4-Valued Semantics Under the OWA: A Deductive Database Approach

Laurent, Dominique

doi:10.1007/978-3-030-44900-1_7

Cited by 3 publications

(13 citation statements)

References 14 publications

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“…In Section 5, we investigate how our approach can be expressed in the context of the Four-valued logic [5] and we show that the semantics of [13] allows to compute the truth value of every tuple t as defined above. The following proposition shows that our notion of inconsistent tuple complies with Definition 3.…”

Section: The Truth-value Of a Tuplementioning

confidence: 99%

“…For example, Figure 3 shows that formulas of the form Φ ∨ ¬Φ are not always true, independently of the truth value of Φ. The reader is referred to the literature [3,5,12,13,20] for more on the properties of Four-valued logic.…”

Section: Basics Of Four-valued Logicmentioning

confidence: 99%

“…Based on Four-valued logic, semantics to rule based languages have been proposed in the literature [12,13]. In this work, we consider as in [13], conjunctive rules of the form:…”

Section: Basics Of Four-valued Logicmentioning

confidence: 99%

“…It has been shown in [13] that the sequence defined by Σ 0 = E and Σ n = Σ Π (Σ n−1 ), for n ≥ 1, is monotonic with respect to k and thus has a limit. This limit, denoted by Σ(Π) is then referred to as the semantics of Π.…”

Section: Basics Of Four-valued Logicmentioning

confidence: 99%

“…Under this restriction, we express our model as a set of rules a la Datalog [10], and we show (see Proposition 5) that the semantics of this set of rules, as defined in [13], is 'equivalent' to tuple truth-value as defined in Definition 4. It is important to note that, in doing so, our purpose is not to obtain a tractable set of rules.…”

Section: Partition Semantics and Four-valued Logicmentioning

confidence: 99%

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Handling Inconsistencies in Tables with Nulls and Functional Dependencies

Laurent¹,

Spyratos²

2021

Preprint

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In this paper we address the problem of handling inconsistencies in tables with missing values (or nulls) and functional dependencies. Although the traditional view is that table instances must respect all functional dependencies imposed on them, it is nevertheless relevant to develop theories about how to handle instances that violate some dependencies.The usual approach to alleviate the impact of inconsistent data on the answers to a query is to introduce the notion of repair: a repair is a minimally different consistent instance and an answer is consistent if it is present in every repair.Our approach is fundamentally different: we use set theoretic semantics for tuples and functional dependencies that allow us to associate each tuple with a truth value among the following: true, false, inconsistent or unknown. The users of the table can then query the set of true tuples as usual. Regarding missing values, we make no assumptions on their existence: a missing value exists only if it is inferred from the functional dependencies of the table.The main contributions of the paper are the following: (a) we introduce a new approach to handle inconsistencies in a table with nulls and functional dependencies, (b) we give algorithms for computing all true, inconsistent and false tuples, (c) we discuss how our approach relates to Belnap's four valued logic, (d) we describe how our approach can be applied to the consolidation of two or more tables and (e) we discuss the relationship between our approach and that of table repairs.

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Section: The Truth-value Of a Tuplementioning

confidence: 99%

Section: Basics Of Four-valued Logicmentioning

confidence: 99%

“…Based on Four-valued logic, semantics to rule based languages have been proposed in the literature [12,13]. In this work, we consider as in [13], conjunctive rules of the form:…”

Section: Basics Of Four-valued Logicmentioning

confidence: 99%

Section: Basics Of Four-valued Logicmentioning

confidence: 99%

Section: Partition Semantics and Four-valued Logicmentioning

confidence: 99%

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Handling Inconsistencies in Tables with Nulls and Functional Dependencies

Laurent¹,

Spyratos²

2021

Preprint

Self Cite

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Deductive databases in four-valued logic: rule semantics and models

Laurent

Spyratos

2022

Journal of Logic and Computation

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In this paper, we investigate rule semantics for deductive databases in the context of four-valued logic. In our approach, a database is a pair $\varDelta =(E,R)$, where $E$ is a set of pairs, each pair associating a ground fact with a truth value (thus, allowing to store true, false or inconsistent facts) and $R$ is a set of rules generalizing standard Datalog rules in the following sense: (i) the head of a rule can be a positive or a negative atom and (ii) the body can involve any among the connectors of four-valued logic. We define the database semantics as the least fixed point of a monotonic operator and we compare this semantics with that of k-existential programs defined by Fitting and paraconsistent extended logic programs defined by Arieli. Our main contribution is to show that, if we consider rules as implications (i.e. if we view the database as a set of formulas) then the semantics of the database is the unique minimal model of the set of database formulas. Here, minimality is understood with respect to the knowledge ordering of four-valued logic satisfying a monotonicity property whereby the truth value of the head of an instantiated rule is greater than that of the body. Moreover, we characterize databases having finite semantics and then, we address the issue of database updating. We argue that our approach allows for a new kind of updates, in which the update result depends not only on the fact involved in the update but also on its current truth value in the database.

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Four-Valued Semantics for Deductive Databases

Laurent,

Spyratos

2021

Preprint

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In this paper, we introduce a novel approach to deductive databases meant to take into account the needs of current applications in the area of data integration. To this end, we extend the formalism of standard deductive databases to the context of Four-valued logic so as to account for unknown, inconsistent, true or false information under the open world assumption. In our approach, a database is a pair (E, R) where E is the extension and R the set of rules. The extension is a set of pairs of the form ϕ, v where ϕ is a fact and v is a value that can be true, inconsistent or false -but not unknown (that is, unknown facts are not stored in the database). The rules follow the form of standard Datalog neg rules but, contrary to standard rules, their head may be a negative atom. Our main contributions are as follows: (i) we give an expression of first-degree entailment in terms of other connectors and exhibit a functionally complete set of basic connectors not involving first-degree entailment, (ii) we define a new operator for handling our new type of rules and show that this operator is monotonic and continuous, thus providing an effective way for defining and computing database semantics, and (iii) we argue that our framework allows for the definition of a new type of updates that can be used in most standard data integration applications.

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4-Valued Semantics Under the OWA: A Deductive Database Approach

Cited by 3 publications

References 14 publications

Handling Inconsistencies in Tables with Nulls and Functional Dependencies

Handling Inconsistencies in Tables with Nulls and Functional Dependencies

Deductive databases in four-valued logic: rule semantics and models

Four-Valued Semantics for Deductive Databases

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