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.

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.

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 Conflict-driven ASP Solving with External Sources and Program Splits

2017 ◽  
Author(s):  
Christoph Redl
Keyword(s):  
Problem Solving ◽  
Nonmonotonic Reasoning ◽  
Answer Set Programming ◽  
New Technique ◽  
External Sources ◽  
A New Technique ◽  
Program Components ◽  
Answer Set

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.

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 Better Paracoherent Answer Sets with Less Resources

2019 ◽  
Vol 19 (5-6) ◽  
pp. 757-772 ◽  
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 ◽  
Answer Set

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.

scholarly journals Omission-Based Abstraction for Answer Set Programs

2020 ◽  
pp. 1-51 ◽  
Author(s):  
ZEYNEP G. SARIBATUR ◽  
THOMAS EITER
Keyword(s):  
Problem Solving ◽  
Answer Set Programming ◽  
Search Space ◽  
Complex Problem ◽  
Experimental Results ◽  
Partial Answer ◽  
Abstraction Refinement ◽  
The Cost ◽  
Answer Sets ◽  
Answer Set

Abstract Abstraction is a well-known approach to simplify a complex problem by over-approximating it with a deliberate loss of information. It was not considered so far in Answer Set Programming (ASP), a convenient tool for problem solving. We introduce a method to automatically abstract ASP programs that preserves their structure by reducing the vocabulary while ensuring an over-approximation (i.e., each original answer set maps to some abstract answer set). This allows for generating partial answer set candidates that can help with approximation of reasoning. Computing the abstract answer sets is intuitively easier due to a smaller search space, at the cost of encountering spurious answer sets. Faithful (non-spurious) abstractions may be used to represent projected answer sets and to guide solvers in answer set construction. For dealing with spurious answer sets, we employ an ASP debugging approach to help with abstraction refinement, which determines atoms as badly omitted and adds them back in the abstraction. As a show case, we apply abstraction to explain unsatisfiability of ASP programs in terms of blocker sets, which are the sets of atoms such that abstraction to them preserves unsatisfiability. Their usefulness is demonstrated by experimental results.

scholarly journals Answering the “why” in answer set programming – A survey of explanation approaches

2019 ◽  
Vol 19 (2) ◽  
pp. 114-203 ◽  
Author(s):  
JORGE FANDINNO ◽  
CLAUDIA SCHULZ
Keyword(s):  
Artificial Intelligence ◽  
Decision Making ◽  
Problem Solving ◽  
Data Protection ◽  
Answer Set Programming ◽  
General Data Protection Regulation ◽  
Causal Graphs ◽  
General Data ◽  
Similarities And Differences ◽  
Answer Set

AbstractArtificial intelligence (AI) approaches to problem-solving and decision-making are becoming more and more complex, leading to a decrease in the understandability of solutions. The European Union’s new General Data Protection Regulation tries to tackle this problem by stipulating a “right to explanation” for decisions made by AI systems. One of the AI paradigms that may be affected by this new regulation is answer set programming (ASP). Thanks to the emergence of efficient solvers, ASP has recently been used for problem-solving in a variety of domains, including medicine, cryptography, and biology. To ensure the successful application of ASP as a problem-solving paradigm in the future, explanations of ASP solutions are crucial. In this survey, we give an overview of approaches that provide an answer to the question ofwhyan answer set is a solution to a given problem, notably off-line justifications, causal graphs, argumentative explanations, and why-not provenance, and highlight their similarities and differences. Moreover, we review methods explaining why a set of literals isnotan answer set or why no solution exists at all.

as Input Language for Answer Set Solvers

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 ◽  
Answer Set

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(·).

scholarly journals Answer Set Programming in a Nutshell

10.29007/tmt3 ◽  
2018 ◽  
Author(s):  
Thomas Eiter
Keyword(s):  
Problem Solving ◽  
Common Sense ◽  
Transitive Closure ◽  
Logic Program ◽  
Answer Set Programming ◽  
Sat Solving ◽  
Common Sense Reasoning ◽  
Recent Developments ◽  
Basic Concepts ◽  
Answer Set

Answer Set Programming (ASP) has emerged in the recent years as a powerful paradigm for declarative problem solving, which has its roots in knowledge representation and non-monotonic logic programming. Similar to SAT solving, the basic idea is to encode solutions to a problem in the models of a non-monotonic logic program, which can be computed by reasoning engines off the shelf. ASP is particularly well-suited for modeling and solving problems which involve common sense reasoning or transitive closure, and has been fruitfully applied to a growing range of applications. Among the latter are also problems in testing and verfication, for which efficient core fragments of ASP that embrace Datalog haven been exploited. This talk gives a brief introduction to ASP, covering the basic concepts, some of its properties and features, and solvers. It further addresses some applications in the context of verification and recent developments in ASP, which bring evaluation closer to other formalisms and logics.

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