In the paper, we present a procedural semantics for fuzzy disjunctive programs - sets of graded strong literal disjunctions. We shall suppose that truth values constitute a complete Boolean lattice L = (L, less than o...
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ISBN:
(数字)9783540360780
ISBN:
(纸本)3540000100
In the paper, we present a procedural semantics for fuzzy disjunctive programs - sets of graded strong literal disjunctions. We shall suppose that truth values constitute a complete Boolean lattice L = (L, less than or equal to, boolean OR, boolean AND, double right arrow, 0, 1). A graded strong literal disjunction is a pair (D, c) where D is a strong literal disjunction of the form l(1)(V) over dot ... (V) over dot l(n) and c is a truth value from the lattice L. A graded disjunction can be understood as a means of the representation of incomplete and uncertain information, where the incompleteness is formalised by its strong literal disjunction, while the uncertainty by its truth degree. In the end, the coincidence of the procedural and fixpoint semantics, proposed in [18], will be reached.
In this paper we consider the basic semantics of stable and partial stable models for disjunctive deductive databases (with default negation), cf. [9, 16]. It is well-known that there are disjunctive deductive databas...
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ISBN:
(纸本)3540649581
In this paper we consider the basic semantics of stable and partial stable models for disjunctive deductive databases (with default negation), cf. [9, 16]. It is well-known that there are disjunctive deductive databases where no stable or partial stable models exist, and these databases are called inconsistent w.r.t. the basic semantics. We define a consistent variant of each class of models, which we call evidential stable and partial evidential stable models. It is shown that if a database is already consistent w.r.t, the basic semantics, then the class of evidential models coincides with the basic class of models. Otherwise, the set of evidential models is a subset of the set of minimal models of the database. This subset is non-empty, if the database is logically consistent. It is determined according to a suitable preference relation, whose underlying idea is to minimize the amount of reasoning by contradiction. The technical ingredients for the construction of the new classes of models are two transformations of disjunctive deductive databases. First, the evidential transformation is used to realize the preference relation, and to define evidential stable models. Secondly, based on the tu-transformation the result is lifted to the three-valued case, that is, partial evidential stable models are defined.
In the paper, we present a procedural semantics for fuzzy disjunctive programs - sets of graded implications of the form: (h(1) boolean OR(...)boolean OR h(n) 0, m greater than or equal to 0) where h(i), b(j) are ato...
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ISBN:
(纸本)3540212582
In the paper, we present a procedural semantics for fuzzy disjunctive programs - sets of graded implications of the form: (h(1) boolean OR(...)boolean OR h(n) <--b(1) &(...)& b(m), c) (n > 0, m greater than or equal to 0) where h(i), b(j) are atoms and c a truth degree from a complete residuated lattice L = (L, less than or equal to, boolean OR, boolean AND, *, double right arrow, 0, 1). A graded implication can be understood as a means of the representation of incomplete and uncertain information;the incompleteness is formalised by the consequent disjunction of the implication, while the uncertainty by its truth degree. We generalise the results for Boolean lattices in [3] to the case of residuated ones. We take into consideration the non-idempotent triangular norm *, instead of the idempotent Lambda, as a truth function for the strong conjunction &. In the end, the coincidence of the proposed procedural semantics and the generalised declarative, fixpoint semantics from [4] will be reached.
In a data exchange setting with target constraints, it is often the case that a given source instance has no solutions. Intuitively, this happens when data sources contain inconsistent or conflicting information that ...
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ISBN:
(纸本)9783319111131;9783319111124
In a data exchange setting with target constraints, it is often the case that a given source instance has no solutions. Intuitively, this happens when data sources contain inconsistent or conflicting information that is exposed by the target constraints at hand. In such cases, the semantics of target queries trivialize, because the certain answers of every target query over the given source instance evaluate to "true". The aim of this paper is to introduce and explore a new framework that gives meaningful semantics in such cases by using the notion of exchange-repairs. Informally, an exchange-repair of a source instance is another source instance that differs minimally from the first, but has a solution. In turn, exchange-repairs give rise to a natural notion of exchange-repair certain answers (in short, XR-certain answers) for target queries in the context of data exchange with target constraints. After exploring the structural properties of exchange-repairs, we focus on the problem of computing the XR-certain answers of conjunctive queries. We show that for schema mappings specified by source-to-target GAV dependencies and target equality-generating dependencies (egds), the XR-certain answers of a target conjunctive query can be rewritten as the consistent answers (in the sense of standard database repairs) of a union of source conjunctive queries over the source schema with respect to a set of egds over the source schema, thus making it possible to use a consistent query-answering system to compute XR-certain answers in data exchange. In contrast, we show that this type of rewriting is not possible for schema mappings specified by source-to-target LAV dependencies and target egds. We then examine the general case of schema mappings specified by source-to-target GLAV constraints, a weakly acyclic set of target tgds and a set of target egds. The main result asserts that, for such settings, the XR-certain answers of conjunctive queries can be rewritten as the certai
We investigate cardinality constraints of the form M -theta K, where M is a set and theta is one of the comparison operators or "greater than or equal to";such a constraint states that "exactly", &...
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ISBN:
(纸本)3540009574
We investigate cardinality constraints of the form M -theta K, where M is a set and theta is one of the comparison operators or "greater than or equal to";such a constraint states that "exactly", "at most", or "at least", respectively, K elements out of the set M have to be chosen. We show how a set C of constraints can be represented by means of a positive-disjunctive deductive database P(c), such that the models of P(c) correspond to the solutions of C. This allows for embedding cardinality constraints into applications dealing with incomplete knowledge. We also present a sound calculus represented by a definite logic program P(cc), which allows for directly reasoning with sets of exactly-cardinality constraints (i.e., where theta is "="). Reasoning with P(cc) is very efficient, and. it can be used for performance reasons before P(c) is evaluated. For obtaining completeness, however, P(c) is necessary, since we show the theoretical result that a sound and complete calculus,for exactly-cardinality constraints does not exist.
In this article, we present a declarative propositional temporal logicprogramming language called TeDiLog that is a combination of the temporal and disjunctive paradigms in logicprogramming. TeDiLog is, syntacticall...
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In this article, we present a declarative propositional temporal logicprogramming language called TeDiLog that is a combination of the temporal and disjunctive paradigms in logicprogramming. TeDiLog is, syntactically, a sublanguage of the well-known Propositional Linear-time Temporal logic (PLTL). TeDiLog allows both eventualities and always-formulas to occur in clause heads and also in clause bodies. To the best of our knowledge, TeDiLog is the first declarative temporal logicprogramming language that achieves this high degree of expressiveness. We establish the logical foundations of our proposal by formally defining operational and logical semantics for TeDiLog and by proving their equivalence. The operational semantics of TeDiLog relies on a restriction of the invariant-free temporal resolution procedure for PLTL that was introduced by Gaintzarain et al. in [2013]. We define a fixpoint semantics that captures the reverse (bottom-up) operational mechanism and prove its equivalence with the logical semantics. We also provide illustrative examples and comparison with other proposals.
In this paper, we describe the research lines in logicprogramming, carried out in Cosenza over a period of more than twenty years, which have recently produced promising industrial exploitation follow-ups. The resear...
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In this paper, we describe the research lines in logicprogramming, carried out in Cosenza over a period of more than twenty years, which have recently produced promising industrial exploitation follow-ups. The research lines have changed over the time but they have kept the initial interest on combining logicprogramming with databases techniques, that has been continuously renewed to cope with new challenges, in our attempt to use theory to solve practical problems.
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