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

2018 ◽  
Vol 18 (3-4) ◽  
pp. 571-588 ◽  
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 ◽  
Answer Set

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.

scholarly journals Meta-Interpretive Learning Using HEX-Programs

2019 ◽  
Author(s):  
Tobias Kaminski ◽  
Thomas Eiter ◽  
Katsumi Inoue
Keyword(s):  
Logic Programming ◽  
Inductive Logic Programming ◽  
Inductive Logic ◽  
Answer Set Programming ◽  
Search Space ◽  
Recent Approach ◽  
Performance Gains ◽  
Pruning Techniques ◽  
Answer Set

Meta-Interpretive Learning (MIL) is a recent approach for Inductive Logic Programming (ILP) implemented in Prolog. Alternatively, MIL-problems can be solved by using Answer Set Programming (ASP), which may result in performance gains due to efficient conflict propagation. However, a straightforward MIL-encoding results in a huge size of the ground program and search space. To address these challenges, we encode MIL in the HEX-extension of ASP, which mitigates grounding issues, and we develop novel pruning techniques.

scholarly journals Disjunctive answer set solvers via templates

2015 ◽  
Vol 16 (4) ◽  
pp. 465-497 ◽  
Author(s):  
REMI BROCHENIN ◽  
MARCO MARATEA ◽  
YULIYA LIERLER
Keyword(s):  
Answer Set Programming ◽  
Declarative Programming ◽  
Stable Model ◽  
Combinatorial Search ◽  
Logic Programs ◽  
Transition Systems ◽  
Satisfiability Solvers ◽  
Programming Paradigm ◽  
New Ideas ◽  
Answer Set

AbstractAnswer set programming is a declarative programming paradigm oriented towards difficult combinatorial search problems. A fundamental task in answer set programming is to compute stable models, i.e., solutions of logic programs. Answer set solvers are the programs that perform this task. The problem of deciding whether a disjunctive program has a stable model is ΣP2-complete. The high complexity of reasoning within disjunctive logic programming is responsible for few solvers capable of dealing with such programs, namely dlv, gnt, cmodels, clasp and wasp. In this paper, we show that transition systems introduced by Nieuwenhuis, Oliveras, and Tinelli to model and analyze satisfiability solvers can be adapted for disjunctive answer set solvers. Transition systems give a unifying perspective and bring clarity in the description and comparison of solvers. They can be effectively used for analyzing, comparing and proving correctness of search algorithms as well as inspiring new ideas in the design of disjunctive answer set solvers. In this light, we introduce a general template, which accounts for major techniques implemented in disjunctive solvers. We then illustrate how this general template captures solvers dlv, gnt, and cmodels. We also show how this framework provides a convenient tool for designing new solving algorithms by means of combinations of techniques employed in different solvers.

scholarly journals Lazy-Grounding for Answer Set Programs with External Source Access

2017 ◽  
Author(s):  
Thomas Eiter ◽  
Tobias Kaminski ◽  
Antonius Weinzierl
Keyword(s):  
Efficient Solution ◽  
Answer Set Programming ◽  
External Source ◽  
Logic Programs ◽  
Real World Application ◽  
Input Program ◽  
Evaluation Algorithm ◽  
External Sources ◽  
New Perspective ◽  
Answer Set

HEX-programs enrich the well-known Answer Set Programming (ASP) paradigm. In HEX, problems are solved using nonmonotonic logic programs with bidirectional access to external sources. ASP evaluation is traditionally based on grounding the input program first, but recent advances in lazy-grounding make the latter also interesting for HEX, as the grounding bottleneck of ASP may be avoided. We explore this issue and present a new evaluation algorithm for HEX-programs based on lazy-grounding solving for ASP. Nonmonotonic dependencies and value invention (i.e., import of new constants) from external sources make an efficient solution nontrivial. However, illustrative benchmarks show a clear advantage of the new algorithm for grounding-intense programs, which is a new perspective to make HEX more suitable for real-world application needs.

scholarly journals Query Answering with Guarded Existential Rules under Stable Model Semantics

2020 ◽  
Vol 34 (03) ◽  
pp. 3017-3024
Author(s):  
Hai Wan ◽  
Guohui Xiao ◽  
Chenglin Wang ◽  
Xianqiao Liu ◽  
Junhong Chen ◽  
...  
Keyword(s):  
Answer Set Programming ◽  
Query Answering ◽  
Prototype System ◽  
Stable Model ◽  
Logic Programs ◽  
Termination Problem ◽  
Answer Set

In this paper, we study the problem of query answering with guarded existential rules (also called GNTGDs) under stable model semantics. Our goal is to use existing answer set programming (ASP) solvers. However, ASP solvers handle only finitely-ground logic programs while the program translated from GNTGDs by Skolemization is not in general. To address this challenge, we introduce two novel notions of (1) guarded instantiation forest to describe the instantiation of GNTGDs and (2) prime block to characterize the repeated infinitely-ground program translated from GNTGDs. Using these notions, we prove that the ground termination problem for GNTGDs is decidable. We also devise an algorithm for query answering with GNTGDs using ASP solvers. We have implemented our approach in a prototype system. The evaluation over a set of benchmarks shows encouraging results.

Phase Transitions for Quantum Search Algorithms

2005 ◽  
Author(s):  
Tad Hogg
Keyword(s):  
Phase Transitions ◽  
Computational Cost ◽  
Search Space ◽  
Search Algorithms ◽  
Quantum Search ◽  
Combinatorial Search ◽  
Problem Structure ◽  
Search Problems ◽  
Quantum Search Algorithms ◽  
The Many

Phase transitions have long been studied empirically in various combinatorial searches and theoretically in simplified models [91, 264, 301, 490]. The analogy with statistical physics [397], explored throughout this volume, shows how the many local choices made during search relate to global properties such as the resulting search cost. These studies have led to a better understanding of typical search behaviors [514] and improved search methods [195, 247, 261, 432, 433]. Among the current research questions in this field are the range of algorithms exhibiting the transition behavior and the algorithm-independent problem properties associated with the difficult instances concentrated near the transition. Towards this end, the present chapter examines quantum computer [123, 126, 158, 486] algorithms for nondeterministic polynomial (NP) combinatorial search problems [191]. As with many conventional methods, they exhibit the easy-hard-easy pattern of computational cost as the degree of constraint in the problems varies. We describe how properties of the search space affect the algorithms and identify an additional structural property, the energy gap, motivated by one quantum algorithm but applicable to a variety of techniques, both quantum and classical. Thus, the study of quantum search algorithms not only extends the range of algorithms exhibiting phase transitions, but also helps identify underlying structural properties. Specifically, the next two sections describe a class of hard search problems and the form of quantum search algorithms proposed to date. The remainder of the chapter presents algorithm behaviors, relevant problem structure, arid an approximate asymptotic analysis of their cost scaling. The final section discusses various open issues in designing and evaluating quantum algorithms, and relating their behavior to problem structure. The k-satisfiability (k -SAT) problem, as discussed earlier in this volume, consists of n Boolean variables and m clauses. A clause is a logical OR of k variables, each of which may be negated. A solution is an assignment, that is, a value for each variable, TRUE or FALSE, satisfying all the clauses. An assignment is said to conflict with any clause it does not satisfy.

scholarly journals onlineSPARC: A Programming Environment for Answer Set Programming

2018 ◽  
Vol 19 (2) ◽  
pp. 262-289 ◽  
Author(s):  
ELIAS MARCOPOULOS ◽  
YUANLIN ZHANG
Keyword(s):  
High School Students ◽  
Logic Programming ◽  
Answer Set Programming ◽  
Programming Environment ◽  
Logic Programs ◽  
School Students ◽  
Major Barrier ◽  
Simple Interface ◽  
Answer Sets ◽  
Answer Set

AbstractRecent progress in logic programming (e.g. the development of the answer set programming (ASP) paradigm) has made it possible to teach it to general undergraduate and even middle/high school students. Given the limited exposure of these students to computer science, the complexity of downloading, installing, and using tools for writing logic programs could be a major barrier for logic programming to reach a much wider audience. We developed onlineSPARC, an online ASP environment with a self-contained file system and a simple interface. It allows users to type/edit logic programs and perform several tasks over programs, including asking a query to a program, getting the answer sets of a program, and producing a drawing/animation based on the answer sets of a program.

scholarly journals A decidable subclass of finitary programs

2010 ◽  
Vol 10 (4-6) ◽  
pp. 481-496 ◽  
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 ◽  
Answer Set

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.

scholarly journals Explanation Generation for Multi-Modal Multi-Agent Path Finding with Optimal Resource Utilization using Answer Set Programming

2020 ◽  
Vol 20 (6) ◽  
pp. 974-989
Author(s):  
AYSU BOGATARKAN ◽  
ESRA ERDEM
Keyword(s):  
Answer Set Programming ◽  
Search Problem ◽  
Path Finding ◽  
Combinatorial Search ◽  
Transportation Modes ◽  
Optimal Resource ◽  
Multi Agent ◽  
Nonexistence Of Solutions ◽  
Velocity Constraints ◽  
Answer Set

AbstractThe multi-agent path finding (MAPF) problem is a combinatorial search problem that aims at finding paths for multiple agents (e.g., robots) in an environment (e.g., an autonomous warehouse) such that no two agents collide with each other, and subject to some constraints on the lengths of paths. We consider a general version of MAPF, called mMAPF, that involves multi-modal transportation modes (e.g., due to velocity constraints) and consumption of different types of resources (e.g., batteries). The real-world applications of mMAPF require flexibility (e.g., solving variations of mMAPF) as well as explainability. Our earlier studies on mMAPF have focused on the former challenge of flexibility. In this study, we focus on the latter challenge of explainability, and introduce a method for generating explanations for queries regarding the feasibility and optimality of solutions, the nonexistence of solutions, and the observations about solutions. Our method is based on answer set programming.

scholarly journals A model building framework for answer set programming with external computations

2015 ◽  
Vol 16 (4) ◽  
pp. 418-464 ◽  
Author(s):  
THOMAS EITER ◽  
MICHAEL FINK ◽  
GIOVAMBATTISTA IANNI ◽  
THOMAS KRENNWALLNER ◽  
CHRISTOPH REDL ◽  
...  
Keyword(s):  
Model Building ◽  
External Source ◽  
Software Systems ◽  
Logic Programs ◽  
New Approach ◽  
Evaluation Approach ◽  
Real World Application ◽  
External Sources ◽  
Model Graph ◽  
Answer Set

AbstractAs software systems are getting increasingly connected, there is a need for equipping nonmonotonic logic programs with access to external sources that are possibly remote and may contain information in heterogeneous formats. To cater for this need,hexprograms were designed as a generalization of answer set programs with an API style interface that allows to access arbitrary external sources, providing great flexibility. Efficient evaluation of such programs however is challenging, and it requires to interleave external computation and model building; to decide when to switch between these tasks is difficult, and existing approaches have limited scalability in many real-world application scenarios. We present a new approach for the evaluation of logic programs with external source access, which is based on a configurable framework for dividing the non-ground program into possibly overlapping smaller parts called evaluation units. The latter will be processed by interleaving external evaluation and model building using an evaluation graph and a model graph, respectively, and by combining intermediate results. Experiments with our prototype implementation show a significant improvement compared to previous approaches. While designed forhex-programs, the new evaluation approach may be deployed to related rule-based formalisms as well.

scholarly journals Reasoning with Forest Logic Programs and f-hybrid knowledge bases

2011 ◽  
Vol 13 (3) ◽  
pp. 395-463
Author(s):  
CRISTINA FEIER ◽  
STIJN HEYMANS
Keyword(s):  
Answer Set Programming ◽  
Knowledge Bases ◽  
Logic Programs ◽  
Decidability Result ◽  
Tree Shape ◽  
Alternative Approach ◽  
Hybrid Framework ◽  
Hybrid Knowledge ◽  
Satisfiability Checking ◽  
Answer Set

AbstractOpen Answer Set Programming (OASP) is an undecidable framework for integrating ontologies and rules. Although several decidable fragments of OASP have been identified, few reasoning procedures exist. In this paper, we provide a sound, complete, and terminating algorithm for satisfiability checking w.r.t. Forest Logic Programs (FoLPs), a fragment of OASP where rules have a tree shape and allow for inequality atoms and constants. The algorithm establishes a decidability result for FoLPs. Although believed to be decidable, so far only the decidability for two small subsets of FoLPs, local FoLPs and acyclic FoLPs, has been shown. We further introduce f-hybrid knowledge bases, a hybrid framework where knowledge bases and FoLPs coexist, and we show that reasoning with such knowledge bases can be reduced to reasoning with FoLPs only. We note that f-hybrid knowledge bases do not require the usual (weakly) DL-safety of the rule component, thus providing a genuine alternative approach to current integration approaches of ontologies and rules.

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