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Abduction in Logic Programming
"... Abduction in Logic Programming started in the late 80s, early 90s, in an attempt to extend logic programming into a framework suitable for a variety of problems in Artificial Intelligence and other areas of Computer Science. This paper aims to chart out the main developments of the field over th ..."
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Cited by 624 (77 self)
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Abduction in Logic Programming started in the late 80s, early 90s, in an attempt to extend logic programming into a framework suitable for a variety of problems in Artificial Intelligence and other areas of Computer Science. This paper aims to chart out the main developments of the field over the last ten years and to take a critical view of these developments from several perspectives: logical, epistemological, computational and suitability to application. The paper attempts to expose some of the challenges and prospects for the further development of the field.
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 456 (102 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 (disjunction-free) 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 state-of-the-art implementation of disjunctive logic programming, and addresses several aspects. As for problem solving, we provide a formal definition of its kernel language, function-free 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 3-complete problems) in a declarative fashion. On the foundational side, we provide a detailed analysis of the computational complexity of the language of
Extending and Implementing the Stable Model Semantics
, 2002
"... A novel logic program like language, weight constraint rules, is developed for answer set programming purposes. It generalizes normal logic programs by allowing weight constraints in place of literals to represent, e.g., cardinality and resource constraints and by providing optimization capabilities ..."
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Cited by 396 (9 self)
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A novel logic program like language, weight constraint rules, is developed for answer set programming purposes. It generalizes normal logic programs by allowing weight constraints in place of literals to represent, e.g., cardinality and resource constraints and by providing optimization capabilities. A declarative semantics is developed which extends the stable model semantics of normal programs. The computational complexity of the language is shown to be similar to that of normal programs under the stable model semantics. A simple embedding of general weight constraint rules to a small subclass of the language called basic constraint rules is devised. An implementation of the language, the smodels system, is developed based on this embedding. It uses a two level architecture consisting of a front-end and a kernel language implementation. The front-end allows restricted use of variables and functions and compiles general weight constraint rules to basic constraint rules. A major part of the work is the development of an ecient search procedure for computing stable models for this kernel language. The procedure is compared with and empirically tested against satis ability checkers and an implementation of the stable model semantics. It offers a competitive implementation of the stable model semantics for normal programs and attractive performance for problems where the new types of rules provide a compact representation.
Logic Programs with Stable Model Semantics as a Constraint Programming Paradigm
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Logic Programming and Knowledge Representation - the A-Prolog perspective
- Artificial Intelligence
, 2002
"... In this paper we give a short introduction to logic programming approach to knowledge representation and reasoning. The intention is to help the reader to develop a 'feel' for the field's history and some of its recent developments. The discussion is mainly limited to logic programs u ..."
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Cited by 98 (2 self)
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In this paper we give a short introduction to logic programming approach to knowledge representation and reasoning. The intention is to help the reader to develop a 'feel' for the field's history and some of its recent developments. The discussion is mainly limited to logic programs under the answer set semantics. For understanding of approaches to logic programming build on well-founded semantics, general theories of argumentation, abductive reasoning, etc., the reader is referred to other publications.
Unfolding Partiality and Disjunctions in Stable Model Semantics
- Proceedings of the Seventh International Conference on Principles of Knowledge Representation and Reasoning (KR 2000), April 12-15
, 2000
"... The paper studies an implementation methodology for partial and disjunctive stable models where partiality and disjunctions are unfolded from a logic program so that an implementation of stable models for normal (disjunction-free) programs can be used as the core inference engine. The unfolding is d ..."
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Cited by 98 (17 self)
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The paper studies an implementation methodology for partial and disjunctive stable models where partiality and disjunctions are unfolded from a logic program so that an implementation of stable models for normal (disjunction-free) programs can be used as the core inference engine. The unfolding is done in two separate steps. Firstly, it is shown that partial stable models can be captured by total stable models using a simple linear and modular program transformation. Hence, reasoning tasks concerning partial models can be solved using an implementation of total models. Disjunctive partial stable models have been lacking implementations which now become available as the translation handles also the disjunctive case. Secondly, it is shown how total stable models of disjunctive programs can be determined by computing stable models for normal programs. Hence, an implementation of stable models of normal programs can be used as a core engine for implementing disjunctiv...
Logic Programming with Ordered Disjunction
- In Proceedings of AAAI-02
, 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 ..."
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Cited by 96 (8 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...
Semi-Stable Semantics
, 2003
"... In this paper, we examine an argument-based semantics called semistable semantics. Semi-stable semantics is quite close to traditional stable semantics in the sense that every stable extension is also a semi-stable extension. One of the advantages of semi-stable semantics is that there exists at le ..."
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Cited by 93 (13 self)
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In this paper, we examine an argument-based semantics called semistable semantics. Semi-stable semantics is quite close to traditional stable semantics in the sense that every stable extension is also a semi-stable extension. One of the advantages of semi-stable semantics is that there exists at least one semi-stable extension. Furthermore, if there also exists at least one stable extension, then the semi-stable extensions coincide with the stable extensions. This, and other properties, make semi-stable semantics an attractive alternative for the more traditional stable semantics, which until now has been widely used in fields such as logic programming and answer set programming.
Probabilistic reasoning with answer sets
- In Proceedings of LPNMR-7
, 2004
"... Abstract. We give a logic programming based account of probability and describe a declarative language P-log capable of reasoning which combines both logical and probabilistic arguments. Several non-trivial examples illustrate the use of P-log for knowledge representation. 1 ..."
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Cited by 91 (11 self)
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Abstract. We give a logic programming based account of probability and describe a declarative language P-log capable of reasoning which combines both logical and probabilistic arguments. Several non-trivial examples illustrate the use of P-log for knowledge representation. 1
