@@ -67,7 +67,7 @@ Our approach extends that based on operators:

* operators specialized in activities with enrichment of constraints from domain experts

Other works follow this approach in particular we follow the steps of the [HoloClean](http://holoclean.io/) cleanup framework which divides into detect and fix,

Other works follow this approach in particular we follow the steps of the [HoloClean](https://holoclean.github.io/) cleanup framework which divides into detect and fix,

we propose our own solution of fix based on learning with neural networks and fuzzy logic rules.

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@@ -79,7 +79,7 @@ This activity is performed by an algorithm that involves a learning phase and th

The algorithm is able to search for optimal local solutions in the logical constraints of domain, time, pitch grain and sample data provided in configuration.

In the configuration of the algorithm the distribution of existing data will be used in the case of hypotheses of low-frequency dirty data or with a clean sample distribution to which reference is made enriched by constraints provided by the domain expert in the form of logical formulas. The alternative values proposed will therefore be respected for the statistical distribution rather than the constraints.

### LTWN: logica espressiva e adeguamento progressivo

### LTNW: logica espressiva e adeguamento progressivo

What we propose here is an approach to our unique knowledge of neural network classifier enriched by fuzzy logic constraints.

Statistical Relational Learning (SRL) approaches have been developed for reasoning under uncertainty and learning in the presence of data and rich knowledge.

It is an alternative logic to the Aristotelian one. In fact, it can be translated into Italian as "nuanced logic" because it rejects the principle of the excluded third of classical logic: if A is A, then A cannot be non-A. The fuzzy logic aims to reach the regulation of a system through the formalization of concepts derived from common experience.

The basic idea is that a quantity can assume not only boolean values (true / false), but a set of values indicating the level of "truth" of a certain expression. For this reason, fuzzy sets (fuzzy sets) are introduced on which "membership" functions are built with a generally triangular or trapezoidal shape.

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@@ -131,9 +131,9 @@ The basic idea is that a quantity can assume not only boolean values (true / fal

Another benefit of the fuzzy logic is that it manages to handle the so-called gain-scheduling with linear combinations of known situations with extreme ease.

### LTWN and databases

### LTNW (LTN Wrapper) and databases

We can use LTWN for the value prediction step to correct or calculate unknown values.

We can use LTNW for the value prediction step to correct or calculate unknown values.

1. definition of space:

construction of constants and variable ranges

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@@ -150,7 +150,7 @@ We can use LTWN for the value prediction step to correct or calculate unknown va

## Application examples

In order to understand how the translation steps of a table are carried out in LTWN, we propose a gradual series of practical examples accompanied by the respective differences that highlight.

In order to understand how the translation steps of a table are carried out in LTNW, we propose a gradual series of practical examples accompanied by the respective differences that highlight.

### Minimal dependency example

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@@ -161,15 +161,11 @@ the first tuple explicitly expressed both values as true.

the second tuple has explicitly expressed only the truth for A.

The test result for B (t2) will be true with rapid convergence, as there is no conflicting information.

Case study: [test_ldb_basic](../docker/docker-ldb/ldb/test/test_basic.txt)

### Minimal example of inconsistency

Starting from the previous categorical case if we add a description that contradicts a constraint, optimization will end by timeout and not by minimizing the distances of the constraints, leaving the value space in an unsecured configuration to satisfy all constraints.

Case study: [test_ldb_basic_contradiction](../docker/docker-ldb/ldb/test/test_basic_contradiction.txt)