Approximate denial constraints

The problem of mining integrity constraints from data has been extensively studied over the past two decades for commonly used types of constraints, including the classic Functional Dependencies (FDs) and the more general Denial Constraints (DCs). In this paper, we investigate the problem of mining from data approximate DCs, that is, DCs that are "almost" satisfied. Approximation allows us to discover more accurate constraints in inconsistent databases and detect rules that are generally correct but may have a few exceptions. It also allows to avoid overfitting and obtain constraints that are more general, more natural, and less contrived. We introduce the algorithm ADCMiner for mining approximate DCs. An important feature of this algorithm is that it does not assume any specific approximation function for DCs, but rather allows for arbitrary approximation functions that satisfy some natural axioms that we define in the paper. We also show how our algorithm can be combined with sampling to return highly accurate results considerably faster.

SOME MODEL-THEORETIC RESULTS ON THE 3-VALUED PARACONSISTENT FIRST-ORDER LOGIC QCIORE

The 3-valued paraconsistent logic Ciore was developed by Carnielli, Marcos and de Amo under the name LFI2, in the study of inconsistent databases from the point of view of logics of formal inconsistency (LFIs). They also considered a first-order version of Ciore called LFI2*. The logic Ciore enjoys extreme features concerning propagation and retropropagation of the consistency operator: a formula is consistent if and only if some of its subformulas is consistent. In addition, Ciore is algebraizable in the sense of Blok and Pigozzi. On the other hand, the logic LFI2* satisfies a somewhat counter-intuitive property: the universal and the existential quantifier are inter-definable by means of the paraconsistent negation, as it happens in classical first-order logic with respect to the classical negation. This feature seems to be unnatural, given that both quantifiers have the classical meaning in LFI2*, and that this logic does not satisfy the De Morgan laws with respect to its paraconsistent negation. The first goal of the present article is to introduce a first-order version of Ciore (which we call QCiore) preserving the spirit of Ciore, that is, without introducing unexpected relationships between the quantifiers. The second goal of the article is to adapt to QCiore the partial structures semantics for the first-order paraconsistent logic LPT1 introduced by Coniglio and Silvestrini, which generalizes the semantic notion of quasi-truth considered by Mikeberg, da Costa and Chuaqui. Finally, some important results of classical Model Theory are obtained for this logic, such as Robinson’s joint consistency theorem, amalgamation and interpolation. Although we focus on QCiore, this framework can be adapted to other 3-valued first-order LFIs.