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Propositional satisfiability in answer-set programming
[article]

2001
*
arXiv
*
pre-print

We show that

arXiv:cs/0107028v1
fatcat:ghcegkwdjbecrhgh2v7ukmek7i
*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

doi:10.1007/978-3-540-24599-5_31
fatcat:fxvkspqlrnfknpnqglo7lyhreq
*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

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. ...

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

2009
*
Lecture Notes in Computer Science
*

Therefore,

doi:10.1007/978-3-642-04238-6_24
fatcat:rewog7vocfez3g4k7vx7xxv5zm
*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]

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]

2008
*
Lecture Notes in Computer Science
*

We show how a fuzzy

doi:10.1007/978-3-540-89982-2_34
fatcat:2vqqo2pgjngx3nigx4f6wdjlne
*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*[3] 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

arXiv:cs/0302038v1
fatcat:qifho2ia75hevn5lhtpgtg3r2m
*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

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*. ...

##
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Interacting Answer Sets
[chapter]

2010
*
Lecture Notes in Computer Science
*

This paper presents a novel application of

doi:10.1007/978-3-642-16867-3_7
fatcat:5znoge62nvgypjn5xgahdk2b3q
*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]

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

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

doi:10.24963/kr.2020/75
dblp:conf/kr/SaribaturE20
fatcat:6a6dbindsfgk5bpw7p4jnimnte
*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]

2009
*
Lecture Notes in Computer Science
*

A number of generalizations of

doi:10.1007/978-3-642-02282-1_44
fatcat:4dtqxxe5hnanpmd4rqszpyf2jq
*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

2007
*
The Journal of Artificial Intelligence Research
*

The standard fixpoint-based semantics of logic

doi:10.1613/jair.2171
fatcat:aeaurkew75fadjdhcmqkuum3ee
*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

2019
*
International Symposium on Imprecise Probabilities and Their Applications
*

Probabilistic

dblp:conf/isipta/Cozman19
fatcat:j35agmnv7fg2tfhyu75pdmpjxu
*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 [18] . ...##
###
On Modular Translations and Strong Equivalence
[chapter]

2005
*
Lecture Notes in Computer Science
*

Given two classes of logic

doi:10.1007/11546207_7
fatcat:da7stnkaqrcatgvnqmfgbk4dtm
*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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