scholarly journals Resilient Logic Programs: Answer Set Programs Challenged by Ontologies

2020 ◽  
Vol 34 (03) ◽  
pp. 2917-2924
Author(s):  
Sanja Lukumbuzya ◽  
Magdalena Ortiz ◽  
Mantas Šimkus
Keyword(s):  
Description Logic ◽  
Logic Program ◽  
Large Fragment ◽  
Logic Programs ◽  
First Order ◽  
Complexity Results ◽  
Answer Sets ◽  
Answer Set

We introduce resilient logic programs (RLPs) that couple a non-monotonic logic program and a first-order (FO) theory or description logic (DL) ontology. Unlike previous hybrid languages, where the interaction between the program and the theory is limited to consistency or query entailment tests, in RLPs answer sets must be ‘resilient’ to the models of the theory, allowing non-output predicates of the program to respond differently to different models. RLPs can elegantly express ∃∀∃-QBFs, disjunctive ASP, and configuration problems under incompleteness of information. RLPs are decidable when a couple of natural assumptions are made: (i) satisfiability of FO theories in the presence of closed predicates is decidable, and (ii) rules are safe in the style of the well-known DL-safeness. We further show that a large fragment of such RLPs can be translated into standard (disjunctive) ASP, for which efficient implementations exist. For RLPs with theories expressed in DLs, we use a novel relaxation of safeness that safeguards rules via predicates whose extensions can be inferred to have a finite bound. We present several complexity results for the case where ontologies are written in some standard DLs.

scholarly journals Optimizing Answer Set Computation via Heuristic-Based Decomposition

2019 ◽  
Vol 19 (04) ◽  
pp. 603-628 ◽  
Author(s):  
FRANCESCO CALIMERI ◽  
SIMONA PERRI ◽  
JESSICA ZANGARI
Keyword(s):  
Logic Programming ◽  
Logic Program ◽  
Answer Set Programming ◽  
Decomposition Techniques ◽  
Logic Programs ◽  
Experimental Activity ◽  
Performance Of Systems ◽  
Answer Sets ◽  
The Impact ◽  
Answer Set

AbstractAnswer Set Programming (ASP) is a purely declarative formalism developed in the field of logic programming and non-monotonic reasoning: computational problems are encoded by logic programs whose answer sets, corresponding to solutions, are computed by an ASP system. Different, semantically equivalent, programs can be defined for the same problem; however, performance of systems evaluating them might significantly vary. We propose an approach for automatically transforming an input logic program into an equivalent one that can be evaluated more efficiently. One can make use of existing tree-decomposition techniques for rewriting selected rules into a set of multiple ones; the idea is to guide and adaptively apply them on the basis of proper new heuristics, to obtain a smart rewriting algorithm to be integrated into an ASP system. The method is rather general: it can be adapted to any system and implement different preference policies. Furthermore, we define a set of new heuristics tailored at optimizing grounding, one of the main phases of the ASP computation; we use them in order to implement the approach into the ASP systemDLV, in particular into its grounding subsystemℐ-DLV, and carry out an extensive experimental activity for assessing the impact of the proposal.

scholarly journals A program-level approach to revising logic programs under the answer set semantics

2010 ◽  
Vol 10 (4-6) ◽  
pp. 565-580 ◽  
Author(s):  
JAMES P. DELGRANDE
Keyword(s):  
Logic Program ◽  
Fundamental Principle ◽  
Logic Programs ◽  
Minimal Set ◽  
Essential Idea ◽  
The One ◽  
Answer Set Semantics ◽  
Answer Sets ◽  
Update Logic ◽  
Answer Set

AbstractAn approach to the revision of logic programs under the answer set semantics is presented. For programs P and Q, the goal is to determine the answer sets that correspond to the revision of P by Q, denoted P * Q. A fundamental principle of classical (AGM) revision, and the one that guides the approach here, is the success postulate. In AGM revision, this stipulates that α ∈ K * α. By analogy with the success postulate, for programs P and Q, this means that the answer sets of Q will in some sense be contained in those of P * Q. The essential idea is that for P * Q, a three-valued answer set for Q, consisting of positive and negative literals, is first determined. The positive literals constitute a regular answer set, while the negated literals make up a minimal set of naf literals required to produce the answer set from Q. These literals are propagated to the program P, along with those rules of Q that are not decided by these literals. The approach differs from work in update logic programs in two main respects. First, we ensure that the revising logic program has higher priority, and so we satisfy the success postulate; second, for the preference implicit in a revision P * Q, the program Q as a whole takes precedence over P, unlike update logic programs, since answer sets of Q are propagated to P. We show that a core group of the AGM postulates are satisfied, as are the postulates that have been proposed for update logic programs.

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.

scholarly journals Temporal logic programs with variables

2016 ◽  
Vol 17 (2) ◽  
pp. 226-243 ◽  
Author(s):  
FELICIDAD AGUADO ◽  
PEDRO CABALAR ◽  
GILBERTO PÉREZ ◽  
CONCEPCIÓN VIDAL ◽  
MARTÍN DIÉGUEZ
Keyword(s):  
Temporal Logic ◽  
Linear Time ◽  
Logic Program ◽  
Answer Set Programming ◽  
Logic Programs ◽  
First Order ◽  
Linear Time Temporal Logic ◽  
Definition Of ◽  
Stable Models ◽  
Answer Set

AbstractIn this note, we consider the problem of introducing variables in temporal logic programs under the formalism of Temporal Equilibrium Logic, an extension of Answer Set Programming for dealing with linear-time modal operators. To this aim, we provide a definition of a first-order version of Temporal Equilibrium Logic that shares the syntax of first-order Linear-time Temporal Logic but has different semantics, selecting some Linear-time Temporal Logic models we call temporal stable models. Then, we consider a subclass of theories (called splittable temporal logic programs) that are close to usual logic programs but allowing a restricted use of temporal operators. In this setting, we provide a syntactic definition of safe variables that suffices to show the property of domain independence – that is, addition of arbitrary elements in the universe does not vary the set of temporal stable models. Finally, we present a method for computing the derivable facts by constructing a non-temporal logic program with variables that is fed to a standard Answer Set Programming grounder. The information provided by the grounder is then used to generate a subset of ground temporal rules which is equivalent to (and generally smaller than) the full program instantiation.

scholarly journals Modeling and Language Extensions

AI Magazine ◽  
2016 ◽  
Vol 37 (3) ◽  
pp. 33-44 ◽  
Author(s):  
Martin Gebser ◽  
Torsten Schaub
Keyword(s):  
Expressive Language ◽  
Logic Program ◽  
Answer Set Programming ◽  
Stable Model ◽  
Logic Programs ◽  
First Order ◽  
High Level Modeling ◽  
High Level ◽  
Answer Sets ◽  
First Order Variables

Answer set programming (ASP) has emerged as an approach to declarative problem solving based on the stable model semantics for logic programs. The basic idea is to represent a computational problem by a logic program, formulating constraints in terms of rules, such that its answer sets correspond to problem solutions. To this end, ASP combines an expressive language for high-level modeling with powerful low-level reasoning capacities, provided by off-the-shelf tools. Compact problem representations take advantage of genuine modeling features of ASP, including (first-order) variables, negation by default, and recursion. In this article, we demonstrate the ASP methodology on two example scenarios, illustrating basic as well as advanced modeling and solving concepts. We also discuss mechanisms to represent and implement extended kinds of preferences and optimization. An overview of further available extensions concludes the article.

scholarly journals A Semantic Characterization ASP Base Revision

2019 ◽  
Vol 66 ◽  
pp. 989-1029
Author(s):  
Laurent Garcia ◽  
Claire Lefèvre ◽  
Igor Stéphan ◽  
Odile Papini ◽  
Éric Würbel
Keyword(s):  
Classical Logic ◽  
Answer Set Programming ◽  
Semantic Content ◽  
Logic Programs ◽  
Rule Based ◽  
Complexity Results ◽  
Base Revision ◽  
Answer Sets ◽  
Answer Set

The paper deals with base revision for Answer Set Programming (ASP). Base revision in classical logic is done by the removal of formulas. Exploiting the non-monotonicity of ASP allows one to propose other revision strategies, namely addition strategy or removal and/or addition strategy. These strategies allow one to define families of rule-based revision operators. The paper presents a semantic characterization of these families of revision operators in terms of answer sets. This semantic characterization allows for equivalently considering the evolution of syntactic logic programs and the evolution of their semantic content. It then studies the logical properties of the proposed operators and gives complexity results.  

scholarly journals Automated Verification of Weak Equivalence within thesmodelsSystem

2007 ◽  
Vol 7 (6) ◽  
pp. 697-744 ◽  
Author(s):  
TOMI JANHUNEN ◽  
EMILIA OIKARINEN
Keyword(s):  
Search Engine ◽  
Logic Program ◽  
General Setting ◽  
Answer Set Programming ◽  
Weak Equivalence ◽  
Logic Programs ◽  
Meta Level ◽  
Level Problem ◽  
Answer Sets ◽  
Answer Set

AbstractIn answer set programming (ASP), a problem at hand is solved by (i) writing a logic program whose answer sets correspond to the solutions of the problem, and by (ii) computing the answer sets of the program using ananswer set solveras a search engine. Typically, a programmer creates a series of gradually improving logic programs for a particular problem when optimizing program length and execution time on a particular solver. This leads the programmer to a meta-level problem of ensuring that the programs are equivalent, i.e., they give rise to the same answer sets. To ease answer set programming at methodological level, we propose a translation-based method for verifying the equivalence of logic programs. The basic idea is to translate logic programsPandQunder consideration into a single logic program EQT(P,Q) whose answer sets (if such exist) yield counter-examples to the equivalence ofPandQ. The method is developed here in a slightly more general setting by taking thevisibilityof atoms properly into account when comparing answer sets. The translation-based approach presented in the paper has been implemented as a translator calledlpeqthat enables the verification of weak equivalence within thesmodelssystem using the same search engine as for the search of models. Our experiments withlpeqandsmodelssuggest that establishing the equivalence of logic programs in this way is in certain cases much faster than naive cross-checking of answer sets.

scholarly journals Loop formulas for description logic programs

2010 ◽  
Vol 10 (4-6) ◽  
pp. 531-545 ◽  
Author(s):  
YISONG WANG ◽  
JIA-HUAI YOU ◽  
LI YAN YUAN ◽  
YI-DONG SHEN
Keyword(s):  
Semantic Web ◽  
Description Logic ◽  
Description Logics ◽  
Answer Set Programming ◽  
Desirable Property ◽  
Logic Programs ◽  
Alternative Semantics ◽  
Answer Set Semantics ◽  
Answer Sets ◽  
Answer Set

AbstractDescription Logic Programs (dl-programs) proposed by Eiter et al. constitute an elegant yet powerful formalism for the integration of answer set programming with description logics, for the Semantic Web. In this paper, we generalize the notions of completion and loop formulas of logic programs to description logic programs and show that the answer sets of a dl-program can be precisely captured by the models of its completion and loop formulas. Furthermore, we propose a new, alternative semantics for dl-programs, called the canonical answer set semantics, which is defined by the models of completion that satisfy what are called canonical loop formulas. A desirable property of canonical answer sets is that they are free of circular justifications. Some properties of canonical answer sets are also explored.

scholarly journals Conflict-driven ASP solving with external sources

2012 ◽  
Vol 12 (4-5) ◽  
pp. 659-679 ◽  
Author(s):  
THOMAS EITER ◽  
MICHAEL FINK ◽  
THOMAS KRENNWALLNER ◽  
CHRISTOPH REDL
Keyword(s):  
Description Logic ◽  
Logic Program ◽  
External Source ◽  
External Information ◽  
Logic Programs ◽  
Learning Techniques ◽  
Bidirectional Communication ◽  
Meta Information ◽  
External Sources ◽  
Answer Set

AbstractAnswer Set Programming (ASP) is a well-known problem solving approach based on nonmonotonic logic programs and efficient solvers. To enable access to external information,hex-programs extend programs withexternal atoms, which allow for a bidirectional communication between the logic program and external sources of computation (e.g., description logic reasoners and Web resources). Current solvers evaluatehex-programs by a translation to ASP itself, in which values of external atoms are guessed and verified after the ordinary answer set computation. This elegant approach does not scale with the number of external accesses in general, in particular in presence of nondeterminism (which is instrumental for ASP). In this paper, we present a novel, native algorithm for evaluatinghex-programs which uses learning techniques. In particular, we extend conflict-driven ASP solving techniques, which prevent the solver from running into the same conflict again, from ordinary tohex-programs. We show how to gain additional knowledge from external source evaluations and how to use it in a conflict-driven algorithm. We first target the uninformed case, i.e., when we have no extra information on external sources, and then extend our approach to the case where additional meta-information is available. Experiments show that learning from external sources can significantly decrease both the runtime and the number of considered candidate compatible sets.

scholarly journals ASPeRiX, a first-order forward chaining approach for answer set computing

2017 ◽  
Vol 17 (3) ◽  
pp. 266-310 ◽  
Author(s):  
CLAIRE LEFÈVRE ◽  
CHRISTOPHER BÉATRIX ◽  
IGOR STÉPHAN ◽  
LAURENT GARCIA
Keyword(s):  
Logic Program ◽  
Combinatorial Problem ◽  
First Order ◽  
Forward Chaining ◽  
Almost All ◽  
Answer Sets ◽  
Theoretical Foundations ◽  
Preliminary Phase ◽  
Natural Way ◽  
Answer Set

AbstractThe natural way to use Answer Set Programming (ASP) to represent knowledge in Artificial Intelligence or to solve a combinatorial problem is to elaborate a first-order logic program with default negation. In a preliminary step, this program with variables is translated in an equivalent propositional one by a first tool: the grounder. Then, the propositional program is given to a second tool: the solver. This last one computes (if they exist) one or many answer sets (stable models) of the program, each answer set encoding one solution of the initial problem. Until today, almost all ASP systems apply this two steps computation. In this article, the projectASPeRiX. is presented as a first-order forward chaining approach for Answer Set Computing. This project was among the first to introduce an approach of answer set computing that escapes the preliminary phase of rule instantiation by integrating it in the search process. The methodology applies a forward chaining of first-order rules that are grounded on the fly by means of previously produced atoms. Theoretical foundations of the approach are presented, the main algorithms of the ASP solverASPeRiX. are detailed and some experiments and comparisons with existing systems are provided.

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