scholarly journals On relation between constraint answer set programming and satisfiability modulo theories

2017 ◽  
Vol 17 (4) ◽  
pp. 559-590
Author(s):  
YULIYA LIERLER ◽  
BENJAMIN SUSMAN
Keyword(s):  
Answer Set Programming ◽  
Research Direction ◽  
Linear Constraints ◽  
Satisfiability Modulo Theories ◽  
Research Areas ◽  
Formal Relation ◽  
Answer Sets ◽  
Theoretical Foundations ◽  
Cross Fertilization ◽  
Answer Set

AbstractConstraint answer set programming is a promising research direction that integrates answer set programming with constraint processing. It is often informally related to the field of satisfiability modulo theories. Yet, the exact formal link is obscured as the terminology and concepts used in these two research areas differ. In this paper, we connect these two research areas by uncovering the precise formal relation between them. We believe that this work will boost the cross-fertilization of the theoretical foundations and the existing solving methods in both areas. As a step in this direction, we provide a translation from constraint answer set programs with integer linear constraints to satisfiability modulo linear integer arithmetic that paves the way to utilizing modern satisfiability modulo theories solvers for computing answer sets of constraint answer set programs.

scholarly journals Constraint Answer Set Programming: Integrational and Translational (or SMT-based) Approaches

2021 ◽  
pp. 1-31
Author(s):  
YULIYA LIERLER
Keyword(s):  
Automated Reasoning ◽  
Hybrid Approach ◽  
Answer Set Programming ◽  
Satisfiability Modulo Theories ◽  
Declarative Programming ◽  
Scheduling Problems ◽  
New Horizons ◽  
Research Areas ◽  
Constraint Processing ◽  
Answer Set

Abstract Constraint answer set programming or CASP, for short, is a hybrid approach in automated reasoning putting together the advances of distinct research areas such as answer set programming, constraint processing, and satisfiability modulo theories. CASP demonstrates promising results, including the development of a multitude of solvers: acsolver, clingcon, ezcsp, idp, inca, dingo, mingo, aspmt2smt, clingo[l,dl], and ezsmt. It opens new horizons for declarative programming applications such as solving complex train scheduling problems. Systems designed to find solutions to constraint answer set programs can be grouped according to their construction into, what we call, integrational or translational approaches. The focus of this paper is an overview of the key ingredients of the design of constraint answer set solvers drawing distinctions and parallels between integrational and translational approaches. The paper also provides a glimpse at the kind of programs its users develop by utilizing a CASP encoding of Traveling Salesman problem for illustration. In addition, we place the CASP technology on the map among its automated reasoning peers as well as discuss future possibilities for the development of CASP.

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 Formal Approach for Cautious Reasoning in Answer Set Programming (Extended Abstract)

2020 ◽  
Author(s):  
Giovanni Amendola ◽  
Carmine Dodaro ◽  
Marco Maratea
Keyword(s):  
Answer Set Programming ◽  
Satisfiability Modulo Theories ◽  
Propositional Satisfiability ◽  
Formal Approach ◽  
Boolean Formulas ◽  
Reasoning Tasks ◽  
Answer Set

The issue of describing in a formal way solving algorithms in various fields such as Propositional Satisfiability (SAT), Quantified SAT, Satisfiability Modulo Theories, Answer Set Programming (ASP), and Constraint ASP, has been relatively recently solved employing abstract solvers. In this paper we deal with cautious reasoning tasks in ASP, and design, implement and test novel abstract solutions, borrowed from backbone computation in SAT. By employing abstract solvers, we also formally show that the algorithms for solving cautious reasoning tasks in ASP are strongly related to those for computing backbones of Boolean formulas. Some of the new solutions have been implemented in the ASP solver WASP, and tested.

scholarly journals Towards Metric Temporal Answer Set Programming

2020 ◽  
Vol 20 (5) ◽  
pp. 783-798
Author(s):  
PEDRO CABALAR ◽  
MARTÍN DIÉGUEZ ◽  
TORSTEN SCHAUB ◽  
ANNA SCHUHMANN
Keyword(s):  
Time Domain ◽  
Dynamic Logic ◽  
Answer Set Programming ◽  
Monotonic Extension ◽  
Theoretical Foundations ◽  
Answer Set

AbstractWe elaborate upon the theoretical foundations of a metric temporal extension of Answer Set Programming. In analogy to previous extensions of ASP with constructs from Linear Temporal and Dynamic Logic, we accomplish this in the setting of the logic of Here-and-There and its non-monotonic extension, called Equilibrium Logic. More precisely, we develop our logic on the same semantic underpinnings as its predecessors and thus use a simple time domain of bounded time steps. This allows us to compare all variants in a uniform framework and ultimately combine them in a common implementation.

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.

SeaLion: An eclipse-based IDE for answer-set programming with advanced debugging support

2013 ◽  
Vol 13 (4-5) ◽  
pp. 657-673 ◽  
Author(s):  
PAULA-ANDRA BUSONIU ◽  
JOHANNES OETSCH ◽  
JÖRG PÜHRER ◽  
PETER SKOČOVSKÝ ◽  
HANS TOMPITS
Keyword(s):  
Source Code ◽  
Answer Set Programming ◽  
Model Driven Engineering ◽  
Development Environment ◽  
Integrated Development ◽  
Model Driven ◽  
Class Diagrams ◽  
The Rich ◽  
Answer Sets ◽  
Answer Set

AbstractIn this paper, we present SeaLion, an integrated development environment (IDE) for answer-set programming (ASP).SeaLionprovides source-code editors for the languages ofGringoandDLVand offers popular amenities like syntax highlighting, syntax checking, code completion, visual program outline, and refactoring functionality. The tool has been realised in the context of a research project whose goal is the development of techniques to support the practical coding process of answer-set programs. In this respect,SeaLionis the first IDE for ASP that provides debugging features that work for real-world answer-set programs and supports the rich languages of modern answer-set solvers. Indeed,SeaLionimplements a stepping-based debugging approach that allows the developer to quickly track down programming errors by simply following his or her intuitions on the intended semantics. Besides that,SeaLionsupports ASP development using model-driven engineering techniques including domain modelling with extended UML class diagrams and visualisation of answer sets in corresponding instance diagrams. Moreover, customised visualisation as well as visual editing of answer sets is realised by the Kara plugin ofSeaLion. Further implemented features are a documentation generator based on the Lana annotation language, support for external solvers, and interoperability with external tools.SeaLioncomes as a plugin of the popular Eclipse platform and provides interfaces for future extensions of the IDE.

scholarly journals Learning weak constraints in answer set programming

2015 ◽  
Vol 15 (4-5) ◽  
pp. 511-525 ◽  
Author(s):  
MARK LAW ◽  
ALESSANDRA RUSSO ◽  
KRYSIA BRODA
Keyword(s):  
Inductive Logic ◽  
Answer Set Programming ◽  
Learning Task ◽  
Learning Preferences ◽  
Learning Framework ◽  
Hypothesis Space ◽  
New Learning ◽  
Weak Constraints ◽  
Answer Sets ◽  
Answer Set

AbstractThis paper contributes to the area of inductive logic programming by presenting a new learning framework that allows the learning of weak constraints in Answer Set Programming (ASP). The framework, calledLearning from Ordered Answer Sets, generalises our previous work on learning ASP programs without weak constraints, by considering a new notion of examples asorderedpairs of partial answer sets that exemplify which answer sets of a learned hypothesis (together with a given background knowledge) arepreferredto others. In this new learning task inductive solutions are searched within a hypothesis space of normal rules, choice rules, and hard and weak constraints. We propose a new algorithm, ILASP2, which is sound and complete with respect to our new learning framework. We investigate its applicability to learning preferences in an interview scheduling problem and also demonstrate that when restricted to the task of learning ASP programs without weak constraints, ILASP2 can be much more efficient than our previously proposed system.

scholarly journals Complex optimization in answer set programming

2011 ◽  
Vol 11 (4-5) ◽  
pp. 821-839 ◽  
Author(s):  
MARTIN GEBSER ◽  
ROLAND KAMINSKI ◽  
TORSTEN SCHAUB
Keyword(s):  
Computational Complexity ◽  
Answer Set Programming ◽  
Pareto Efficiency ◽  
Modeling Techniques ◽  
Complex Optimization ◽  
Answer Sets ◽  
Implementation Technique ◽  
Preference Handling ◽  
Answer Set ◽  
Qualitative Preferences

AbstractPreference handling and optimization are indispensable means for addressing nontrivial applications in Answer Set Programming (ASP). However, their implementation becomes difficult whenever they bring about a significant increase in computational complexity. As a consequence, existing ASP systems do not offer complex optimization capacities, supporting, for instance, inclusion-based minimization or Pareto efficiency. Rather, such complex criteria are typically addressed by resorting to dedicated modeling techniques, likesaturation. Unlike the ease of common ASP modeling, however, these techniques are rather involved and hardly usable by ASP laymen. We address this problem by developing a general implementation technique by means of meta-prpogramming, thus reusing existing ASP systems to capture various forms of qualitative preferences among answer sets. In this way, complex preferences and optimization capacities become readily available for ASP applications.

scholarly journals Graphs and colorings for answer set programming

2006 ◽  
Vol 6 (1-2) ◽  
pp. 61-106 ◽  
Author(s):  
KATHRIN KONCZAK ◽  
THOMAS LINKE ◽  
TORSTEN SCHAUB
Keyword(s):  
Proof Theory ◽  
Answer Set Programming ◽  
Logic Programs ◽  
Algorithmic Approach ◽  
Dependency Graphs ◽  
Basic Strategy ◽  
Content System ◽  
Formal Properties ◽  
Answer Sets ◽  
Answer Set

We investigate the usage of rule dependency graphs and their colorings for characterizing and computing answer sets of logic programs. This approach provides us with insights into the interplay between rules when inducing answer sets. We start with different characterizations of answer sets in terms of totally colored dependency graphs that differ in graph-theoretical aspects. We then develop a series of operational characterizations of answer sets in terms of operators on partial colorings. In analogy to the notion of a derivation in proof theory, our operational characterizations are expressed as (non-deterministically formed) sequences of colorings, turning an uncolored graph into a totally colored one. In this way, we obtain an operational framework in which different combinations of operators result in different formal properties. Among others, we identify the basic strategy employed by the noMoRe system and justify its algorithmic approach. Furthermore, we distinguish operations corresponding to Fitting's operator as well as to well-founded semantics.

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