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24
An epistemic foundation of stable model semantics
, 2003
"... The stable model semantics has become a dominating approach for the management of negation in logic programming. It relies mainly on the closed world assumption to complete the available knowledge and its formulation has its founding root in the socalled GelfondLifschitz transform. The primary goa ..."
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The stable model semantics has become a dominating approach for the management of negation in logic programming. It relies mainly on the closed world assumption to complete the available knowledge and its formulation has its founding root in the socalled GelfondLifschitz transform. The primary goal of this work is to present an alternative and epistemic based characterization of the stable model semantics, to the GelfondLifschitz transform. In particular, we show that the stable model semantics can be defined entirely as an extension of the KripkeKleene semantics and, thus, (i) does rely on the classical management of negation; and (ii) does not require any program transformation. Indeed, we show that the closed world assumption can be seen as an additional source for ‘falsehood ’ to be added cumulatively to the KripkeKleene semantics. Our approach is purely algebraic and can abstract from the particular formalism of choice as it is based on monotone operators (under the knowledge order) over bilattices only.
An algebraic account of modularity in IDlogic
 In Proc. LPNMR’05
, 2005
"... Abstract. IDlogic uses ideas from the field of logic programming to extend second order logic with nonmonotone inductive defintions. In this work, we reformulate the semantics of this logic in terms of approximation theory, an algebraic theory which generalizes the semantics of several nonmonoton ..."
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Abstract. IDlogic uses ideas from the field of logic programming to extend second order logic with nonmonotone inductive defintions. In this work, we reformulate the semantics of this logic in terms of approximation theory, an algebraic theory which generalizes the semantics of several nonmonotonic reasoning formalisms. This allows us to apply certain abstract modularity theorems, developed within the framework of approximation theory, to IDlogic. As such, we are able to offer elegant and simple proofs of generalizations of known theorems, as well as some new results. 1
On the Transformation of ObjectOriented Conceptual Models to Logical Theories
 In Proc. 21st International Conference on Conceptual Modeling (ER2002
"... This paper describes a semiautomatic transformation fi'om objectoriented conceptual models to logical theories. By associating a logical theory with a conceptual model, we are able to combine the best of both worlds. On one hand, the objectoriented software development paradigm is recognized ..."
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This paper describes a semiautomatic transformation fi'om objectoriented conceptual models to logical theories. By associating a logical theory with a conceptual model, we are able to combine the best of both worlds. On one hand, the objectoriented software development paradigm is recognized to be wellsuited to build maintainable and communicable conceptual models. On the other hand, the logical programming paradigm offers very powerful and semantically founded concepts to represent knowledge and the use of logical inference systems makes it possible to prototype solutions to computational tasks.
A Tarskian Informal Semantics for Answer Set Programming ∗
"... 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 i ..."
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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 socalled GenerateDefineTest programs.
intuitionism and truthknowledge duality: Concepts and foundations,” http://www.cs.umd.edu/∼ zoran
, 2006
"... We propose a family of intuitionistic bilattices with full truthknowledge duality (Dbilattices) for a logic programming. The first family of perfect Dbilattices is composed by Boolean algebras with even number of atoms: the simplest of them, based on intuitionistic truthfunctionally complete ext ..."
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We propose a family of intuitionistic bilattices with full truthknowledge duality (Dbilattices) for a logic programming. The first family of perfect Dbilattices is composed by Boolean algebras with even number of atoms: the simplest of them, based on intuitionistic truthfunctionally complete extension of Belnap’s 4valued bilattice, can be used in paraconsistent programming, that is, for knowledge bases with incomplete and inconsistent information. The other two families are useful for a probability theory where the uncertainty in the knowledge about a piece of information is in the form of belief types: as an interval (lower and upper boundary) probability or as a confidence level. Such programs can be parameterized by different kinds of probabilistic conjunctive/disjunctive strategies for their rules, based on intuitionistic implication. Such a framework offers a clear semantics for the satisfaction relation, and allows the extension of logic languages with intuitionistic implications also in the body of rules. From a theoretical point of view we introduce also a duality in higherorder bilatices, as in Temporal Probabilistic Logic, constructed as functional spaces over ordinary dual bilattices. Then we show the full truthknowledge duality for a fixpoint semantics of logic programs based on dual bilattices. Finally we develop also an autoreferential version of Stone’s Representation Theorem for the dual bilattices. 1
Constraint programming with unrestricted quantification
"... Abstract. Search problems occur widely in AI, and a number of generalpurpose constraintbased methods for solving them have been developed. Convenient modelling of many problems is enabled by use of quantifiers of various sorts, but the most prominent approaches support only limited use of quantifie ..."
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Abstract. Search problems occur widely in AI, and a number of generalpurpose constraintbased methods for solving them have been developed. Convenient modelling of many problems is enabled by use of quantifiers of various sorts, but the most prominent approaches support only limited use of quantifiers. A recently proposed constraint programming framework, based on classical logic and the notion of expansion of a finite structure with new relations, supports unrestricted use of both firstorder and secondorder quantifiers. The framework can be parameterized to capture various complexity classes, including NP and Σ p k for any k. Secondorder quantifiers can be used to concisely model search problems at any of these complexity levels. Firstorder quantifiers can be used freely for modelling convenience, without affecting the complexity level which is determined by the secondorder quantifiers. We explain this framework, discuss the roles of quantifiers, and give some examples. 1
An IDLogic Formalization of the Composition of Autonomous Databases
"... Abstract. We introduce a declarative approach for a coherent composition of autonomous databases. For this we use IDlogic, a formalism that extends classical logic with inductive definitions. We consider IDlogic theories that express, at the same time, the two basic challenges in database composit ..."
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Abstract. We introduce a declarative approach for a coherent composition of autonomous databases. For this we use IDlogic, a formalism that extends classical logic with inductive definitions. We consider IDlogic theories that express, at the same time, the two basic challenges in database composition problems: relating different schemas of the local databases to one global schema (schema integration) and amalgamating the distributed and possibly contradictory data to one consistent database (data integration). We show that our framework supports different methods for schema integration (as well as their combinations) and that it provides a straightforward way of dealing with inconsistent data. Moreover, in this context database repair and consistent query answering are easily implemented by a variety of reasoning systems. 1
Reasoning with preferences in IDLogic
"... In a lot of applications experts have apart from the pure definitional and assertional knowledge some meta knowledge about what they prefer to be in their intended worlds. This paper presents a framework for dealing with preferences embedded in IDLogic, a logic with inductive definitions as the bas ..."
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In a lot of applications experts have apart from the pure definitional and assertional knowledge some meta knowledge about what they prefer to be in their intended worlds. This paper presents a framework for dealing with preferences embedded in IDLogic, a logic with inductive definitions as the basic concept combined with first order logic sentences. In the obtained framework preference rules are transformed into an inductive definition. In that process the domain expert has to make a number of decisions to obtain the final representation. This ensures the flexibility of the framework. To clarify...
Compositionality Results for Stratified Nonmonotone Operators
, 2002
"... Approximation theory is an extension of Tarski's least fixpoint theory of monotone lattice operators to the generalised case of arbitrary nonmonotone operators. Approximation theory captures intuitions and principles found in several nonmonotonic reasoning systems and describes all main 2, 3 and 4 ..."
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Approximation theory is an extension of Tarski's least fixpoint theory of monotone lattice operators to the generalised case of arbitrary nonmonotone operators. Approximation theory captures intuitions and principles found in several nonmonotonic reasoning systems and describes all main 2, 3 and 4valued semantics of logic programming, default logic and autoepistemic logic.
Marc Denecker
"... Temporal reasoning has always been a major test case for knowledge representation formalisms. In this paper, we develop an inductive variant of the situation calculus using the Logic for NonMonotone Inductive Definitions (NMID). This logic has been proposed recently and is an extension of clas ..."
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Temporal reasoning has always been a major test case for knowledge representation formalisms. In this paper, we develop an inductive variant of the situation calculus using the Logic for NonMonotone Inductive Definitions (NMID). This logic has been proposed recently and is an extension of classical logic. It allows for a uniform represention of various forms of definitions, including monotone inductive definitions and nonmonotone forms of inductive definitions such as iterated induction and induction over wellfounded posets. In the NMIDaxiomatisation of the situation calculus, fluents and causality predicates are defined by simultaneous induction on the wellfounded poset of situations. The inductive approach allows us to solve the ramification problem for the situation calculus in a uniform and modular way. Our solution is among the most general solutions for the ramification problem in the situation calculus. Using previously developed modularity techniques, we show that the basic variant of the inductive situation calculus without ramification rules is equivalent to Reiterstyle situation calculus.