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 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.

scholarly journals Knowledge Forgetting in Answer Set Programming

2014 ◽  
Vol 50 ◽  
pp. 31-70 ◽  
Author(s):  
Y. Wang ◽  
Y. Zhang ◽  
Y. Zhou ◽  
M. Zhang
Keyword(s):  
Logic Program ◽  
Answer Set Programming ◽  
Irrelevant Information ◽  
Semantic Knowledge ◽  
Decision Problems ◽  
Stable Model ◽  
Logic Programs ◽  
Knowledge Based ◽  
Substitution Principle ◽  
Answer Set

The ability of discarding or hiding irrelevant information has been recognized as an important feature for knowledge based systems, including answer set programming. The notion of strong equivalence in answer set programming plays an important role for different problems as it gives rise to a substitution principle and amounts to knowledge equivalence of logic programs. In this paper, we uniformly propose a semantic knowledge forgetting, called HT- and FLP-forgetting, for logic programs under stable model and FLP-stable model semantics, respectively. Our proposed knowledge forgetting discards exactly the knowledge of a logic program which is relevant to forgotten variables. Thus it preserves strong equivalence in the sense that strongly equivalent logic programs will remain strongly equivalent after forgetting the same variables. We show that this semantic forgetting result is always expressible; and we prove a representation theorem stating that the HT- and FLP-forgetting can be precisely characterized by Zhang-Zhou's four forgetting postulates under the HT- and FLP-model semantics, respectively. We also reveal underlying connections between the proposed forgetting and the forgetting of propositional logic, and provide complexity results for decision problems in relation to the forgetting. An application of the proposed forgetting is also considered in a conflict solving scenario.

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

2006 ◽  
Vol 6 (1-2) ◽  
pp. 23-60 ◽  
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

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.

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 Complexity and compilation of GZ-aggregates in answer set programming

2015 ◽  
Vol 15 (4-5) ◽  
pp. 574-587 ◽  
Author(s):  
MARIO ALVIANO ◽  
NICOLA LEONE
Keyword(s):  
Answer Set Programming ◽  
Vicious Circle ◽  
Prototype System ◽  
Stable Model ◽  
Logic Programs ◽  
Vicious Circle Principle ◽  
Similarities And Differences ◽  
Compilation Techniques ◽  
Answer Set

AbstractGelfond and Zhang recently proposed a new stable model semantics based on Vicious Circle Principle in order to improve the interpretation of logic programs with aggregates. The paper focuses on this proposal, and analyzes the complexity of both coherence testing and cautious reasoning under the new semantics. Some surprising results highlight similarities and differences versus mainstream stable model semantics for aggregates. Moreover, the paper reports on the design of compilation techniques for implementing the new semantics on top of existing ASP solvers, which eventually lead to realize a prototype system that allows for experimenting with Gelfond-Zhang's aggregates.

scholarly journals Grounding and Solving in Answer Set Programming

AI Magazine ◽  
2016 ◽  
Vol 37 (3) ◽  
pp. 25-32 ◽  
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

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.

Action language ℬ𝒞+

2015 ◽  
Vol 30 (4) ◽  
pp. 899-922 ◽  
Author(s):  
Joseph Babb ◽  
Joohyung Lee
Keyword(s):  
Main Idea ◽  
Answer Set Programming ◽  
Stable Model ◽  
Formal Models ◽  
Transition Systems ◽  
Action Languages ◽  
Action Language ◽  
Language Constructs ◽  
High Level ◽  
Answer Set

Abstract Action languages are formal models of parts of natural language that are designed to describe effects of actions. Many of these languages can be viewed as high-level notations of answer set programs structured to represent transition systems. However, the form of answer set programs considered in the earlier work is quite limited in comparison with the modern Answer Set Programming (ASP) language, which allows several useful constructs for knowledge representation, such as choice rules, aggregates and abstract constraint atoms. We propose a new action language called BC +, which closes the gap between action languages and the modern ASP language. The main idea is to define the semantics of BC + in terms of general stable model semantics for propositional formulas, under which many modern ASP language constructs can be identified with shorthands for propositional formulas. Language BC  + turns out to be sufficiently expressive to encompass the best features of other action languages, such as languages B , C , C + and BC . Computational methods available in ASP solvers are readily applicable to compute BC +, which led to an implementation of the language by extending system cplus2asp .

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 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 ASP (): Answer Set Programming with Algebraic Constraints

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 ◽  
Answer Set

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.

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