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

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.

2018 ◽  
Vol 19 (2) ◽  
pp. 262-289 ◽  
Author(s):  
ELIAS MARCOPOULOS ◽  
YUANLIN ZHANG

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.


2019 ◽  
Vol 19 (5-6) ◽  
pp. 891-907
Author(s):  
MARIO ALVIANO ◽  
CARMINE DODARO ◽  
JOHANNES K. FICHTE ◽  
MARKUS HECHER ◽  
TOBIAS PHILIPP ◽  
...  

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.


2007 ◽  
Vol 7 (6) ◽  
pp. 697-744 ◽  
Author(s):  
TOMI JANHUNEN ◽  
EMILIA OIKARINEN

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.


Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 881
Author(s):  
M. Eugenia Cornejo ◽  
David Lobo ◽  
Jesús Medina

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.


AI Magazine ◽  
2016 ◽  
Vol 37 (3) ◽  
pp. 25-32 ◽  
Author(s):  
Benjamin Kaufmann ◽  
Nicola Leone ◽  
Simona Perri ◽  
Torsten Schaub

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.


2009 ◽  
pp. 2261-2267
Author(s):  
Fernando Zacarías Flores ◽  
Dionicio Zacarías Flores ◽  
Rosalba Cuapa Canto ◽  
Luis Miguel Guzmán Muñoz

Updates, is a central issue in relational databases and knowledge databases. In the last years, it has been well studied in the non-monotonic reasoning paradigm. Several semantics for logic program updates have been proposed (Brewka, Dix, & Knonolige 1997), (De Schreye, Hermenegildo, & Pereira, 1999) (Katsumo & Mendelzon, 1991). However, recently a set of proposals has been characterized to propose mechanisms of updates based on logic and logic programming. All these mechanisms are built on semantics based on structural properties (Eiter, Fink, Sabattini & Thompits, 2000) (Leite, 2002) (Banti, Alferes & Brogi, 2003) (Zacarias, 2005). Furthermore, all these semantic ones coincide in considering the AGM proposal as the standard model in the update theory, for their wealth in properties. The AGM approach, introduced in (Alchourron, Gardenfors & Makinson, 1985) is the dominating paradigm in the area, but in the context of monotonic logic. All these proposals analyze and reinterpret the AGM postulates under the Answer Set Programming (ASP) such as (Eiter, Fink, Sabattini & Thompits, 2000). However, the majority of the adapted AGM and update postulates are violated by update programs, as shown in(De Schreye, Hermenegildo, & Pereira, 1999).


2019 ◽  
Vol 19 (5-6) ◽  
pp. 688-704
Author(s):  
GIOVANNI AMENDOLA ◽  
FRANCESCO RICCA

AbstractIn the last years, abstract argumentation has met with great success in AI, since it has served to capture several non-monotonic logics for AI. Relations between argumentation framework (AF) semantics and logic programming ones are investigating more and more. In particular, great attention has been given to the well-known stable extensions of an AF, that are closely related to the answer sets of a logic program. However, if a framework admits a small incoherent part, no stable extension can be provided. To overcome this shortcoming, two semantics generalizing stable extensions have been studied, namely semi-stable and stage. In this paper, we show that another perspective is possible on incoherent AFs, called paracoherent extensions, as they have a counterpart in paracoherent answer set semantics. We compare this perspective with semi-stable and stage semantics, by showing that computational costs remain unchanged, and moreover an interesting symmetric behaviour is maintained.


2015 ◽  
Vol 16 (1) ◽  
pp. 59-110 ◽  
Author(s):  
CLAUDIA SCHULZ ◽  
FRANCESCA TONI

AbstractAn answer set is a plain set of literals which has no further structure that would explain why certain literals are part of it and why others are not. We show how argumentation theory can help to explain why a literal is or is not contained in a given answer set by defining two justification methods, both of which make use of the correspondence between answer sets of a logic program and stable extensions of the assumption-based argumentation (ABA) framework constructed from the same logic program.Attack Treesjustify a literal in argumentation-theoretic terms, i.e. using arguments and attacks between them, whereasABA-Based Answer Set Justificationsexpress the same justification structure in logic programming terms, that is using literals and their relationships. Interestingly, an ABA-Based Answer Set Justification corresponds to an admissible fragment of the answer set in question, and an Attack Tree corresponds to an admissible fragment of the stable extension corresponding to this answer set.


2006 ◽  
Vol 6 (1-2) ◽  
pp. 61-106 ◽  
Author(s):  
KATHRIN KONCZAK ◽  
THOMAS LINKE ◽  
TORSTEN SCHAUB

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.


2014 ◽  
Vol 50 ◽  
pp. 31-70 ◽  
Author(s):  
Y. Wang ◽  
Y. Zhang ◽  
Y. Zhou ◽  
M. Zhang

The ability of discarding or hiding irrelevant information has been recognized as an important feature for knowledge based systems, including answer set programming. The notion of strong equivalence in answer set programming plays an important role for different problems as it gives rise to a substitution principle and amounts to knowledge equivalence of logic programs. In this paper, we uniformly propose a semantic knowledge forgetting, called HT- and FLP-forgetting, for logic programs under stable model and FLP-stable model semantics, respectively. Our proposed knowledge forgetting discards exactly the knowledge of a logic program which is relevant to forgotten variables. Thus it preserves strong equivalence in the sense that strongly equivalent logic programs will remain strongly equivalent after forgetting the same variables. We show that this semantic forgetting result is always expressible; and we prove a representation theorem stating that the HT- and FLP-forgetting can be precisely characterized by Zhang-Zhou's four forgetting postulates under the HT- and FLP-model semantics, respectively. We also reveal underlying connections between the proposed forgetting and the forgetting of propositional logic, and provide complexity results for decision problems in relation to the forgetting. An application of the proposed forgetting is also considered in a conflict solving scenario.


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