scholarly journals Module theorem for the general theory of stable models

2012 ◽  
Vol 12 (4-5) ◽  
pp. 719-735 ◽  
Author(s):  
JOSEPH BABB ◽  
JOOHYUNG LEE
Keyword(s):  
General Theory ◽  
General Class ◽  
Answer Set Programming ◽  
Splitting Theorem ◽  
Logic Programs ◽  
Input Output ◽  
Answer Sets ◽  
Output Interface ◽  
Stable Models ◽  
Answer Set

AbstractThe module theorem by Janhunen et al. demonstrates how to provide a modular structure in answer set programming, where each module has a well-defined input/output interface which can be used to establish the compositionality of answer sets. The theorem is useful in the analysis of answer set programs, and is a basis of incremental grounding and reactive answer set programming. We extend the module theorem to the general theory of stable models by Ferraris et al. The generalization applies to non-ground logic programs allowing useful constructs in answer set programming, such as choice rules, the count aggregate, and nested expressions. Our extension is based on relating the module theorem to the symmetric splitting theorem by Ferraris et al. Based on this result, we reformulate and extend the theory of incremental answer set computation to a more general class of programs.

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 onlineSPARC: A Programming Environment for Answer Set Programming

2018 ◽  
Vol 19 (2) ◽  
pp. 262-289 ◽  
Author(s):  
ELIAS MARCOPOULOS ◽  
YUANLIN ZHANG
Keyword(s):  
High School Students ◽  
Logic Programming ◽  
Answer Set Programming ◽  
Programming Environment ◽  
Logic Programs ◽  
School Students ◽  
Major Barrier ◽  
Simple Interface ◽  
Answer Sets ◽  
Answer Set

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.

scholarly journals Graphs and colorings for answer set programming

2006 ◽  
Vol 6 (1-2) ◽  
pp. 61-106 ◽  
Author(s):  
KATHRIN KONCZAK ◽  
THOMAS LINKE ◽  
TORSTEN SCHAUB
Keyword(s):  
Proof Theory ◽  
Answer Set Programming ◽  
Logic Programs ◽  
Algorithmic Approach ◽  
Dependency Graphs ◽  
Basic Strategy ◽  
Content System ◽  
Formal Properties ◽  
Answer Sets ◽  
Answer Set

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.

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 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 Applications of intuitionistic logic in Answer Set Programming

2004 ◽  
Vol 4 (3) ◽  
pp. 325-354 ◽  
Author(s):  
MAURICIO OSORIO ◽  
JUAN A. NAVARRO ◽  
JOSÉ ARRAZOLA
Keyword(s):  
Recent Result ◽  
Intuitionistic Logic ◽  
Answer Set Programming ◽  
Minimal Models ◽  
Logic Programs ◽  
Intermediate Logics ◽  
Answer Set Semantics ◽  
Answer Sets ◽  
Answer Set

We present some applications of intermediate logics in the field of Answer Set Programming (ASP). A brief, but comprehensive introduction to the answer set semantics, intuitionistic and other intermediate logics is given. Some equivalence notions and their applications are discussed. Some results on intermediate logics are shown, and applied later to prove properties of answer sets. A characterization of answer sets for logic programs with nested expressions is provided in terms of intuitionistic provability, generalizing a recent result given by Pearce. It is known that the answer set semantics for logic programs with nested expressions may select non-minimal models. Minimal models can be very important in some applications, therefore we studied them; in particular we obtain a characterization, in terms of intuitionistic logic, of answer sets which are also minimal models. We show that the logic G3 characterizes the notion of strong equivalence between programs under the semantic induced by these models. Finally we discuss possible applications and consequences of our results. They clearly state interesting links between ASP and intermediate logics, which might bring research in these two areas together.

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.

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 Forgetting in Modular Answer Set Programming

2019 ◽  
Vol 33 ◽  
pp. 2843-2850 ◽  
Author(s):  
Ricardo Gonçalves ◽  
Tomi Janhunen ◽  
Matthias Knorr ◽  
João Leite ◽  
Stefan Woltran
Keyword(s):  
Answer Set Programming ◽  
Input Output ◽  
Impossibility Results ◽  
Modular Programming ◽  
The Creation ◽  
Large Software ◽  
Answer Sets ◽  
Answer Set

Modular programming facilitates the creation and reuse of large software, and has recently gathered considerable interest in the context of Answer Set Programming (ASP). In this setting, forgetting, or the elimination of middle variables no longer deemed relevant, is of importance as it allows one to, e.g., simplify a program, make it more declarative, or even hide some of its parts without affecting the consequences for those parts that are relevant. While forgetting in the context of ASP has been extensively studied, its known limitations make it unsuitable to be used in Modular ASP. In this paper, we present a novel class of forgetting operators and show that such operators can always be successfully applied in Modular ASP to forget all kinds of atoms – input, output and hidden – overcoming the impossibility results that exist for general ASP. Additionally, we investigate conditions under which this class of operators preserves the module theorem in Modular ASP, thus ensuring that answer sets of modules can still be composed, and how the module theorem can always be preserved if we further allow the reconfiguration of modules.

scholarly journals Linear-Time Temporal Answer Set Programming

2021 ◽  
pp. 1-55
Author(s):  
FELICIDAD AGUADO ◽  
PEDRO CABALAR ◽  
MARTÍN DIÉGUEZ ◽  
GILBERTO PÉREZ ◽  
TORSTEN SCHAUB ◽  
...  
Keyword(s):  
Temporal Logic ◽  
Linear Time ◽  
Selection Criterion ◽  
Answer Set Programming ◽  
Logic Programs ◽  
Modal Operators ◽  
Linear Time Temporal Logic ◽  
Stable Models ◽  
Answer Set

Abstract In this survey, we present an overview on (Modal) Temporal Logic Programming in view of its application to Knowledge Representation and Declarative Problem Solving. The syntax of this extension of logic programs is the result of combining usual rules with temporal modal operators, as in Linear-time Temporal Logic (LTL). In the paper, we focus on the main recent results of the non-monotonic formalism called Temporal Equilibrium Logic (TEL) that is defined for the full syntax of LTL but involves a model selection criterion based on Equilibrium Logic, a well known logical characterization of Answer Set Programming (ASP). As a result, we obtain a proper extension of the stable models semantics for the general case of temporal formulas in the syntax of LTL. We recall the basic definitions for TEL and its monotonic basis, the temporal logic of Here-and-There (THT), and study the differences between finite and infinite trace length. We also provide further useful results, such as the translation into other formalisms like Quantified Equilibrium Logic and Second-order LTL, and some techniques for computing temporal stable models based on automata constructions. In the remainder of the paper, we focus on practical aspects, defining a syntactic fragment called (modal) temporal logic programs closer to ASP, and explaining how this has been exploited in the construction of the solver telingo, a temporal extension of the well-known ASP solver clingo that uses its incremental solving capabilities.

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