Stable Model Semantics

14,000,000 Leading Edge Experts on the ideXlab platform

Scan Science and Technology

Contact Leading Edge Experts & Companies

Scan Science and Technology

Contact Leading Edge Experts & Companies

The Experts below are selected from a list of 5775 Experts worldwide ranked by ideXlab platform

Ravi Palla - One of the best experts on this subject based on the ideXlab platform.

Ilkka Niemelä - One of the best experts on this subject based on the ideXlab platform.

  • unfolding partiality and disjunctions in Stable Model Semantics
    ACM Transactions on Computational Logic, 2006
    Co-Authors: Tomi Janhunen, Ilkka Niemelä, Patrik Simons, Dietmar Seipel, Jiahuai You
    Abstract:

    This article 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. First, 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 Stable Models can be solved using an implementation of total Stable Models. Disjunctive partial Stable Models have been lacking implementations which now become available as the translation handles also the disjunctive case. Second, it is shown how total Stable Models of disjunctive programs can be determined by computing Stable Models for normal programs. Thus an implementation of Stable Models of normal programs can be used as a core engine for implementing disjunctive programs. The feasibility of the approach is demonstrated by constructing a system for computing Stable Models of disjunctive programs using the SModelS system as the core engine. The performance of the resulting system is compared to that of DLV, which is a state-of-the-art system for disjunctive programs.

  • unfolding partiality and disjunctions in Stable Model Semantics
    arXiv: Artificial Intelligence, 2003
    Co-Authors: Tomi Janhunen, Ilkka Niemelä, Patrik Simons, Dietmar Seipel, Jiahuai You
    Abstract:

    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 Stable Models can be solved using an implementation of total Stable 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 disjunctive programs. The feasibility of the approach is demonstrated by constructing a system for computing Stable Models of disjunctive programs using the sModels system as the core engine. The performance of the resulting system is compared to that of dlv which is a state-of-the-art special purpose system for disjunctive programs.

  • extending and implementing the Stable Model Semantics
    Artificial Intelligence, 2002
    Co-Authors: Patrik Simons, Ilkka Niemelä, Timo Soininen
    Abstract:

    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 efficient search procedure for computing Stable Models for this kernel language. The procedure is compared with and empirically tested against satisfiability 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.

  • des a challenge problem for nonmonotonic reasoning systems
    arXiv: Artificial Intelligence, 2000
    Co-Authors: Maarit Hietalahti, Fabio Massacci, Ilkka Niemelä
    Abstract:

    The US Data Encryption Standard, DES for short, is put forward as an interesting benchmark problem for nonmonotonic reasoning systems because (i) it provides a set of test cases of industrial relevance which shares features of randomly generated problems and real-world problems, (ii) the representation of DES using normal logic programs with the Stable Model Semantics is simple and easy to understand, and (iii) this subclass of logic programs can be seen as an interesting special case for many other formalizations of nonmonotonic reasoning. In this paper we present two encodings of DES as logic programs: a direct one out of the standard specifications and an optimized one extending the work of Massacci and Marraro. The computational properties of the encodings are studied by using them for DES key search with the SModels system as the implementation of the Stable Model Semantics. Results indicate that the encodings and SModels are quite competitive: they outperform state-of-the-art SAT-checkers working with an optimized encoding of DES into SAT and are comparable with a SAT-checker that is customized and tuned for the optimized SAT encoding.

  • Stable Model Semantics of weight constraint rules
    International Conference on Logic Programming, 1999
    Co-Authors: Ilkka Niemelä, Patrik Simons, Timo Soininen
    Abstract:

    A generalization of logic program rules is proposed where rules are built from weight constraints with type information for each predicate instead of simple literals. These kinds of constraints are useful for concisely representing different kinds of choices as well as cardinality, cost and resource constraints in combinatorial problems such as product configuration. A declarative Semantics for the rules is presented which generalizes the Stable Model Semantics of normal logic programs. It is shown that for ground rules the complexity of the relevant decision problems stays in NP. The first implementation of the language handles a decidable subset where function symbols are not allowed. It is based on a new procedure for computing Stable Models for ground rules extending normal programs with choice and weight constructs and a compilation technique where a weight rule with variables is transformed to a set of such simpler ground rules.

Joohyung Lee - One of the best experts on this subject based on the ideXlab platform.

  • first order Stable Model Semantics with intensional functions
    Artificial Intelligence, 2019
    Co-Authors: Michael Bartholomew, Joohyung Lee
    Abstract:

    Abstract In classical logic, nonBoolean fluents, such as the location of an object, can be naturally described by functions. However, this is not the case in answer set programs, where the values of functions are pre-defined, and nonmonotonicity of the Semantics is related to minimizing the extents of predicates but has nothing to do with functions. We extend the first-order Stable Model Semantics by Ferraris, Lee, and Lifschitz to allow intensional functions—functions that are specified by a logic program just like predicates are specified. We show that many known properties of the Stable Model Semantics are naturally extended to this formalism and compare it with other related approaches to incorporating intensional functions. Furthermore, we use this extension as a basis for defining Answer Set Programming Modulo Theories (ASPMT), analogous to the way that Satisfiability Modulo Theories (SMT) is defined, allowing for SMT-like effective first-order reasoning in the context of Answer Set Programming (ASP). Using SMT solving techniques involving functions, ASPMT can be applied to domains containing real numbers and alleviates the grounding problem. We show that other approaches to integrating ASP and CSP/SMT can be related to special cases of ASPMT in which functions are limited to non-intensional ones.

  • integrating rules and ontologies in the first order Stable Model Semantics preliminary report
    10th International Symposium on Logical Formalizations of Commonsense Reasoning Commonsense 2011, 2019
    Co-Authors: Joohyung Lee, Ravi Palla
    Abstract:

    We present an approach to integrating rules and ontologies on the basis of the first-order Stable Model Semantics proposed by Ferraris, Lee and Lifschitz. We show that some existing integration proposals can be uniformly reformulated in terms of the first-order Stable Model Semantics. The reformulations are simpler than the original proposals in the sense that they do not refer to grounding.

  • weighted rules under the Stable Model Semantics
    Principles of Knowledge Representation and Reasoning, 2016
    Co-Authors: Joohyung Lee, Yi Wang
    Abstract:

    We introduce the concept of weighted rules under the Stable Model Semantics following the log-linear Models of Markov Logic. This provides versatile methods to overcome the deterministic nature of the Stable Model Semantics, such as resolving inconsistencies in answer set programs, ranking Stable Models, associating probability to Stable Models, and applying statistical inference to computing weighted Stable Models. We also present formal comparisons with related formalisms, such as answer set programs, Markov Logic, ProbLog, and P-log.

  • a probabilistic extension of the Stable Model Semantics
    National Conference on Artificial Intelligence, 2015
    Co-Authors: Joohyung Lee, Yi Wang
    Abstract:

    We present a probabilistic extension of logic programs under the Stable Model Semantics, inspired by the idea of Markov Logic Networks. The proposed language, called LP MLN , is a generalization of logic programs under the Stable Model Semantics, and as such, embraces the rich body of research in knowledge representation. The language is also a generalization of ProbLog, and is closely related to Markov Logic Networks, which implies that the computation can be carried out by the techniques developed for them.  LP MLN appears to be a natural language for probabilistic answer set programming, and as an example we show how an elaboration tolerant representation of transition systems in answer set programs can be naturally extended to the probabilistic setting.

  • markov logic style weighted rules under the Stable Model Semantics
    International Conference on Lightning Protection, 2015
    Co-Authors: Joohyung Lee, Yunsong Meng, Yi Wang
    Abstract:

    We introduce the language LP MLN that extends logic programs under the Stable Model Semantics to allow weighted rules similar to the way Markov Logic considers weighted formulas. LP MLN is a proper extension of the Stable Model Semantics to enable probabilistic reasoning, providing a way to handle inconsistency in answer set programming. We also show that the recently established logical relationship between Pearl’s Causal Models and answer set programs can be extended to the probabilistic setting via LP MLN .

Yan Zhang - One of the best experts on this subject based on the ideXlab platform.

  • expressiveness of logic programs under the general Stable Model Semantics
    ACM Transactions on Computational Logic, 2017
    Co-Authors: Heng Zhang, Yan Zhang
    Abstract:

    Stable Model Semantics had been recently generalized to non-Herbrand structures by several works, which provides a unified framework and solid logical foundations for answer set programming. This article focuses on the expressiveness of normal and disjunctive logic programs under general Stable Model Semantics. A translation from disjunctive logic programs to normal logic programs is proposed for infinite structures. Over finite structures, some disjunctive logic programs are proved to be intranslatable to normal logic programs if the arities of auxiliary predicates and functions are bounded in a certain way. The equivalence of the expressiveness of normal logic programs and disjunctive logic programs over arbitrary structures is also shown to coincide with that over finite structures and coincide with whether the complexity class NP is closed under complement. Moreover, to obtain a more explicit picture of the expressiveness, some intertranslatability results between logic program classes, and fragments of second-order logic are established.

  • query answering with inconsistent existential rules under Stable Model Semantics
    arXiv: Artificial Intelligence, 2016
    Co-Authors: Hai Wan, Heng Zhang, Peng Xiao, Haoran Huang, Yan Zhang
    Abstract:

    Traditional inconsistency-tolerent query answering in ontology-based data access relies on selecting maximal components of an ABox/database which are consistent with the ontology. However, some rules in ontologies might be unreliable if they are extracted from ontology learning or written by unskillful knowledge engineers. In this paper we present a framework of handling inconsistent existential rules under Stable Model Semantics, which is defined by a notion called rule repairs to select maximal components of the existential rules. Surprisingly, for R-acyclic existential rules with R-stratified or guarded existential rules with stratified negations, both the data complexity and combined complexity of query answering under the rule {repair Semantics} remain the same as that under the conventional query answering Semantics. This leads us to propose several approaches to handle the rule {repair Semantics} by calling answer set programming solvers. An experimental evaluation shows that these approaches have good scalability of query answering under rule repairs on realistic cases.

  • query answering with inconsistent existential rules under Stable Model Semantics
    National Conference on Artificial Intelligence, 2016
    Co-Authors: Hai Wan, Heng Zhang, Peng Xiao, Haoran Huang, Yan Zhang
    Abstract:

    Classical inconsistency-tolerant query answering relies on selecting maximal components of an ABox/database which are consistent with the ontology. However, some rules in ontologies might be unreliable if they are extracted from ontology learning or written by unskillful knowledge engineers. In this paper we present a framework of handling inconsistent existential rules under Stable Model Semantics, which is defined by a notion called rule repairs to select maximal components of the existential rules. Surprisingly, for R-acyclic existential rules with R-stratified or guarded existential rules with stratified negations, both the data complexity and combined complexity of query answering under the rule repair Semantics remain the same as that under the conventional query answering Semantics. This leads us to propose several approaches to handle the rule repair Semantics by calling answer set programming solvers. An experimental evaluation shows that these approaches have good scalability of query answering under rule repairs on realistic cases.

  • expressiveness of logic programs under general Stable Model Semantics
    arXiv: Artificial Intelligence, 2014
    Co-Authors: Heng Zhang, Yan Zhang
    Abstract:

    The Stable Model Semantics had been recently generalized to non-Herbrand structures by several works, which provides a unified framework and solid logical foundations for answer set programming. This paper focuses on the expressiveness of normal and disjunctive programs under the general Stable Model Semantics. A translation from disjunctive programs to normal programs is proposed for infinite structures. Over finite structures, some disjunctive programs are proved to be intranslatable to normal programs if the arities of auxiliary predicates and functions are bounded in a certain way. The equivalence of the expressiveness of normal programs and disjunctive programs over arbitrary structures is also shown to coincide with that over finite structures, and coincide with whether NP is closed under complement. Moreover, to capture the exact expressiveness, some intertranslatability results between logic program classes and fragments of second-order logic are obtained.

Miroslaw Truszczynski - One of the best experts on this subject based on the ideXlab platform.

  • On Equivalence of Infinitary Formulas under the Stable Model Semantics
    Theory and Practice of Logic Programming, 2014
    Co-Authors: Amelia Harrison, Vladimir Lifschitz, Miroslaw Truszczynski
    Abstract:

    Propositional formulas that are equivalent in intuitionistic logic, or in its extension known as the logic of here-and-there, have the same Stable Models. We extend this theorem to propositional formulas with infinitely long conjunctions and disjunctions and show how to apply this generalization to proving properties of aggregates in answer set programming.

  • on equivalence of infinitary formulas under the Stable Model Semantics
    arXiv: Logic in Computer Science, 2014
    Co-Authors: Amelia Harrison, Vladimir Lifschitz, Miroslaw Truszczynski
    Abstract:

    Propositional formulas that are equivalent in intuitionistic logic, or in its extension known as the logic of here-and-there, have the same Stable Models. We extend this theorem to propositional formulas with infinitely long conjunctions and disjunctions and show how to apply this generalization to proving properties of aggregates in answer set programming. To appear in Theory and Practice of Logic Programming (TPLP).

  • on equivalent transformations of infinitary formulas under the Stable Model Semantics
    International Conference on Logic Programming, 2013
    Co-Authors: Amelia Harrison, Vladimir Lifschitz, Miroslaw Truszczynski
    Abstract:

    It has been known for a long time that intuitionistically equivalent formulas have the same Stable Models. We extend this theorem to propositional formulas with infinitely long conjunctions and disjunctions and show how to apply this generalization to proving properties of aggregates in answer set programming.

  • a tarskian informal Semantics for answer set programming
    International Conference on Logic Programming, 2012
    Co-Authors: Marc Denecker, Miroslaw Truszczynski, Yuliya Lierler, Joost Vennekens
    Abstract:

    In their seminal papers on Stable Model Semantics, Gelfond and Lifschitz introduced ASP by casting programs as epistemic theories, in which rules represent statements about the knowledge of a rational agent. To the best of our knowledge, theirs is still the only published systematic account of the intuitive meaning of rules and programs under the Stable Semantics. In current ASP practice, however, we find numerous applications in which rational agents no longer seem to play any role. Therefore, we propose here an alternative explanation of the intuitive meaning of ASP programs, in which they are not viewed as statements about an agent's beliefs, but as objective statements about the world. We argue that this view is more natural for a large part of current ASP practice, in particular the so-called Generate-Define-Test programs.

  • Stable Models and an alternative logic programming paradigm
    The Logic Programming Paradigm, 1999
    Co-Authors: Victor W. Marek, Miroslaw Truszczynski
    Abstract:

    In this paper we reexamine the place and role of Stable Model Semantics in logic programming and contrast it with a least Herbrand Model approach to Horn programs. We demonstrate that inherent features of Stable Model Semantics naturally lead to a logic programming system that offers an interesting alternative to more traditional logic programming styles of Horn logic programming, stratified logic programming and logic programming with well-founded Semantics. The proposed approach is based on the interpretation of program clauses as constraints. In this setting, a program does not describe a single intended Model, but a family of its Stable Models. These Stable Models encode solutions to the constraint satisfaction problem described by the program. Our approach imposes restrictions on the syntax of logic programs. In particular, function symbols are eliminated from the language. We argue that the resulting logic programming system is well-attuned to problems in the class NP, has a well-defined domain of applications, and an emerging methodology of programming. We point out that what makes the whole approach viable is recent progress in implementations of algorithms to compute Stable Models of propositional logic programs.

Related terms

Stable Model Semantics - 15 days free trial to Access Experts & Abstracts