11 research outputs found
Relating Constraint Answer Set Programming Languages and Algorithms
Recently a logic programming language AC was proposed by Mellarkod et al. (2008) to integrate answer set programming and constraint logic programming. Soon after that, a CLINGCON language integrating answer set programming and finite domain constraints, as well as an EZCSP language integrating answer set programming and constraint logic programming were introduced. The development of these languages and systems constitutes the appearance of a new AI subarea called constraint answer set programming. All these languages have something in common. In particular, they aim at developing new efficient inference algorithms that combine traditional answer set programming procedures and other methods in constraint programming. Yet, the exact relation between the constraint answer set programming languages and the underlying systems is not well understood. In this paper we address this issue by formally stating the precise relation between several constraint answer set programming languages - AC, CLINGCON, EZCSP - as well as the underlying systems
On Relation between Constraint Answer Set Programming and Satisfiability Modulo Theories
Constraint 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 booster 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.Comment: Under consideration in Theory and Practice of Logic Programming
(TPLP
CASP Solutions for Planning in Hybrid Domains
CASP is an extension of ASP that allows for numerical constraints to be added
in the rules. PDDL+ is an extension of the PDDL standard language of automated
planning for modeling mixed discrete-continuous dynamics.
In this paper, we present CASP solutions for dealing with PDDL+ problems,
i.e., encoding from PDDL+ to CASP, and extensions to the algorithm of the EZCSP
CASP solver in order to solve CASP programs arising from PDDL+ domains. An
experimental analysis, performed on well-known linear and non-linear variants
of PDDL+ domains, involving various configurations of the EZCSP solver, other
CASP solvers, and PDDL+ planners, shows the viability of our solution.Comment: Under consideration in Theory and Practice of Logic Programming
(TPLP
Technical Communications of ICLP
Abstract Abstract solvers are a recently employed method to formally analyze algorithms that earns some advantages w.r.t. traditional ways such as pseudo-code-based description. Abstract solvers proved to be a useful tool for describing, comparing and composing solving techniques in various fields such as SAT, SMT, ASP, CASP. In ASP, abstract solvers have been so far employed for describing solvers for brave reasoning tasks. In this paper we apply, for the first time, this methodology to the analysis of ASP solvers for cautious reasoning tasks. We describe and compare the available approaches in the literature, which employ techniques for computing over-and under-approximations of the solution, the last including "coherence tests" for deciding the inclusion of a single atom in the solution, a technique borrowed from backbone computation of CNF formulas. Then, we show how to improve the current abstract solvers with new techniques, in order to design new solving algorithms
On the semantics of hybrid ASP systems based on Clingo
[Abstract]: Over the last decades, the development of Answer Set Programming (ASP) has brought about an expressive modeling language powered by highly performant systems. At the same time, it gets more and more difficult to provide semantic underpinnings capturing the resulting constructs and inferences. This is even more severe when it comes to hybrid ASP languages and systems that are often needed to handle real-world applications. We address this challenge and introduce the concept of abstract and structured theories that allow us to formally elaborate upon their integration with ASP. We then use this concept to make the semantic characterization of clingo’s theory-reasoning framework precise. This provides us with a formal framework in which we can elaborate upon the formal properties of existing hybridizations of clingo, such as clingcon, clingo[dl], and clingo[lp].This work was supported by DFG grant SCHA 550/11, Germany, by grant PID2020-116201GB-I00 funded by MCIN/AEI/ 10.13039/501100011033, Spain, by Xunta de Galicia and the European Union, GPC ED431B 2022/33, by European COST action CA17124 DigForASP, EU, and by the National Science Foundation (NSF 95-3101-0060-402), USA.Xunta de Galicia; ED431B 2022/33Deutsche Forschungsgemeinschaft; SCHA 550/11United States. National Science Foundation; NSF 95-3101-0060-40
The EZSMT Solver: Constraint Answer Set Solving meets SMT
Constraint 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 thesis, by connecting these two areas, we begin the cross-fertilization of not only of the theoretical foundations of both areas but also of the existing solving technologies. We present the system EZSMT, one of the first solvers of this nature, which is able to take a large class of constraint answer set programs and rewrite them into Satisfiability Modulo Theories programs so that Satisfiability Modulo Theories technology can be used to process these programs
ASP(AC): Answer Set Programming with Algebraic Constraints
Weighted 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(AC)), 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(AC)
can be exploited for effective problem-solving in a rich framework. This work
is under consideration for acceptance in Theory and Practice of Logic
Programming.Comment: 32 pages, 16 pages are appendi