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105
The DLV System for Knowledge Representation and Reasoning
 ACM Transactions on Computational Logic
, 2002
"... Disjunctive Logic Programming (DLP) is an advanced formalism for knowledge representation and reasoning, which is very expressive in a precise mathematical sense: it allows to express every property of finite structures that is decidable in the complexity class ΣP 2 (NPNP). Thus, under widely believ ..."
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Cited by 320 (78 self)
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Disjunctive Logic Programming (DLP) is an advanced formalism for knowledge representation and reasoning, which is very expressive in a precise mathematical sense: it allows to express every property of finite structures that is decidable in the complexity class ΣP 2 (NPNP). Thus, under widely believed assumptions, DLP is strictly more expressive than normal (disjunctionfree) logic programming, whose expressiveness is limited to properties decidable in NP. Importantly, apart from enlarging the class of applications which can be encoded in the language, disjunction often allows for representing problems of lower complexity in a simpler and more natural fashion. This paper presents the DLV system, which is widely considered the stateoftheart implementation of disjunctive logic programming, and addresses several aspects. As for problem solving, we provide a formal definition of its kernel language, functionfree disjunctive logic programs (also known as disjunctive datalog), extended by weak constraints, which are a powerful tool to express optimization problems. We then illustrate the usage of DLV as a tool for knowledge representation and reasoning, describing a new declarative programming methodology which allows one to encode complex problems (up to ∆P 3complete problems) in a declarative fashion. On the foundational side, we provide a detailed analysis of the computational complexity of the language of
Logic Programming with Ordered Disjunction
 In Proceedings of AAAI02
, 2002
"... Logic programs with ordered disjunction (LPODs) combine ideas underlying Qualitative Choice Logic (Brewka, Benferhat, & Le Berre 2002) and answer set programming. Logic programming under answer set semantics is extended with a new connective called ordered disjunction. The new connective allows us t ..."
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Cited by 75 (7 self)
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Logic programs with ordered disjunction (LPODs) combine ideas underlying Qualitative Choice Logic (Brewka, Benferhat, & Le Berre 2002) and answer set programming. Logic programming under answer set semantics is extended with a new connective called ordered disjunction. The new connective allows us to represent alternative, ranked options for problem solutions in the heads of rules: A × B intuitively means: if possible A, but if A is not possible then at least B. The semantics of logic programs...
Answer set optimization
 PROC. IJCAI03
, 2003
"... We investigate the combination of answer set programming and qualitative optimization techniques. Answer set optimization programs (ASO programs) have two parts. The generating program produces answer sets representing possible solutions. The preference program expresses user preferences. It induces ..."
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Cited by 33 (6 self)
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We investigate the combination of answer set programming and qualitative optimization techniques. Answer set optimization programs (ASO programs) have two parts. The generating program produces answer sets representing possible solutions. The preference program expresses user preferences. It induces a preference relation on the answer sets of based on the degree to which rules are satisfied. We discuss possible applications of ASO programming, give complexity results and propose implementation techniques. We also analyze the relationship between A SO programs and CPnetworks.
Preferred Answer Sets for Ordered Logic Programs
 In European Conference on Logics for Artificial Intelligence (JELIA
, 2002
"... We extend answer set semantics to deal with inconsistent programs (containing classical negation), by finding a "best" answer set. Within the context of inconsistent programs, it is natural to have a partial order on rules, representing a preference for satisfying certain rules, possibly at the c ..."
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Cited by 30 (7 self)
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We extend answer set semantics to deal with inconsistent programs (containing classical negation), by finding a "best" answer set. Within the context of inconsistent programs, it is natural to have a partial order on rules, representing a preference for satisfying certain rules, possibly at the cost of violating less important ones. We show that such a rule order induces a natural order on extended answer sets, the minimal elements of which we call preferred answer sets. We characterize the expressiveness of the resulting semantics and show that it can simulate negation as failure as well as disjunction. We illustrate an application of the approach by considering database repairs, where minimal repairs are shown to correspond to preferred answer sets.
Planning with preferences using logic programming
, 2006
"... We present a declarative language,PP, for the highlevel specification of preferences between possible solutions (or trajectories) of a planning problem. This novel language allows users to elegantly express nontrivial, multidimensional preferences and priorities over such preferences. The semanti ..."
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Cited by 23 (3 self)
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We present a declarative language,PP, for the highlevel specification of preferences between possible solutions (or trajectories) of a planning problem. This novel language allows users to elegantly express nontrivial, multidimensional preferences and priorities over such preferences. The semantics ofPP allows the identification of most preferred trajectories for a given goal. We also provide an answer set programming implementation of planning problems with PP preferences.
The Independent Choice Logic and Beyond
"... Abstract. The Independent Choice Logic began in the early 90’s as a way to combine logic programming and probability into a coherent framework. The idea of the Independent Choice Logic is straightforward: there is a set of independent choices with a probability distribution over each choice, and a l ..."
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Cited by 18 (5 self)
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Abstract. The Independent Choice Logic began in the early 90’s as a way to combine logic programming and probability into a coherent framework. The idea of the Independent Choice Logic is straightforward: there is a set of independent choices with a probability distribution over each choice, and a logic program that gives the consequences of the choices. There is a measure over possible worlds that is defined by the probabilities of the independent choices, and what is true in each possible world is given by choices made in that world and the logic program. ICL is interesting because it is a simple, natural and expressive representation of rich probabilistic models. This paper gives an overview of the work done over the last decade and half, and points towards the considerable work ahead, particularly in the areas of lifted inference and the problems of existence and identity. 1
Complex Preferences for Answer Set Optimization
, 2004
"... preference description language PDL . This language allows us to combine qualitative and quantitative, penalty based preferences in a flexible way. This makes it possible to express complex preferences which are needed in many realistic optimization settings. We show that several preference hand ..."
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Cited by 18 (2 self)
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preference description language PDL . This language allows us to combine qualitative and quantitative, penalty based preferences in a flexible way. This makes it possible to express complex preferences which are needed in many realistic optimization settings. We show that several preference handling methods described in the literature are special cases of our approach. We also demonstrate that PDL expressions can be compiled to logic programs which can be used as tester programs in a generateandimprove method for finding optimal answer sets.
Semantic Forgetting in Answer Set Programming
, 2008
"... The notion of forgetting, also known as variable elimination, has been investigated extensively in the context of classical logic, but less so in (nonmonotonic) logic programming and nonmonotonic reasoning. The few approaches that exist are based on syntactic modifications of a program at hand. In t ..."
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Cited by 17 (5 self)
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The notion of forgetting, also known as variable elimination, has been investigated extensively in the context of classical logic, but less so in (nonmonotonic) logic programming and nonmonotonic reasoning. The few approaches that exist are based on syntactic modifications of a program at hand. In this paper, we establish a declarative theory of forgetting for disjunctive logic programs under answer set semantics that is fully based on semantic grounds. The suitability of this theory is justified by a number of desirable properties. In particular, one of our results shows that our notion of forgetting can be entirely captured by classical forgetting. We present several algorithms for computing a representation of the result of forgetting, and provide a characterization of the computational complexity of reasoning from a logic program under forgetting. As applications of our approach, we present a fairly general framework for resolving conflicts in inconsistent knowledge bases that are represented by disjunctive logic programs, and we show how the semantics of inheritance logic programs and update logic programs from the literature can be characterized through forgetting. The basic idea of the conflict resolution framework is to weaken the preferences of each agent by forgetting certain knowledge that causes inconsistency. In particular, we show how to use the notion of forgetting to provide an elegant solution for preference elicitation in disjunctive logic programming.
Reconstructing the Evolutionary History of IndoEuropean Languages Using Answer Set Programming
 In Proceedings of the 5th International Symposium on Practical Aspects of Declarative Languages(PADL 2003
, 2003
"... Abstract. The evolutionary history of languages can be modeled as a tree, called a phylogeny, where the leaves represent the extant languages, the internal vertices represent the ancestral languages, and the edges represent the genetic relations between the languages. Languages not only inherit char ..."
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Cited by 16 (4 self)
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Abstract. The evolutionary history of languages can be modeled as a tree, called a phylogeny, where the leaves represent the extant languages, the internal vertices represent the ancestral languages, and the edges represent the genetic relations between the languages. Languages not only inherit characteristics from their ancestors but also sometimes borrow them from other languages. Such borrowings can be represented by additional nontree edges. This paper addresses the problem of computing a small number of additional edges that turn a phylogeny into a "perfect phylogenetic network". To solve this problem, we use answer set programming, which represents a given computational problem as a logic program whose answer sets correspond to solutions. Using the answer set solver smodels, with some heuristics and optimization techniques, we have generated a few conjectures regarding the evolution of IndoEuropean languages.
A uniform approach to logic programming semantics
 Theory and Practice of Logic Programming
, 2005
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