Nicolás Madrid

On Coherence and Consistence in Fuzzy Answer Set Semantics for Residuated Logic Programs

In this work we recall the first steps towards the definition of an answer set semantics for residuated logic programs with negation, and concentrate on the development of relationships between the notions of coherence and consistence of an interpretation.

Measuring Inconsistency in Fuzzy Answer Set Semantics

Recent approaches have shown that the measurement of the amount of inconsistent information contained in a logic theory can be useful to infer positive information. This paper deals with the definition of measures of inconsistency in the residuated-logic-programming paradigm under the fuzzy answer set semantics. This fuzzy framework provides a soft mechanism to control the amount of information inferred and, thus, controlling the inconsistencies by modifying slightly the truth values of some rules.

A top-k query answering procedure for fuzzy logic programming

We present a top-k query answering procedure for Fuzzy Logic Programming, in which arbitrary computable functions may appear in the rule bodies to manipulate truth values. The top-k ranking problem, i.e. determining the top k answers to a query, becomes important as soon as the set of facts becomes quite large.

On the existence and unicity of stable models in normal residuated logic programs

We introduce a sufficient condition which guarantees the existence of stable models for a normal residuated logic program interpreted on the truth-space [0, 1] n . Specifically, the continuity of the connectives involved in the program ensures the existence of stable models. Then, we study conditions which guarantee the uniqueness of stable models in the particular case of the product t-norm, its residuated implication and the standard negation.

Lane departure warning for mobile devices based on a fuzzy representation of images

The use of driver assistance systems is a current trend in the car industry. However, most driver assistance systems require the use of multiple sensors, increasing the cost of their implementation in cars and making them inaccessible to many users. In this paper, we present an efficient Lane Departure Warning system for mobile devices, which is real-time, accurate and accessible to most users. On the one hand, the accuracy of the system relies on Line Detection based on Hough Transforms, a combination that has proven to be reliable for this goal in many approaches. On the other hand, the reduction of the computational time, to achieve real-time processing, is due mainly to a proposed fuzzy representation of images. Finally, we also present various tests that show that the system proposed runs at up to 20 FPS on a mobile device (with a dual-core CPU at 1.0 GHz) with a resolution of 320240px.

On the measure of incoherence in extended residuated logic programs

In this paper we continue analyzing the introduction of negation into the framework of residuated logic programming [18], [19]; specifically, we focus on extended programs, in which strong negation is introduced. The classical approach to extended logic programs consists in considering negated literals as new, independent, ones and, then apply the usual monotonic approach (based on the fix-point semantics and the TP operator); if the least fix-point so obtained is inconsistent, then the approach fails and no meaning is attached to the program. This paper introduces several approaches to considering consistence (under the term coherence) into a fuzzy setting, and studies some of their properties.

Measuring Instability in Normal Residuated Logic Programs: Discarding Information

Inconsistency in the framework of general residuated logic programs can be, somehow, decomposed in two notions: incoherence and instability. In this work, we focus on the measure of instability of normal residuated programs. Some measures are provided and initial results are obtained in terms of the amount of information that have to be discarded in order to recover stability.

The Notion of Weak-Contradiction: Definition and Measures

In this paper, we present a way to represent contradiction between fuzzy sets. This representation is given in terms of the notion of f-weak-contradiction. Unlike other approaches, we do not define contradiction just by using one of the relations of f-weak-contradiction but by considering the whole set of relations. This consideration avoids the need to fix an operator beforehand in order to take into account all the information between two fuzzy sets. As a result, we characterize the contradiction between fuzzy sets and define a family of measures of contradiction satisfying four interesting properties: symmetry; antitonicity; if the intersection is empty, then the measure is one; and if there is an element in the intersection with degree of membership 1, then the measure is zero.

Upper bounding overlaps by groupings

The notions of overlapping and grouping arise from the problem how to assign an object to exactly one class among several available. In this respect, overlaps and groupings are connected with t-norms and t-conorms. However, there are some properties of t-norms and t-conorms that are not valid for overlaps and groupings, for example, that any t-norm is less than or equal than any t-conorm. This fact motivates the proposed research. Specifically, we determine conditions to ensure that an overlap is smaller than a certain grouping and methods to define operators satisfying such ordering. The relevance of this study is visible at the end of the paper by the inclusion of an illustrative example in the context of image processing.

Measuring instability in normal residuated logic programs: Adding information

Inconsistency in the framework of general resid-uated logic programs can be, somehow, decomposed into two notions: incoherence and instability. In this work, we focus on the measure of instability of normal residuated programs. Some measures were already provided and initial results obtained in terms of the amount of information that have to be discarded in order to recover stability; in this paper, our interest is focused precisely on the case in which stability can be recovered by adding information to our program.