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 Abstract Solvers for Computing Cautious Consequences of ASP programs

2019 ◽  
Vol 19 (5-6) ◽  
pp. 740-756
Author(s):  
GIOVANNI AMENDOLA ◽  
CARMINE DODARO ◽  
MARCO MARATEA
Keyword(s):  
State Of The Art ◽  
Answer Set Programming ◽  
Satisfiability Modulo Theories ◽  
Benchmark Problems ◽  
Propositional Satisfiability ◽  
New Techniques ◽  
The Past ◽  
Boolean Formulas ◽  
Reasoning Tasks ◽  
Answer Set

AbstractAbstract solvers are a method to formally analyze algorithms that have been profitably used for describing, comparing and composing solving techniques in various fields such as Propositional Satisfiability (SAT), Quantified SAT, Satisfiability Modulo Theories, Answer Set Programming (ASP), and Constraint ASP.In this paper, we design, implement and test novel abstract solutions for cautious reasoning tasks in ASP. We show how to improve the current abstract solvers for cautious reasoning in ASP with new techniques borrowed from backbone computation in SAT, in order to design new solving algorithms. By doing so, 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. We implement some of the new solutions in the ASP solver wasp and show that their performance are comparable to state-of-the-art solutions on the benchmark problems from the past ASP Competitions.

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 Harnessing Incremental Answer Set Solving for Reasoning in Assumption-Based Argumentation

2021 ◽  
pp. 1-18
Author(s):  
TUOMO LEHTONEN ◽  
JOHANNES P. WALLNER ◽  
MATTI JӒRVISALO
Keyword(s):  
Logic Programming ◽  
Answer Set Programming ◽  
Polynomial Hierarchy ◽  
Np Hard ◽  
Abstraction Refinement ◽  
Recent Advances ◽  
Structured Argumentation ◽  
Reasoning Tasks ◽  
Answer Set

Abstract Assumption-based argumentation (ABA) is a central structured argumentation formalism. As shown recently, answer set programming (ASP) enables efficiently solving NP-hard reasoning tasks of ABA in practice, in particular in the commonly studied logic programming fragment of ABA. In this work, we harness recent advances in incremental ASP solving for developing effective algorithms for reasoning tasks in the logic programming fragment of ABA that are presumably hard for the second level of the polynomial hierarchy, including skeptical reasoning under preferred semantics as well as preferential reasoning. In particular, we develop non-trivial counterexample-guided abstraction refinement procedures based on incremental ASP solving for these tasks. We also show empirically that the procedures are significantly more effective than previously proposed algorithms for the tasks.

scholarly journals Fuzzy answer set computation via satisfiability modulo theories

2015 ◽  
Vol 15 (4-5) ◽  
pp. 588-603 ◽  
Author(s):  
MARIO ALVIANO ◽  
RAFAEL PEÑALOZA
Keyword(s):  
Fuzzy Logic ◽  
Structural Properties ◽  
Answer Set Programming ◽  
Satisfiability Modulo Theories ◽  
Prototype System ◽  
Imprecise Information ◽  
Fuzzy Connectives ◽  
Answer Set

AbstractFuzzy answer set programming (FASP) combines two declarative frameworks, answer set programming and fuzzy logic, in order to model reasoning by default over imprecise information. Several connectives are available to combine different expressions; in particular the Gödel and Łukasiewicz fuzzy connectives are usually considered, due to their properties. Although the Gödel conjunction can be easily eliminated from rule heads, we show through complexity arguments that such a simplification is infeasible in general for all other connectives. The paper analyzes a translation of FASP programs into satisfiability modulo theories (SMT), which in general produces quantified formulas because of the minimality of the semantics. Structural properties of many FASP programs allow to eliminate the quantification, or to sensibly reduce the number of quantified variables. Indeed, integrality constraints can replace recursive rules commonly used to force Boolean interpretations, and completion subformulas can guarantee minimality for acyclic programs with atomic heads. Moreover, head cycle free rules can be replaced by shifted subprograms, whose structure depends on the eliminated head connective, so that ordered completion may replace the minimality check if also Łukasiewicz disjunction in rule bodies is acyclic. The paper also presents and evaluates a prototype system implementing these translations.

scholarly journals Answer Set Programming Based on Propositional Satisfiability

2006 ◽  
Vol 36 (4) ◽  
pp. 345-377 ◽  
Author(s):  
Enrico Giunchiglia ◽  
Yuliya Lierler ◽  
Marco Maratea
Keyword(s):  
Answer Set Programming ◽  
Propositional Satisfiability ◽  
Answer Set

scholarly journals Planning with Incomplete Information in Quantified Answer Set Programming

2021 ◽  
pp. 1-17
Author(s):  
JORGE FANDINNO ◽  
FRANCOIS LAFERRIERE ◽  
JAVIER ROMERO ◽  
TORSTEN SCHAUB ◽  
TRAN CAO SON
Keyword(s):  
Incomplete Information ◽  
Answer Set Programming ◽  
Transition Function ◽  
Logic Programs ◽  
Quantified Boolean Formulas ◽  
Boolean Formulas ◽  
Simple Formalism ◽  
Planning Problems ◽  
Answer Set ◽  
Conditional Planning

Abstract We present a general approach to planning with incomplete information in Answer Set Programming (ASP). More precisely, we consider the problems of conformant and conditional planning with sensing actions and assumptions. We represent planning problems using a simple formalism where logic programs describe the transition function between states, the initial states and the goal states. For solving planning problems, we use Quantified Answer Set Programming (QASP), an extension of ASP with existential and universal quantifiers over atoms that is analogous to Quantified Boolean Formulas (QBFs). We define the language of quantified logic programs and use it to represent the solutions different variants of conformant and conditional planning. On the practical side, we present a translation-based QASP solver that converts quantified logic programs into QBFs and then executes a QBF solver, and we evaluate experimentally the approach on conformant and conditional planning benchmarks.

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.

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