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Recursive Aggregates in Disjunctive Logic Programs: Semantics and Complexity [chapter]

Wolfgang Faber, Nicola Leone, Gerald Pfeifer
2004 Lecture Notes in Computer Science  
In this paper we define a semantics for disjunctive programs with arbitrary aggregates (including monotone, antimonotone, and nonmonotone aggregates).  ...  This semantics is a fully declarative, genuine generalization of the answer set semantics for disjunctive logic programming (DLP).  ...  disjunctive programs with has been given; but only monotone aggregates are considered.  ... 
doi:10.1007/978-3-540-30227-8_19 fatcat:mgzdt5pw5nf4fovr3iq5uuhh6u

Knowledge Representation Using High-Level Non-monotonic Reasoning [chapter]

Mauricio Osorio, Juan Carlos Nieves, Fernando Zacarias, Erika Saucedo
2000 Lecture Notes in Computer Science  
We introduce the new paradigm of High-Level Non-Monotonic reasoning (HLNM).  ...  This paradigm is the consolidation of our recent results on disjunctions, sets, explicit and implicit negation, and partialorder clauses.  ...  Introduction Knowledge based systems can be modeled adequately using non-monotonic logic, because it provides formal methods that enable intelligent systems to operate properly when they are faced with  ... 
doi:10.1007/10720076_2 fatcat:pj4ezi3hsrdoje52erbbzkhtmq

Aggregate Semantics for Propositional Answer Set Programs [article]

Mario Alviano, Wolfgang Faber, Martin Gebser
2021 arXiv   pre-print
While the utility of incorporating aggregate expressions in the modeling language has been realized almost simultaneously with the inception of the first ASP solving systems, a general semantics of aggregates  ...  The attractiveness of ASP builds on an expressive high-level modeling language along with the availability of powerful off-the-shelf solving systems.  ...  Answer Set Checking Starting with Check for (non-disjunctive) programs P including monotone or anti-monotone aggregate expressions only, we have that the task stays in P for all aggregate semantics.  ... 
arXiv:2109.08662v1 fatcat:ix5jozpscnfzffoumuak2io3bi

An FLP-Style Answer-Set Semantics for Abstract-Constraint Programs with Disjunctions

Johannes Oetsch, Jörg Pührer, Hans Tompits, Marc Herbstritt
2012 International Conference on Logic Programming  
We introduce an answer-set semantics for abstract-constraint programs with disjunction in rule heads in the style of Faber, Leone, and Pfeifer (FLP).  ...  To this end, we extend the definition of an answer set for logic programs with aggregates in rule bodies using the usual FLP-reduct.  ...  Unfounded sets for disjunctive logic programs with arbitrary aggregates.  ... 
doi:10.4230/lipics.iclp.2012.222 dblp:conf/iclp/OetschPT12 fatcat:q5w45ucfdbemjcxmuni4ihvwuy

Optimal models of disjunctive logic programs: semantics, complexity, and computation

N. Leone, F. Scarcello, V.S. Subrahmanian
2004 IEEE Transactions on Knowledge and Data Engineering  
Almost all semantics for logic programs with negation identify a set, SEMðP Þ, of models of program P , as the intended semantics of P , and any model M in this class is considered a possible meaning of  ...  In this paper, we develop a logic program semantics based on Optimal Models.  ...  Computing an Optimal Stable Model of a Positive Program with a Monotonic Aggregation Strategy Algorithm Optimal_Stable_Model (see Fig. 1 ) shows how to compute an optimal stable model of a disjunctive  ... 
doi:10.1109/tkde.2004.1269672 fatcat:sicnlphusnhonnd5hspkf5jkay

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  
These approaches generalize the fixpoint-based and the level mapping based answer set semantics of normal logic programs to the case of logic programs with arbitrary types of c-atoms.  ...  We show that the newly defined semantics coincide with previously introduced semantics for logic programs with monotone c-atoms, and they extend the original answer set semantics of normal logic programs  ...  The first approach is based on a generalization of the immediate consequence operator for programs with aggregates of and the second is built on a generalization of the notion of well-supported models  ... 
doi:10.1613/jair.2171 fatcat:aeaurkew75fadjdhcmqkuum3ee

Semantics and complexity of recursive aggregates in answer set programming

Wolfgang Faber, Gerald Pfeifer, Nicola Leone
2011 Artificial Intelligence  
In this paper we define a semantics for programs with arbitrary aggregates (including monotone, antimonotone, and nonmonotone aggregates) in the full ASP language allowing also for disjunction in the head  ...  We prove that our semantics guarantees the minimality (and therefore the incomparability) of answer sets, and we demonstrate that it coincides with the standard answer set semantics on aggregate-free programs  ...  Acknowledgements This work has greatly benefited from interesting discussions with and comments of Paolo Ferraris, Michael Gelfond, Vladimir Lifschitz, Nikolay Pelov.  ... 
doi:10.1016/j.artint.2010.04.002 fatcat:ne4yxukwcza2pauef3cntd6goe

Characterizations of Stable Model Semantics for Logic Programs with Arbitrary Constraint Atoms [article]

Yi-Dong Shen, Jia-Huai You, Li-Yan Yuan
2009 arXiv   pre-print
The resulting semantics turns out to coincide with the one defined by Son et al., which is based on a fixpoint approach.  ...  As a result, our approach to the stable model semantics for logic programs with constraint atoms generalizes a number of previous approaches.  ...  Representing basic programs by normal programs The semantics of logic programs with c-atoms or aggregates have been studied by the unfolding approach (Pelov et al. 2003; .  ... 
arXiv:0904.4727v1 fatcat:wbjal5ctuzbnpozazmk442c2ym

A Strongly Grounded Stable Model Semantics for Full Propositional Language [article]

Shahab Tasharrofi
2012 arXiv   pre-print
Answer set programming is one of the most praised frameworks for declarative programming in general and non-monotonic reasoning in particular.  ...  ., the justification for pertinence of an atom in an intended model may be its own pertinence).  ...  However, [11] takes an operational approach and uses an immediate consequence operator (a generalization of van Emeden-Kowalski one-step provability operator [15] ) to describe their intended models  ... 
arXiv:1211.2986v2 fatcat:6wal7eghbjbtvpjpcvyv4wolu4

Characterizations of stable model semantics for logic programs with arbitrary constraint atoms

YI-DONG SHEN, JIA-HUAI YOU, LI-YAN YUAN
2009 Theory and Practice of Logic Programming  
As a result, our approach to the stable model semantics for logic programs with constraint atoms generalizes a number of previous approaches.  ...  The resulting semantics turns out to coincide with the one defined by Sonet al. (2007), which is based on a fixpoint 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).  ... 
doi:10.1017/s1471068409990056 fatcat:gx5fqtzt4zagxeszwcdev4eygy

Well-Supported Semantics for Logic Programs with Generalized Rules [chapter]

Jia-Huai You, Yi-Dong Shen, Kewen Wang
2012 Lecture Notes in Computer Science  
In this paper, we address this issue by considering general logic programs, which consist of disjunctive rules with arbitrary propositional formulas in rule bodies.  ...  Finally, we show that previously proposed well-supported semantics for aggregate programs and description logic programs are rooted in the justified stable semantics of general programs.  ...  The other is the family of the semantics defined by fixpoints of a monotonic operator. Such a definition typically carries a form of justified reasoning, natively.  ... 
doi:10.1007/978-3-642-30743-0_39 fatcat:vhg5zu27qzhrlbgquhpm3roj7e

Properties of Answer Set Programming with Convex Generalized Atoms [article]

Mario Alviano, Wolfgang Faber
2013 arXiv   pre-print
In recent years, Answer Set Programming (ASP), logic programming under the stable model or answer set semantics, has seen several extensions by generalizing the notion of an atom in these programs: be  ...  Several semantics with differing characteristics have been proposed for these extensions, rendering the big picture somewhat blurry.  ...  In [9] it is stated that many semantics (and in particular, FLP and PSP) "agree on [...] programs with convex aggregates" because "they can be regarded as special programs with monotone constraints."  ... 
arXiv:1312.6096v1 fatcat:equ44iyiezeidkle44uckaypdy

Default Knowledge in Logic Programs with Uncertainty [chapter]

Yann Loyer, Umberto Straccia
2003 Lecture Notes in Computer Science  
For reasons of generality, we present our work in the framework presented in [17] as a unifying umbrella for many of the proposed approaches to the management of uncertainty in logic programming.  ...  The goal of this paper is to allow the reasoning with non-uniform default assumptions, i.e. with any arbitrary assignment of default values to the atoms.  ...  Let P be an np-program and let I be an approximate interpretation of Assumption-based semantics In this section we define the semantics of an np-program w.r.t. a given assumption.  ... 
doi:10.1007/978-3-540-24599-5_32 fatcat:imfs7bgur5ezpb52i525txhtxm

Well-founded and stable semantics of logic programs with aggregates

NIKOLAY PELOV, MARC DENECKER, MAURICE BRUYNOOGHE
2007 Theory and Practice of Logic Programming  
The semantics is based on the concept of a three-valuedimmediate consequence operatorof an aggregate program.  ...  AbstractIn this paper, we present a framework for the semantics and the computation of aggregates in the context of logic programming.  ...  For example, a stratified aggregate program P has a two-valuedD-well-founded model which is equal to the uniqueD-stable model of P and the standard model of P for any three-valued interpretationD of the  ... 
doi:10.1017/s1471068406002973 fatcat:xkp6vgk3knbqvl2cnk44cxng6y

Strong Equivalence of Logic Programs with Abstract Constraint Atoms [chapter]

Guohua Liu, Randy Goebel, Tomi Janhunen, Ilkka Niemelä, Jia-Huai You
2011 Lecture Notes in Computer Science  
We first give a general characterization of strong equivalence based on a new definition of program reduct for logic programs with abstract constraints.  ...  Logic programs with abstract constraint atoms provide a unifying framework for studying logic programs with various kinds of constraints.  ...  This extends previous work on logic programs with monotone c-atoms [11] . We study strong equivalence of a particular class of program revisions: constraint replacements.  ... 
doi:10.1007/978-3-642-20895-9_15 fatcat:w2a47udkl5atrpy43mrkln457u
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