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### Propositional satisfiability in answer-set programming [article]

Deborah East, Miroslaw Truszczynski
2001 arXiv   pre-print
We show that propositional logic and its extensions can support answer-set programming in the same way stable logic programming and disjunctive logic programming do.  ...  We present encouraging performance results for our approach --- we show it to be competitive with smodels, a state-of-the-art answer-set programming system based on stable logic programming.  ...  Our goal in this paper is to propose answer-set programming formalisms based on propositional logic and its extensions.  ...

### Loop Formulas for Disjunctive Logic Programs [chapter]

2003 Lecture Notes in Computer Science
Our main result, generalizing the Lin/Zhao theorem, shows that answer sets for a disjunctive program can be characterized as the models of its completion that satisfy the loop formulas.  ...  The concept of a tight program and Fages' theorem are extended to disjunctive programs as well. 1 In this paper, we study propositional (grounded) logic programs only, and refer to the propositional case  ...  In view of Fages' theorem, answer sets for a tight program can be computed by a satisfiability solver (SAT solver) [Babovich et al., 2000] .  ...

### What is answer set programming to propositional satisfiability

Yuliya Lierler
2016 Constraints
Satisfiability solvers and answer set solvers are the software systems that find satisfying interpretations and answer sets for given propositional formulas and logic programs, respectively.  ...  Niemelä, Marek, and Truszczyński coined answer set programming paradigm in 1999: in this paradigm a logic program encodes problem specifications in a way that the answer sets of a logic program represent  ...  Lecture notes by Lifschitz on Reducing graph coloring to SAT available at https:// www.cs.utexas.edu/users/vl/teaching/lbai/coloring.pdf inspired the running examples in Sections 2 and 3.  ...

### A Default Approach to Semantics of Logic Programs with Constraint Atoms [chapter]

Yi-Dong Shen, Jia-Huai You
2009 Lecture Notes in Computer Science
Therefore, answer sets are defined in a way closely related to default extensions.  ...  Furthermore, answer sets by the minimal-model based semantics can be recast in our approach.  ...  Yi-Dong Shen is supported in part by NSFC grants 60673103, 60721061 and 60833001, and by the National High-tech R&D Program (863 Program).  ...

### DATALOG with constraints - an answer-set programming system [article]

Deborah East, Miroslaw Truszczynski
2000 arXiv   pre-print
Answer-set programming (ASP) has emerged recently as a viable programming paradigm well attuned to search problems in AI, constraint satisfaction and combinatorics.  ...  We discuss an implementation of DC and present results of experimental study of the effectiveness of DC, comparing it with CSAT, a satisfiability checker and SMODELS implementation of stable logic programming  ...  We say that a set M ⊆ At C (T ) satisfies T (is an answer set of T ) if 1.  ...

### Compiling Fuzzy Answer Set Programs to Fuzzy Propositional Theories [chapter]

Jeroen Janssen, Stijn Heymans, Dirk Vermeir, Martine De Cock
2008 Lecture Notes in Computer Science
We show how a fuzzy answer set program can be compiled to an equivalent fuzzy propositional theory whose models correspond to the answer sets of the program.  ...  This creates a basis for constructing fuzzy answer set solvers, such as solvers based on fuzzy SAT-solvers or on linear programming.  ...  Fuzzy Answer Set Programming Fuzzy answer set programming  is an extension of regular answer set programming (see e.g.  ...

### Tight Logic Programs [article]

2003 arXiv   pre-print
This note is about the relationship between two theories of negation as failure -- one based on program completion, the other based on stable models, or answer sets.  ...  We extend the definition of tightness and Fages' theorem to programs with nested expressions in the bodies of rules, and study tight logic programs containing the definition of the transitive closure of  ...  Special thanks to Hudson Turner for many useful suggestions, including the use of poslit in the definition of tightness instead of the more complicated condition from (Erdem and Lifschitz 2001a) , and  ...

### A Model-Theoretic Counterpart of Loop Formulas

Joohyung Lee
2005 International Joint Conference on Artificial Intelligence
In an important recent paper, Lin and Zhao introduced the concept of a loop formula, and showed that the answer sets for a logic program are exactly the models of Clark's completion of the program that  ...  satisfy the loop formulas.  ...  Wolfgang Faber suggested that there may be a relationship between loop formulas and unfounded sets. Nicola Leone gave pointers to earlier work on unfounded sets and on assumption sets.  ...

Chiaki Sakama, Tran Cao Son
2010 Lecture Notes in Computer Science
This paper presents a novel application of answer set programming to concept learning in nonmonotonic logic programs.  ...  Given an extended logic program as a background theory, we introduce techniques for inducing new rules using answer sets of the program.  ...  In this setting, a background theory and examples work as constraints which inductive hypotheses should satisfy, and induction in nonmonotonic logic programs is realized by computing answer sets of a program  ...

### Guarded Open Answer Set Programming [chapter]

Stijn Heymans, Davy Van Nieuwenborgh, Dirk Vermeir
2005 Lecture Notes in Computer Science
In [21, 19] , ASP with (finite) propositional programs is reduced to propositional satisfiability checking.  ...  an answer set semantics in FPL.  ...  Satisfiability checking w.r.t. (L)GPs is 2-EXPTIME-complete.  ...

### A Semantic Perspective on Omission Abstraction in ASP

Zeynep G. Saribatur, Thomas Eiter
2020 Proceedings of the Seventeenth International Conference on Principles of Knowledge Representation and Reasoning
The recently introduced notion of ASP abstraction is on reducing the vocabulary of a program while ensuring over-approximation of its answer sets, with a focus on having a syntactic operator that constructs  ...  We demonstrate how omission abstraction fits into the overall spectrum, by also investigating its behavior in the semantics of a program in the framework of HT logic.  ...  However, spurious answer sets may appear in omit(P, A), i.e., answer sets which can not be mapped back to some original answer set. Example 1.  ...

### General Fuzzy Answer Set Programs [chapter]

Jeroen Janssen, Steven Schockaert, Dirk Vermeir, Martine De Cock
2009 Lecture Notes in Computer Science
A number of generalizations of answer set programming have been proposed in the literature to deal with vagueness, uncertainty, and partial rule satisfaction.  ...  We introduce a unifying framework that entails most of the existing approaches to fuzzy answer set programming.  ...  to answer set optimization and valued constraint satisfaction.  ...

### Answer Sets for Logic Programs with Arbitrary Abstract Constraint Atoms

T. C. Son, E. Pontelli, P. H. Tu
2007 The Journal of Artificial Intelligence Research
The standard fixpoint-based semantics of logic programs is generalized in two directions, called answer set by reduct and answer set by complement.  ...  In this paper, we present two alternative approaches to defining answer sets for logic programs with arbitrary types of abstract constraint atoms (c-atoms).  ...  Definition in In the next proposition, we study the minimality and supportedness properties of answer sets of basic programs. Proposition 5 (Minimality of Answer Sets) 1.  ...

### The Joy of Probabilistic Answer Set Programming

Fábio Gagliardi Cozman
2019 International Symposium on Imprecise Probabilities and Their Applications
Probabilistic answer set programming (PASP) combines rules, facts, and independent probabilistic facts. Often one restricts such programs so that every query yields a sharp probability value.  ...  The purpose of this paper is to argue that a very useful modeling language is obtained by adopting a particular credal semantics for PASP, where one associates with each consistent program a credal set  ...  Background: Answer Set Programming Answer Set Programming (ASP) is a programming paradigm that emerged from research in logic programming; we here review basic syntactic and semantic notions  .  ...

### On Modular Translations and Strong Equivalence [chapter]

Paolo Ferraris
2005 Lecture Notes in Computer Science
Given two classes of logic programs, we may be interested in modular translations from one class into the other that are sound wth respect to the answer set semantics.  ...  The main theorem of this paper characterizes the existence of such a translation in terms of strong equivalence.  ...  The concept of an answer set is defined first for programs not containing negation as failure: a set X of atoms is an answer set for such a program Π if X is a minimal set satisfying Π.  ...
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