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11
On loop formulas with variables
 In Proceedings of the International Conference on Knowledge Representation and Reasoning (KR
, 2008
"... Recently Ferraris, Lee and Lifschitz proposed a new definition of stable models that does not refer to grounding, which applies to the syntax of arbitrary firstorder sentences. We show its relation to the idea of loop formulas with variables by Chen, Lin, Wang and Zhang, and generalize their loop f ..."
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Cited by 11 (5 self)
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Recently Ferraris, Lee and Lifschitz proposed a new definition of stable models that does not refer to grounding, which applies to the syntax of arbitrary firstorder sentences. We show its relation to the idea of loop formulas with variables by Chen, Lin, Wang and Zhang, and generalize their loop formulas to disjunctive programs and to arbitrary firstorder sentences. We also extend the syntax of logic programs to allow explicit quantifiers, and define its semantics as a subclass of the new language of stable models by Ferraris et al. Such programs inherit from the general language the ability to handle nonmonotonic reasoning under the stable model semantics even in the absence of the unique name and the domain closure assumptions, while yielding more succinct loop formulas than the general language due to the restricted syntax. We also show certain syntactic conditions under which query answering for an extended program can be reduced to entailment checking in firstorder logic, providing a way to apply firstorder theorem provers to reasoning about nonHerbrand stable models.
Logic Programs with Intensional Functions (Preliminary Report
 In: ICLP11 WorkshoponAnswerSetProgrammingandOtherComputingParadigms(ASPOCP11)(Jul 2011
"... The stable model semantics treats a logic program as a mechanism for specifying its intensional predicates. In this paper we discuss a modification of that semantics in which functions, rather than predicates, are intensional. The idea of the new definition comes from nonmonotonic causal logic. ..."
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Cited by 10 (1 self)
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The stable model semantics treats a logic program as a mechanism for specifying its intensional predicates. In this paper we discuss a modification of that semantics in which functions, rather than predicates, are intensional. The idea of the new definition comes from nonmonotonic causal logic.
Functional stable model semantics and answer set programming modulo theories
 In Proceedings of International Conference on Principles of Knowledge Representation and Reasoning (KR
, 2012
"... ”Answer Set Programming Modulo Theories (ASPMT) ” is a recently proposed framework which tightly integrates answer set programming (ASP) and satisfiability modulo theories (SMT). Its mathematical foundation is the functional stable model semantics, an enhancement of the traditional stable model sema ..."
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Cited by 5 (5 self)
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”Answer Set Programming Modulo Theories (ASPMT) ” is a recently proposed framework which tightly integrates answer set programming (ASP) and satisfiability modulo theories (SMT). Its mathematical foundation is the functional stable model semantics, an enhancement of the traditional stable model semantics to allow defaults involving functions as well as predicates. This talk will discuss how ASPMT can provide a way to overcome limitations of the propositional setting of ASP, how action language C+ can be reformulated in terms of ASPMT, and how it can be 3 4 Answer Set Programming (ASP) Declarative programming paradigm. Suitable for knowledge intensive
178 Stable Model Semantics and FirstOrder Loop Formulas
 In Proceedings of International Joint Conference on Artificial Intelligence (IJCAI
, 2005
"... Lin and Zhao’s theorem on loop formulas states that in the propositional case the stable model semantics of a logic program can be completely characterized by propositional loop formulas, but this result does not fully carry over to the firstorder case. We investigate the precise relationship betwe ..."
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Cited by 3 (1 self)
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Lin and Zhao’s theorem on loop formulas states that in the propositional case the stable model semantics of a logic program can be completely characterized by propositional loop formulas, but this result does not fully carry over to the firstorder case. We investigate the precise relationship between the firstorder stable model semantics and firstorder loop formulas, and study conditions under which the former can be represented by the latter. In order to facilitate the comparison, we extend the definition of a firstorder loop formula which was limited to a nondisjunctive program, to a disjunctive program and to an arbitrary firstorder theory. Based on the studied relationship we extend the syntax of a logic program with explicit quantifiers, which allows us to do reasoning involving nonHerbrand stable models using firstorder reasoners. Such programs can be viewed as a special class of firstorder theories under the stable model semantics, which yields more succinct loop formulas than the general language due to their restricted syntax. 1.
Datalog Programs and Their Stable Models
"... Abstract. This paper is about the functionality of software systems used in answer set programming (ASP). ASP languages are viewed here, in the spirit of Datalog, as mechanisms for characterizing intensional (output) predicates in terms of extensional (input) predicates. Our approach to the semantic ..."
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Cited by 2 (0 self)
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Abstract. This paper is about the functionality of software systems used in answer set programming (ASP). ASP languages are viewed here, in the spirit of Datalog, as mechanisms for characterizing intensional (output) predicates in terms of extensional (input) predicates. Our approach to the semantics of ASP programs is based on the concept of a stable model defined in terms of a modification of parallel circumscription. 1
Relational Theories with Null Values and NonHerbrand Stable Models
"... Generalized relational theories with null values in the sense of Reiter are firstorder theories that provide a semantics for relational databases with incomplete information. In this paper we show that any such theory can be turned into an equivalent logic program, so that models of the theory can ..."
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Generalized relational theories with null values in the sense of Reiter are firstorder theories that provide a semantics for relational databases with incomplete information. In this paper we show that any such theory can be turned into an equivalent logic program, so that models of the theory can be generated using computational methods of answer set programming. As a step towards this goal, we develop a general method for calculating stable models under the domain closure assumption but without the unique name assumption. 1
Proceedings of the TwentyThird International Joint Conference on Artificial Intelligence Functional Stable Model Semantics and Answer Set Programming Modulo Theories
"... Recently there has been an increasing interest in incorporating “intensional ” functions in answer set programming. Intensional functions are those whose values can be described by other functions and predicates, rather than being predefined as in the standard answer set programming. We demonstrate ..."
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Recently there has been an increasing interest in incorporating “intensional ” functions in answer set programming. Intensional functions are those whose values can be described by other functions and predicates, rather than being predefined as in the standard answer set programming. We demonstrate that the functional stable model semantics plays an important role in the framework of “Answer Set Programming Modulo Theories (ASPMT) ” —a tight integration of answer set programming and satisfiability modulo theories, under which existing integration approaches can be viewed as special cases where the role of functions is limited. We show that “tight ” ASPMT programs can be translated into SMT instances, which is similar to the known relationship between ASP and SAT. 1
Proceedings, Eleventh International Conference on Principles of Knowledge Representation and Reasoning (2008) On Loop Formulas with Variables
"... Recently Ferraris, Lee and Lifschitz proposed a new definition of stable models that does not refer to grounding, which applies to the syntax of arbitrary firstorder sentences. We show its relation to the idea of loop formulas with variables by Chen, Lin, Wang and Zhang, and generalize their loop f ..."
Abstract
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Recently Ferraris, Lee and Lifschitz proposed a new definition of stable models that does not refer to grounding, which applies to the syntax of arbitrary firstorder sentences. We show its relation to the idea of loop formulas with variables by Chen, Lin, Wang and Zhang, and generalize their loop formulas to disjunctive programs and to arbitrary firstorder sentences. We also extend the syntax of logic programs to allow explicit quantifiers, and define its semantics as a subclass of the new language of stable models by Ferraris et al. Such programs inherit from the general language the ability to handle nonmonotonic reasoning under the stable model semantics even in the absence of the unique name and the domain closure assumptions, while yielding more succinct loop formulas than the general language due to the restricted syntax. We also show certain syntactic conditions under which query answering for an extended program can be reduced to entailment checking in firstorder logic, providing a way to apply firstorder theorem provers to reasoning about nonHerbrand stable models.
E������ � E�������
, 2012
"... �e growing need for computer aided processing of knowledge has led to an increasing interest in description logics (DLs), which are applied to encode knowledge in order to make it explicit and accessible to logical reasoning. DLs and in particular the family around the DL �� � have therefore been th ..."
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�e growing need for computer aided processing of knowledge has led to an increasing interest in description logics (DLs), which are applied to encode knowledge in order to make it explicit and accessible to logical reasoning. DLs and in particular the family around the DL �� � have therefore been thoroughly investigated w.r.t. their complexity theory and proof theory. �e question arises which expressiveness these logics actually have. �e expressiveness of a logic can be inferred by a model theoretic characterisation. On concept level, these DLs are akin to modal logics whose model theoretic properties have been investigated. Yet the model theoretic investigation of the DLs with their TBoxes, which are an original part of DLs usually not considered in context of modal logics, have remained unstudied. �is thesis studies the model theoretic properties of ���, ����, ����, as well as ����, �����, ����� � and ��. It presents model theoretic properties, which characterise these logics as fragments of the first order logic (FO). �e characterisations are not only carried out on concept level and on concept
Under consideration for publication in Theory and Practice of Logic Programming 1 Relational Theories with Null Values and NonHerbrand Stable Models
, 2003
"... Generalized relational theories with null values in the sense of Reiter are firstorder theories that provide a semantics for relational databases with incomplete information. In this paper we show that any such theory can be turned into an equivalent logic program, so that models of the theory can ..."
Abstract
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Generalized relational theories with null values in the sense of Reiter are firstorder theories that provide a semantics for relational databases with incomplete information. In this paper we show that any such theory can be turned into an equivalent logic program, so that models of the theory can be generated using computational methods of answer set programming. As a step towards this goal, we develop a general method for calculating stable models under the domain closure assumption but without the unique name assumption. 1