scholarly journals Dual-normal logic programs – the forgotten class

2015 ◽  
Vol 15 (4-5) ◽  
pp. 495-510 ◽  
Author(s):  
JOHANNES K. FICHTE ◽  
MIROSŁAW TRUSZCZYŃSKI ◽  
STEFAN WOLTRAN
Keyword(s):  
Answer Set Programming ◽  
Expressive Power ◽  
Declarative Programming ◽  
The Novel ◽  
Logic Programs ◽  
Programming Paradigm ◽  
Normal Logic ◽  
Consistency Problem ◽  
Theoretical Standpoint ◽  
Answer Set

AbstractDisjunctive Answer Set Programming is a powerful declarative programming paradigm with complexity beyond NP. Identifying classes of programs for which the consistency problem is in NP is of interest from the theoretical standpoint and can potentially lead to improvements in the design of answer set programming solvers. One of such classes consists of dual-normal programs, where the number of positive body atoms in proper rules is at most one. Unlike other classes of programs, dual-normal programs have received little attention so far. In this paper we study this class. We relate dual-normal programs to propositional theories and to normal programs by presenting several inter-translations. With the translation from dual-normal to normal programs at hand, we introduce the novel class of body-cycle free programs, which are in many respects dual to head-cycle free programs. We establish the expressive power of dual-normal programs in terms of SE- and UE-models, and compare them to normal programs. We also discuss the complexity of deciding whether dual-normal programs are strongly and uniformly equivalent.

scholarly journals Inconsistency Proofs for ASP: The ASP - DRUPE Format

2019 ◽  
Vol 19 (5-6) ◽  
pp. 891-907
Author(s):  
MARIO ALVIANO ◽  
CARMINE DODARO ◽  
JOHANNES K. FICHTE ◽  
MARKUS HECHER ◽  
TOBIAS PHILIPP ◽  
...  
Keyword(s):  
Logic Program ◽  
Answer Set Programming ◽  
Boolean Satisfiability ◽  
Logic Programs ◽  
Disjunctive Logic Programs ◽  
Normal Logic ◽  
Consistency Problem ◽  
Unit Propagation ◽  
Answer Sets ◽  
Answer Set

AbstractAnswer Set Programming (ASP) solvers are highly-tuned and complex procedures that implicitly solve the consistency problem, i.e., deciding whether a logic program admits an answer set. Verifying whether a claimed answer set is formally a correct answer set of the program can be decided in polynomial time for (normal) programs. However, it is far from immediate to verify whether a program that is claimed to be inconsistent, indeed does not admit any answer sets. In this paper, we address this problem and develop the new proof format ASP-DRUPE for propositional, disjunctive logic programs, including weight and choice rules. ASP-DRUPE is based on the Reverse Unit Propagation (RUP) format designed for Boolean satisfiability. We establish correctness of ASP-DRUPE and discuss how to integrate it into modern ASP solvers. Later, we provide an implementation of ASP-DRUPE into the wasp solver for normal logic programs.

Answer Sets and the Language of Answer Set Programming

AI Magazine ◽  
2016 ◽  
Vol 37 (3) ◽  
pp. 7-12 ◽  
Author(s):  
Vladimir Lifschitz
Keyword(s):  
Answer Set Programming ◽  
Declarative Programming ◽  
Logic Programs ◽  
Special Issue ◽  
Programming Paradigm ◽  
Introductory Article ◽  
Answer Set Semantics ◽  
Answer Sets ◽  
Semantics Of Logic Programs ◽  
Answer Set

Answer set programming is a declarative programming paradigm based on the answer set semantics of logic programs. This introductory article provides the mathematical background for the discussion of answer set programming in other contributions to this special issue.

scholarly journals Disjunctive answer set solvers via templates

2015 ◽  
Vol 16 (4) ◽  
pp. 465-497 ◽  
Author(s):  
REMI BROCHENIN ◽  
MARCO MARATEA ◽  
YULIYA LIERLER
Keyword(s):  
Answer Set Programming ◽  
Declarative Programming ◽  
Stable Model ◽  
Combinatorial Search ◽  
Logic Programs ◽  
Transition Systems ◽  
Satisfiability Solvers ◽  
Programming Paradigm ◽  
New Ideas ◽  
Answer Set

AbstractAnswer set programming is a declarative programming paradigm oriented towards difficult combinatorial search problems. A fundamental task in answer set programming is to compute stable models, i.e., solutions of logic programs. Answer set solvers are the programs that perform this task. The problem of deciding whether a disjunctive program has a stable model is ΣP2-complete. The high complexity of reasoning within disjunctive logic programming is responsible for few solvers capable of dealing with such programs, namely dlv, gnt, cmodels, clasp and wasp. In this paper, we show that transition systems introduced by Nieuwenhuis, Oliveras, and Tinelli to model and analyze satisfiability solvers can be adapted for disjunctive answer set solvers. Transition systems give a unifying perspective and bring clarity in the description and comparison of solvers. They can be effectively used for analyzing, comparing and proving correctness of search algorithms as well as inspiring new ideas in the design of disjunctive answer set solvers. In this light, we introduce a general template, which accounts for major techniques implemented in disjunctive solvers. We then illustrate how this general template captures solvers dlv, gnt, and cmodels. We also show how this framework provides a convenient tool for designing new solving algorithms by means of combinations of techniques employed in different solvers.

scholarly journals Using linear constraints for logic program termination analysis

2016 ◽  
Vol 16 (3) ◽  
pp. 353-377 ◽  
Author(s):  
MARCO CALAUTTI ◽  
SERGIO GRECO ◽  
CRISTIAN MOLINARO ◽  
IRINA TRUBITSYNA
Keyword(s):  
Global Analysis ◽  
Logic Program ◽  
Answer Set Programming ◽  
Expressive Power ◽  
Linear Constraints ◽  
The Body ◽  
The Novel ◽  
Logic Programs ◽  
Infinite Domains ◽  
Program Termination

AbstractIt is widely acknowledged that function symbols are an important feature in answer set programming, as they make modelling easier, increase the expressive power, and allow us to deal with infinite domains. The main issue with their introduction is that the evaluation of a program might not terminate and checking whether it terminates or not is undecidable. To cope with this problem, several classes of logic programs have been proposed where the use of function symbols is restricted but the program evaluation termination is guaranteed. Despite the significant body of work in this area, current approaches do not include many simple practical programs whose evaluation terminates. In this paper, we present the novel classes ofrule-boundedandcycle-bounded programs, which overcome different limitations of current approaches by performing a more global analysis of how terms are propagated from the body to the head of rules. Results on the correctness, the complexity, and the expressivity of the proposed approach are provided.

scholarly journals Extended ASP Tableaux and rule redundancy in normal logic programs

2008 ◽  
Vol 8 (5-6) ◽  
pp. 691-716 ◽  
Author(s):  
MATTI JÄRVISALO ◽  
EMILIA OIKARINEN
Keyword(s):  
Answer Set Programming ◽  
Proof System ◽  
Logic Programs ◽  
Interesting Insight ◽  
Extension Rule ◽  
Normal Logic ◽  
Relationship Of ◽  
The Relationship ◽  
Resolution Proof ◽  
Answer Set

AbstractWe introduce an extended tableau calculus for answer set programming (ASP). The proof system is based on the ASP tableaux defined in the work by Gebser and Schaub (Tableau calculi for answer set programming. In Proceedings of the 22nd International Conference on Logic Programming (ICLP 2006), S. Etalle and M. Truszczynski, Eds. Lecture Notes in Computer Science, vol. 4079. Springer, 11–25) with an added extension rule. We investigate the power of Extended ASP Tableaux both theoretically and empirically. We study the relationship of Extended ASP Tableaux with the Extended Resolution proof system defined by Tseitin for sets of clauses, and separate Extended ASP Tableaux from ASP Tableaux by giving a polynomial-length proof for a family of normal logic programs {Φn} for which ASP Tableaux has exponential-length minimal proofs with respect to n. Additionally, Extended ASP Tableaux imply interesting insight into the effect of program simplification on the lengths of proofs in ASP. Closely related to Extended ASP Tableaux, we empirically investigate the effect of redundant rules on the efficiency of ASP solving.

scholarly journals Relating Multi-Adjoint Normal Logic Programs to Core Fuzzy Answer Set Programs from a Semantical Approach

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 881
Author(s):  
M. Eugenia Cornejo ◽  
David Lobo ◽  
Jesús Medina
Keyword(s):  
Fuzzy Logic ◽  
Logic Programming ◽  
Programming Language ◽  
Answer Set Programming ◽  
Logic Programs ◽  
The Core ◽  
Normal Logic ◽  
Answer Sets ◽  
Stable Models ◽  
Answer Set

This paper relates two interesting paradigms in fuzzy logic programming from a semantical approach: core fuzzy answer set programming and multi-adjoint normal logic programming. Specifically, it is shown how core fuzzy answer set programs can be translated into multi-adjoint normal logic programs and vice versa, preserving the semantics of the starting program. This translation allows us to combine the expressiveness of multi-adjoint normal logic programming with the compactness and simplicity of the core fuzzy answer set programming language. As a consequence, theoretical properties and results which relate the answer sets to the stable models of the respective logic programming frameworks are obtained. Among others, this study enables the application of the existence theorem of stable models developed for multi-adjoint normal logic programs to ensure the existence of answer sets in core fuzzy answer set programs.

scholarly journals Functional answer set programming

2011 ◽  
Vol 11 (2-3) ◽  
pp. 203-233 ◽  
Author(s):  
PEDRO CABALAR
Keyword(s):  
General Framework ◽  
Answer Set Programming ◽  
Direct Connection ◽  
Logic Programs ◽  
Safety Condition ◽  
Normal Logic ◽  
Answer Set

AbstractIn this paper we propose an extension of Answer Set Programming (ASP) to deal with (possibly partial) evaluable functions. To this aim, we start from the most general logical counterpart of ASP, Quantified Equilibrium Logic (QEL), and propose a variant QEL=ℱwhere the set of functions is partitioned into Herbrand functions (orconstructors) and evaluable functions (oroperations). We show how this extension has a direct connection to Scott'sLogic of Existence, and introduce several useful derived operators, some of them directly borrowed from Scott's formalisation. Using this general framework for arbitrary theories, we proceed to focus on a syntactic subclass that corresponds to normal logic programs with evaluable functions and equality. We provide a translation of this class into function-free normal programs and consider a safety condition so that the resulting program is also safe, under the usual meaning in ASP. Finally, we also establish a formal comparison to Lin and Wang's approach (FASP) dealing with evaluable total functions.

scholarly journals Guarded resolution for Answer Set Programming

2010 ◽  
Vol 11 (1) ◽  
pp. 111-123 ◽  
Author(s):  
V. W. MAREK ◽  
J. B. REMMEL
Keyword(s):  
Answer Set Programming ◽  
Proof System ◽  
Logic Programs ◽  
Resolution Rule ◽  
Theoretic Concept ◽  
Stable Semantics ◽  
Normal Logic ◽  
Propositional Theory ◽  
Stable Models ◽  
Answer Set

AbstractWe investigate a proof system based on a guarded resolution rule and show its adequacy for the stable semantics of normal logic programs. As a consequence, we show that Gelfond–Lifschitz operator can be viewed as a proof-theoretic concept. As an application, we find a propositional theory EP whose models are precisely stable models of programs. We also find a class of propositional theories 𝓒P with the following properties. Propositional models of theories in 𝓒P are precisely stable models of P, and the theories in 𝓒T are of the size linear in the size of P.

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 Query Answering with Guarded Existential Rules under Stable Model Semantics

2020 ◽  
Vol 34 (03) ◽  
pp. 3017-3024
Author(s):  
Hai Wan ◽  
Guohui Xiao ◽  
Chenglin Wang ◽  
Xianqiao Liu ◽  
Junhong Chen ◽  
...  
Keyword(s):  
Answer Set Programming ◽  
Query Answering ◽  
Prototype System ◽  
Stable Model ◽  
Logic Programs ◽  
Termination Problem ◽  
Answer Set

In this paper, we study the problem of query answering with guarded existential rules (also called GNTGDs) under stable model semantics. Our goal is to use existing answer set programming (ASP) solvers. However, ASP solvers handle only finitely-ground logic programs while the program translated from GNTGDs by Skolemization is not in general. To address this challenge, we introduce two novel notions of (1) guarded instantiation forest to describe the instantiation of GNTGDs and (2) prime block to characterize the repeated infinitely-ground program translated from GNTGDs. Using these notions, we prove that the ground termination problem for GNTGDs is decidable. We also devise an algorithm for query answering with GNTGDs using ASP solvers. We have implemented our approach in a prototype system. The evaluation over a set of benchmarks shows encouraging results.

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