Set Solvers

10.1017/s1471068421000351 ◽

2021 ◽

pp. 1-17

Author(s):

KYLIAN VAN DESSEL ◽

JO DEVRIENDT ◽

JOOST VENNEKENS

Keyword(s):

Problem Solving ◽

Technological Progress ◽

Nonmonotonic Reasoning ◽

Answer Set Programming ◽

Input Language ◽

Inference System ◽

Domain Experts ◽

First Order ◽

Classical Setting ◽

Abstract Technological progress in Answer Set Programming (ASP) has been stimulated by the use of common standards, such as the ASP-Core-2 language. While ASP has its roots in nonmonotonic reasoning, efforts have also been made to reconcile ASP with classical first-order (FO) logic. This has resulted in the development of FO(·), an expressive extension of FO, which allows ASP-like problem solving in a purely classical setting. This language may be more accessible to domain experts already familiar with FO and may be easier to combine with other formalisms that are based on classical logic. It is supported by the IDP inference system, which has successfully competed in a number of ASP competitions. Here, however, technological progress has been hampered by the limited number of systems that are available for FO(·). In this paper, we aim to address this gap by means of a translation tool that transforms an FO(·) specification into ASP-Core-2, thereby allowing ASP-Core-2 solvers to be used as solvers for FO(·) as well. We present experimental results to show that the resulting combination of our translation with an off-the-shelf ASP solver is competitive with the IDP system as a way of solving problems formulated in FO(·).

Grounding and Solving in Answer Set Programming

AI Magazine ◽

10.1609/aimag.v37i3.2672 ◽

2016 ◽

Vol 37 (3) ◽

pp. 25-32 ◽

Cited By ~ 27

Author(s):

Benjamin Kaufmann ◽

Nicola Leone ◽

Simona Perri ◽

Torsten Schaub

Keyword(s):

Problem Solving ◽

Propositional Logic ◽

Logic Program ◽

Answer Set Programming ◽

Key Issues ◽

Answer Sets ◽

Answer set programming is a declarative problem solving paradigm that rests upon a workflow involving modeling, grounding, and solving. While the former is described by Gebser and Schaub (2016), we focus here on key issues in grounding, or how to systematically replace object variables by ground terms in a effective way, and solving, or how to compute the answer sets of a propositional logic program obtained by grounding.

Reasoning about Cardinal Directions between 3-Dimensional Extended Objects using Answer Set Programming

10.1017/s1471068420000411 ◽

2020 ◽

Vol 20 (6) ◽

pp. 942-957

Author(s):

Yusuf Izmirlioglu ◽

Esra Erdem

Keyword(s):

Nonmonotonic Reasoning ◽

Answer Set Programming ◽

3 Dimensional ◽

3D Space ◽

Formal Framework ◽

Different Types ◽

New Type ◽

Cardinal Directions ◽

AbstractWe propose a novel formal framework (called 3D-NCDC-ASP) to represent and reason about cardinal directions between extended objects in 3-dimensional (3D) space, using Answer Set Programming (ASP). 3D-NCDC-ASP extends Cardinal Directional Calculus (CDC) with a new type of default constraints, and NCDC-ASP to 3D. 3D-NCDC-ASP provides a flexible platform offering different types of reasoning: Nonmonotonic reasoning with defaults, checking consistency of a set of constraints on 3D cardinal directions between objects, explaining inconsistencies, and inferring missing CDC relations. We prove the soundness of 3D-NCDC-ASP, and illustrate its usefulness with applications.

Exploiting Answer Set Programming with External Sources for Meta-Interpretive Learning

10.1017/s1471068418000261 ◽

2018 ◽

Vol 18 (3-4) ◽

pp. 571-588 ◽

Cited By ~ 2

Author(s):

TOBIAS KAMINSKI ◽

THOMAS EITER ◽

KATSUMI INOUE

Keyword(s):

Experimental Evaluation ◽

Answer Set Programming ◽

Background Knowledge ◽

Search Space ◽

Combinatorial Search ◽

Logic Programs ◽

Search Problems ◽

External Sources ◽

Performance Gains ◽

AbstractMeta-Interpretive Learning (MIL) learns logic programs from examples by instantiating meta-rules, which is implemented by the Metagol system based on Prolog. Viewing MIL-problems as combinatorial search problems, they can alternatively be solved by employing Answer Set Programming (ASP), which may result in performance gains as a result of efficient conflict propagation. However, a straightforward ASP-encoding of MIL results in a huge search space due to a lack of procedural bias and the need for grounding. To address these challenging issues, we encode MIL in the HEX-formalism, which is an extension of ASP that allows us to outsource the background knowledge, and we restrict the search space to compensate for a procedural bias in ASP. This way, the import of constants from the background knowledge can for a given type of meta-rules be limited to relevant ones. Moreover, by abstracting from term manipulations in the encoding and by exploiting the HEX interface mechanism, the import of such constants can be entirely avoided in order to mitigate the grounding bottleneck. An experimental evaluation shows promising results.

A decidable subclass of finitary programs

10.1017/s1471068410000232 ◽

2010 ◽

Vol 10 (4-6) ◽

pp. 481-496 ◽

Cited By ~ 8

Author(s):

SABRINA BASELICE ◽

PIERO A. BONATTI

Keyword(s):

Problem Solving ◽

Answer Set Programming ◽

Stable Model ◽

Unique Combination ◽

Logic Programs ◽

Trade Off ◽

Full Support ◽

Odd Cycles ◽

AbstractAnswer set programming—the most popular problem solving paradigm based on logic programs—has been recently extended to support uninterpreted function symbols (Syrjänen 2001, Bonatti 2004; Simkus and Eiter 2007; Gebseret al. 2007; Baseliceet al. 2009; Calimeriet al. 2008). All of these approaches have some limitation. In this paper we propose a class of programs called FP2 that enjoys a different trade-off between expressiveness and complexity. FP2 is inspired by the extension of finitary normal programs with local variables introduced in (Bonatti 2004, Section 5). FP2 programs enjoy the following unique combination of properties: (i) the ability of expressing predicates with infinite extensions; (ii) full support for predicates with arbitrary arity; (iii) decidability of FP2 membership checking; (iv) decidability of skeptical and credulous stable model reasoning for call-safe queries. Odd cycles are supported by composing FP2 programs with argument restricted programs.

ASP (): Answer Set Programming with Algebraic Constraints

10.1017/s1471068420000393 ◽

2020 ◽

Vol 20 (6) ◽

pp. 895-910

Author(s):

THOMAS EITER ◽

RAFAEL KIESEL

Keyword(s):

Problem Solving ◽

Answer Set Programming ◽

Qualitative Information ◽

Algebraic Computation ◽

Generic Framework ◽

Algebraic Constraints ◽

Effective Problem ◽

AbstractWeighted Logic is a powerful tool for the specification of calculations over semirings that depend on qualitative information. Using a novel combination of Weighted Logic and Here-and-There (HT) Logic, in which this dependence is based on intuitionistic grounds, we introduce Answer Set Programming with Algebraic Constraints (ASP($\mathcal A \mathcal C$)), where rules may contain constraints that compare semiring values to weighted formula evaluations. Such constraints provide streamlined access to a manifold of constructs available in ASP, like aggregates, choice constraints, and arithmetic operators. They extend some of them and provide a generic framework for defining programs with algebraic computation, which can be fruitfully used e.g. for provenance semantics of datalog programs. While undecidable in general, expressive fragments of ASP($\mathcal A \mathcal C$) can be exploited for effective problem solving in a rich framework.

Thedlvhexsystem for knowledge representation: recent advances (system description)

10.1017/s1471068416000211 ◽

2016 ◽

Vol 16 (5-6) ◽

pp. 866-883 ◽

Cited By ~ 2

Author(s):

CHRISTOPH REDL

Keyword(s):

Knowledge Representation ◽

Real World ◽

Answer Set Programming ◽

Current Status ◽

System Description ◽

Recent Advances ◽

Real World Applications ◽

External Sources ◽

AbstractThedlvhexsystem implements thehex-semantics, which integrates answer set programming (ASP) with arbitrary external sources. Since its first release ten years ago, significant advancements were achieved. Most importantly, the exploitation of properties of external sources led to efficiency improvements and flexibility enhancements of the language, and technical improvements on the system side increased user's convenience. In this paper, we present the current status of the system and point out the most important recent enhancements over early versions. While existing literature focuses on theoretical aspects and specific components, a bird's eye view of the overall system is missing. In order to promote the system for real-world applications, we further present applications which were already successfully realized on top ofdlvhex.

Targeted Memory Reactivation During Sleep Improves Next-Day Problem Solving

Psychological Science ◽

10.1177/0956797619873344 ◽

2019 ◽

Vol 30 (11) ◽

pp. 1616-1624 ◽

Cited By ~ 2

Author(s):

Kristin E. G. Sanders ◽

Samuel Osburn ◽

Ken A. Paller ◽

Mark Beeman

Keyword(s):

Information Processing ◽

Problem Solving ◽

Empirical Support ◽

Memory Studies ◽

Difficult Problem ◽

New Technique ◽

Current Experiment ◽

Memory Reactivation ◽

Puzzle Solving ◽

A New Technique

Many people have claimed that sleep has helped them solve a difficult problem, but empirical support for this assertion remains tentative. The current experiment tested whether manipulating information processing during sleep impacts problem incubation and solving. In memory studies, delivering learning-associated sound cues during sleep can reactivate memories. We therefore predicted that reactivating previously unsolved problems could help people solve them. In the evening, we presented 57 participants with puzzles, each arbitrarily associated with a different sound. While participants slept overnight, half of the sounds associated with the puzzles they had not solved were surreptitiously presented. The next morning, participants solved 31.7% of cued puzzles, compared with 20.5% of uncued puzzles (a 55% improvement). Moreover, cued-puzzle solving correlated with cued-puzzle memory. Overall, these results demonstrate that cuing puzzle information during sleep can facilitate solving, thus supporting sleep’s role in problem incubation and establishing a new technique to advance understanding of problem solving and sleep cognition.

Towards automated integration of guess and check programs in answer set programming: a meta-interpreter and applications

10.1017/s1471068405002577 ◽

2006 ◽

Vol 6 (1-2) ◽

pp. 23-60 ◽

Cited By ~ 12

Author(s):

THOMAS EITER ◽

AXEL POLLERES

Keyword(s):

Problem Solving ◽

Logic Program ◽

Answer Set Programming ◽

Polynomial Hierarchy ◽

Logic Programs ◽

Complete Problems ◽

Polynomial Size ◽

Disjunctive Logic Programs ◽

Np Complete ◽

Answer set programming (ASP) with disjunction offers a powerful tool for declaratively representing and solving hard problems. Many NP-complete problems can be encoded in the answer set semantics of logic programs in a very concise and intuitive way, where the encoding reflects the typical “guess and check” nature of NP problems: The property is encoded in a way such that polynomial size certificates for it correspond to stable models of a program. However, the problem-solving capacity of full disjunctive logic programs (DLPs) is beyond NP, and captures a class of problems at the second level of the polynomial hierarchy. While these problems also have a clear “guess and check” structure, finding an encoding in a DLP reflecting this structure may sometimes be a non-obvious task, in particular if the “check” itself is a co-NP-complete problem; usually, such problems are solved by interleaving separate guess and check programs, where the check is expressed by inconsistency of the check program. In this paper, we present general transformations of head-cycle free (extended) disjunctive logic programs into stratified and positive (extended) disjunctive logic programs based on meta-interpretation techniques. The answer sets of the original and the transformed program are in simple correspondence, and, moreover, inconsistency of the original program is indicated by a designated answer set of the transformed program. Our transformations facilitate the integration of separate “guess” and “check” programs, which are often easy to obtain, automatically into a single disjunctive logic program. Our results complement recent results on meta-interpretation in ASP, and extend methods and techniques for a declarative “guess and check” problem solving paradigm through ASP.

Better Paracoherent Answer Sets with Less Resources

10.1017/s1471068419000176 ◽

2019 ◽

Vol 19 (5-6) ◽

pp. 757-772 ◽

Cited By ~ 1

Author(s):

GIOVANNI AMENDOLA ◽

CARMINE DODARO ◽

FRANCESCO RICCA

Keyword(s):

Problem Solving ◽

Equilibrium Model ◽

State Of The Art ◽

Answer Set Programming ◽

Evaluation Technique ◽

Answer Set Semantics ◽

Computational Resources ◽

Answer Sets ◽

Modeling Feature ◽

AbstractAnswer Set Programming (ASP) is a well-established formalism for logic programming. Problem solving in ASP requires to write an ASP program whose answers sets correspond to solutions. Albeit the non-existence of answer sets for some ASP programs can be considered as a modeling feature, it turns out to be a weakness in many other cases, and especially for query answering. Paracoherent answer set semantics extend the classical semantics of ASP to draw meaningful conclusions also from incoherent programs, with the result of increasing the range of applications of ASP. State of the art implementations of paracoherent ASP adopt the semi-equilibrium semantics, but cannot be lifted straightforwardly to compute efficiently the (better) split semi-equilibrium semantics that discards undesirable semi-equilibrium models. In this paper an efficient evaluation technique for computing a split semi-equilibrium model is presented. An experiment on hard benchmarks shows that better paracoherent answer sets can be computed consuming less computational resources than existing methods.