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

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 ◽  
Answer Set

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.

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 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 Here and There with Arithmetic

2021 ◽  
pp. 1-15
Author(s):  
VLADIMIR LIFSCHITZ
Keyword(s):  
Programming Language ◽  
Propositional Logic ◽  
Answer Set Programming ◽  
The Other ◽  
Arithmetic Operations ◽  
First Order ◽  
The Relationship ◽  
Answer Set

Abstarct In the theory of answer set programming, two groups of rules are called strongly equivalent if, informally speaking, they have the same meaning in any context. The relationship between strong equivalence and the propositional logic of here-and-there allows us to establish strong equivalence by deriving rules of each group from rules of the other. In the process, rules are rewritten as propositional formulas. We extend this method of proving strong equivalence to an answer set programming language that includes operations on integers. The formula representing a rule in this language is a first-order formula that may contain comparison symbols among its predicate constants, and symbols for arithmetic operations among its function constants. The paper is under consideration for acceptance in TPLP.

Program completion in the input language of GRINGO

2017 ◽  
Vol 17 (5-6) ◽  
pp. 855-871 ◽  
Author(s):  
AMELIA HARRISON ◽  
VLADIMIR LIFSCHITZ ◽  
DHANANJAY RAJU
Keyword(s):  
Reverse Engineering ◽  
Large Class ◽  
Logic Program ◽  
Answer Set Programming ◽  
Program Completion ◽  
Engineering Process ◽  
Input Language ◽  
Definition Of ◽  
Answer Set

AbstractWe argue that turning a logic program into a set of completed definitions can be sometimes thought of as the “reverse engineering” process of generating a set of conditions that could serve as a specification for it. Accordingly, it may be useful to define completion for a large class of Answer Set Programming (ASP) programs and to automate the process of generating and simplifying completion formulas. Examining the output produced by this kind of software may help programmers to see more clearly what their program does, and to what degree its behavior conforms with their expectations. As a step toward this goal, we propose here a definition of program completion for a large class of programs in the input language of the ASP grounder gringo, and study its properties.

STRATEGIES TO DEFEND A PROTAGONIST OF AN EVENT

2010 ◽  
Vol 19 (04) ◽  
pp. 439-464
Author(s):  
SARA BOUTOUHAMI ◽  
DANIEL KAYSER
Keyword(s):  
Natural Language ◽  
Experimental Validation ◽  
Answer Set Programming ◽  
First Order ◽  
Starting Point ◽  
First Results ◽  
Argumentative Strategies ◽  
Complete Set ◽  
Car Accident ◽  
Answer Set

We aim at controlling the biases that exist in every description, in order to give the best possible image of one of the protagonists of an event. Starting from a supposedly complete set of propositions accounting for an event, we develop various argumentative strategies (insinuation, justification, reference to customary norms) to imply the facts that cannot be simply omitted but have the "wrong" orientation w.r.t. the protagonist we defend. By analyzing these different strategies, a contribution of this work is to provide a number of relevant parameters to take into account in developing and evaluating systems aiming at understanding natural language (NL) argumentations. The source of inspiration for this work is a corpus of 160 texts where each text describes a (different) car accident. Its result, for a given accident, is a set of first-order literals representing the essential facts of a description intended to defend one of the protagonists. An implementation in Answer Set Programming is underway. A couple of examples showing how to extract, from the same starting point, a defense for the two opposite sides are provided. Experimental validation of this work is in progress, and its first results are reported.

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.

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