A mathematical study of fuzzy logic; an algebraic approach

Fuzzy set theory and Fuzzy logic is studied from a mathematical point of view. The main goal is to investigatecommon mathematical structures in various fuzzy logical inference systems and to establish a general mathematical basis for fuzzy logic when considered as multi-valued logic. The study is composed of six distinct publications. The first paper deals with Mattila'sLPC+Ch Calculus. THis fuzzy inference system is an attempt to introduce linguistic objects to mathematical logic without defining these objects mathematically.LPC+Ch Calculus is analyzed from algebraic point of view and it is demonstratedthat suitable factorization of the set of well formed formulae (in fact, Lindenbaum algebra) leads to a structure called ET-algebra and introduced in the beginning of the paper. On its basis, all the theorems presented by Mattila and many others can be proved in a simple way which is demonstrated in the Lemmas 1 and 2and Propositions 1-3. The conclusion critically discusses some other issues of LPC+Ch Calculus, specially that no formal semantics for it is given.In the second paper the characterization of solvability of the relational equation RoX=T, where R, X, T are fuzzy relations, X the unknown one, and o the minimum-induced composition by Sanchez, is extended to compositions induced by more general products in the general value lattice. Moreover, the procedure also applies to systemsof equations. In the third publication common features in various fuzzy logicalsystems are investigated. It turns out that adjoint couples and residuated lattices are very often present, though not always explicitly expressed. Some minor new results are also proved.The fourth study concerns Novak's paper, in which Novak introduced first-order fuzzy logic and proved, among other things, the semantico-syntactical completeness of this logic. He also demonstrated that the algebra of his logic is a generalized residuated lattice. In proving that the examination of Novak's logic can be reduced to the examination of locally finite MV-algebras.In the fifth paper a multi-valued sentential logic with values of truth in an injective MV-algebra is introduced and the axiomatizability of this logic is proved. The paper developes some ideas of Goguen and generalizes the results of Pavelka on the unit interval. Our proof for the completeness is purely algebraic. A corollary of the Completeness Theorem is that fuzzy logic on the unit interval is semantically complete if, and only if the algebra of the valuesof truth is a complete MV-algebra. The Compactness Theorem holds in our well-defined fuzzy sentential logic, while the Deduction Theorem and the Finiteness Theorem do not. Because of its generality and good-behaviour, MV-valued logic can be regarded as a mathematical basis of fuzzy reasoning. The last paper is a continuation of the fifth study. The semantics and syntax of fuzzy predicate logic with values of truth in ana injective MV-algerba are introduced, and a list of universally valid sentences is established. The system is proved to be semanticallycomplete. This proof is based on an idea utilizing some elementary properties of injective MV-algebras and MV-homomorphisms, and is purely algebraic.

Boris Vian dans ses poèmes

El artículo se propone mostrar cómo el estudio de los poemas y canciones de Boris Vian sólo cobra sentido mediante un análisis de conjunto. Tras la aparente dispersión de temas y estilos, bajo la apariencia superficial, cómica y en ocasiones incluso grotesca y banal de sus poemas y canciones, se oculta una unidad y una coherencia profundas y minuciosamente calculadas. Para expresarla Vian huye de las limitaciones de la lógica heredada de Aristóteles y opta por utilizar la técnica del collage, yuxtaponiendo una pluralidad de situaciones y acciones en las que lo real se entremezcla con lo imaginario, cuyo resultado final es la representación de una realidad única, indivisible y a la vez relativa y singular en función de cada individuo, en la que los aparentes antagonismos se revelan como elementos complementarios en el proceso de individualización y conocimiento del «yo» interior.

Adding similarity-based reasoning capabilities to a Horn fragment of possibilistic logic with fuzzy constants

PLFC is a first-order possibilistic logic dealing with fuzzy constants and fuzzily restricted quantifiers. The refutation proof method in PLFC is mainly based on a generalized resolution rule which allows an implicit graded unification among fuzzy constants. However, unification for precise object constants is classical. In order to use PLFC for similarity-based reasoning, in this paper we extend a Horn-rule sublogic of PLFC with similarity-based unification of object constants. The Horn-rule sublogic of PLFC we consider deals only with disjunctive fuzzy constants and it is equipped with a simple and efficient version of PLFC proof method. At the semantic level, it is extended by equipping each sort with a fuzzy similarity relation, and at the syntactic level, by fuzzily “enlarging” each non-fuzzy object constant in the antecedent of a Horn-rule by means of a fuzzy similarity relation.

Formalizing argumentative reasoning in a possibilistic logic programming setting with fuzzy unification

Possibilistic Defeasible Logic Programming (P-DeLP) is a logic programming language which combines features from argumentation theory and logic programming, incorporating the treatment of possibilistic uncertainty at the object-language level. In spite of its expressive power, an important limitation in P-DeLP is that imprecise, fuzzy information cannot be expressed in the object language. One interesting alternative for solving this limitation is the use of PGL+, a possibilistic logic over Gödel logic extended with fuzzy constants. Fuzzy constants in PGL+ allow expressing disjunctive information about the unknown value of a variable, in the sense of a magnitude, modelled as a (unary) predicate. The aim of this article is twofold: firstly, we formalize DePGL+, a possibilistic defeasible logic programming language that extends P-DeLP through the use of PGL+ in order to incorporate fuzzy constants and a fuzzy unification mechanism for them. Secondly, we propose a way to handle conflicting arguments in the context of the extended framework.

A logic programming framework for possibilistic argumentation: formalization and logical properties

In the last decade defeasible argumentation frameworks have evolved to become a sound setting to formalize commonsense, qualitative reasoning. The logic programming paradigm has shown to be particularly useful for developing different argument-based frameworks on the basis of different variants of logic programming which incorporate defeasible rules. Most of such frameworks, however, are unable to deal with explicit uncertainty, nor with vague knowledge, as defeasibility is directly encoded in the object language. This paper presents Possibilistic Logic Programming (P-DeLP), a new logic programming language which combines features from argumentation theory and logic programming, incorporating as well the treatment of possibilistic uncertainty. Such features are formalized on the basis of PGL, a possibilistic logic based on G¨odel fuzzy logic. One of the applications of P-DeLP is providing an intelligent agent with non-monotonic, argumentative inference capabilities. In this paper we also provide a better understanding of such capabilities by defining two non-monotonic operators which model the expansion of a given program P by adding new weighed facts associated with argument conclusions and warranted literals, respectively. Different logical properties for the proposed operators are studied

Trabecular bone score (TBS) as a new complementary approach for osteoporosis evaluation in clinical practice.

Trabecular bone score (TBS) is a recently-developed analytical tool that performs novel grey-level texture measurements on lumbar spine dual X-ray absorptiometry (DXA) images, and thereby captures information relating to trabecular microarchitecture. In order for TBS to usefully add to bone mineral density (BMD) and clinical risk factors in osteoporosis risk stratification, it must be independently associated with fracture risk, readily obtainable, and ideally, present a risk which is amenable to osteoporosis treatment. This paper summarizes a review of the scientific literature performed by a Working Group of the European Society for Clinical and Economic Aspects of Osteoporosis and Osteoarthritis. Low TBS is consistently associated with an increase in both prevalent and incident fractures that is partly independent of both clinical risk factors and areal BMD (aBMD) at the lumbar spine and proximal femur. More recently, TBS has been shown to have predictive value for fracture independent of fracture probabilities using the FRAX® algorithm. Although TBS changes with osteoporosis treatment, the magnitude is less than that of aBMD of the spine, and it is not clear how change in TBS relates to fracture risk reduction. TBS may also have a role in the assessment of fracture risk in some causes of secondary osteoporosis (e.g., diabetes, hyperparathyroidism and glucocorticoid-induced osteoporosis). In conclusion, there is a role for TBS in fracture risk assessment in combination with both aBMD and FRAX.

Absence of complementary sex determination in the parasitoid wasp genus Asobara (Hymenoptera: Braconidae).

An attractive way to improve our understanding of sex determination evolution is to study the underlying mechanisms in closely related species and in a phylogenetic perspective. Hymenopterans are well suited owing to the diverse sex determination mechanisms, including different types of Complementary Sex Determination (CSD) and maternal control sex determination. We investigated different types of CSD in four species within the braconid wasp genus Asobara that exhibit diverse life-history traits. Nine to thirteen generations of inbreeding were monitored for diploid male production, brood size, offspring sex ratio, and pupal mortality as indicators for CSD. In addition, simulation models were developed to compare these observations to predicted patterns for multilocus CSD with up to ten loci. The inbreeding regime did not result in diploid male production, decreased brood sizes, substantially increased offspring sex ratios nor in increased pupal mortality. The simulations further allowed us to reject CSD with up to ten loci, which is a strong refutation of the multilocus CSD model. We discuss how the absence of CSD can be reconciled with the variation in life-history traits among Asobara species, and the ramifications for the phylogenetic distribution of sex determination mechanisms in the Hymenoptera.

Use of alternative and complementary therapies in labor and delivery care: a cross-sectional study of midwives" training in Catalan hospitals accredited as centers for normal birth

Background: The use of complementary and alternative medicine (CAM) and complementary and alternative therapies (CAT) during pregnancy is increasing. Scientific evidence for CAM and CAT in the field of obstetrics mainly covers pain relief in labor. Midwives are responsible for labor and delivery care: hence, their knowledge of CAM and CAT is important. The aims of this study are to describe the professional profile of midwives who provide care for natural childbirth in Catalan hospitals accredited as centers for normal birth, to assess midwives" level of training in CAT and their use of these therapies, and to identify specific resources for CAT in labor wards. Methods: A descriptive, cross-sectional, quantitative method was used to assess the level of training and use of CAT by midwives working at 28 hospitals in Catalonia, Spain, accredited as public normal birth centers. Results: Just under a third of midwives (30.4%) trained in CAT after completion of basic training. They trained in an average of 5.97 therapies (SD 3.56). The number of CAT in which the midwives were trained correlated negatively with age (r = - 0.284; p < 0.001) and with their time working at the hospital in years (r = - 0.136; p = 0.036). Midwives trained in CAT considered that the following therapies were useful or very useful for pain relief during labor and delivery: relaxation techniques (64.3%), hydrotherapy (84.8%) and the application of compresses to the perineum (75.9%). The availability of resources for providing CAT during normal birth care varied widely from center to center. Conclusions: Age may influence attitudes towards training. It is important to increase the number of midwives trained in CAM for pain relief during childbirth, in order to promote the use of CAT and ensure efficiency and safety. CAT resources at accredited hospitals providing normal childbirth care should also be standardized.

Use of alternative and complementary therapies in labor and delivery care: a cross-sectional study of midwives" training in Catalan hospitals accredited as centers for normal birth

Background: The use of complementary and alternative medicine (CAM) and complementary and alternative therapies (CAT) during pregnancy is increasing. Scientific evidence for CAM and CAT in the field of obstetrics mainly covers pain relief in labor. Midwives are responsible for labor and delivery care: hence, their knowledge of CAM and CAT is important. The aims of this study are to describe the professional profile of midwives who provide care for natural childbirth in Catalan hospitals accredited as centers for normal birth, to assess midwives" level of training in CAT and their use of these therapies, and to identify specific resources for CAT in labor wards. Methods: A descriptive, cross-sectional, quantitative method was used to assess the level of training and use of CAT by midwives working at 28 hospitals in Catalonia, Spain, accredited as public normal birth centers. Results: Just under a third of midwives (30.4%) trained in CAT after completion of basic training. They trained in an average of 5.97 therapies (SD 3.56). The number of CAT in which the midwives were trained correlated negatively with age (r = - 0.284; p < 0.001) and with their time working at the hospital in years (r = - 0.136; p = 0.036). Midwives trained in CAT considered that the following therapies were useful or very useful for pain relief during labor and delivery: relaxation techniques (64.3%), hydrotherapy (84.8%) and the application of compresses to the perineum (75.9%). The availability of resources for providing CAT during normal birth care varied widely from center to center. Conclusions: Age may influence attitudes towards training. It is important to increase the number of midwives trained in CAM for pain relief during childbirth, in order to promote the use of CAT and ensure efficiency and safety. CAT resources at accredited hospitals providing normal childbirth care should also be standardized.

Evaluation of drug-induced neurotoxicity based on metabolomics, proteomics and electrical activity measurements in complementary CNS in vitro models.

The present study was performed in an attempt to develop an in vitro integrated testing strategy (ITS) to evaluate drug-induced neurotoxicity. A number of endpoints were analyzed using two complementary brain cell culture models and an in vitro blood-brain barrier (BBB) model after single and repeated exposure treatments with selected drugs that covered the major biological, pharmacological and neuro-toxicological responses. Furthermore, four drugs (diazepam, cyclosporine A, chlorpromazine and amiodarone) were tested more in depth as representatives of different classes of neurotoxicants, inducing toxicity through different pathways of toxicity. The developed in vitro BBB model allowed detection of toxic effects at the level of BBB and evaluation of drug transport through the barrier for predicting free brain concentrations of the studied drugs. The measurement of neuronal electrical activity was found to be a sensitive tool to predict the neuroactivity and neurotoxicity of drugs after acute exposure. The histotypic 3D re-aggregating brain cell cultures, containing all brain cell types, were found to be well suited for OMICs analyses after both acute and long term treatment. The obtained data suggest that an in vitro ITS based on the information obtained from BBB studies and combined with metabolomics, proteomics and neuronal electrical activity measurements performed in stable in vitro neuronal cell culture systems, has high potential to improve current in vitro drug-induced neurotoxicity evaluation.

Empirics of the international inequality in CO2 emissions intensity: explanatory factors according to complementary decomposition methodologies

This paper analyses the international inequalities in CO2 emissions intensity for the period 1971- 2009 and assesses explanatory factors. Multiplicative, group and additive methodologies of inequality decomposition are employed. The first allows us to clarify the separated role of the carbonisation index and the energy intensity in the pattern observed for inequalities in CO2 intensities; the second allows us to understand the role of regional groups; and the third allows us to investigate the role of different fossil energy sources (coal, oil and gas). The results show that, first, the reduction in global emissions intensity has coincided with a significant reduction in international inequality. Second, the bulk of this inequality and its reduction are attributed to differences between the groups of countries considered. Third, coal is the main energy source explaining these inequalities, although the growth in the relative contribution of gas is also remarkable. Fourth, the bulk of inequalities between countries and its decline are explained by differences in energy intensities, although there are significant differences in the patterns demonstrated by different groups of countries.

DEVELOPMENT OF LOGIC IN INDIA: SIGNIFICANCE OF 'THE DUOLOGUE BETWEEN PĀYĀSI AND KASSAPA' ("LONG DISCOURSES")

ABSTRACT 'The Duologue of King/Governor Pāyāsi' ("Long Discourses") has long been recognised as a source for the proto-materialism current at the time of the Buddha. What needs to be stressed is the significance of the text as a pointer to the development of Logic in India. Perception (observation and experiment employing the joint method of agreement and difference), which is an accepted method of experimental enquiry, and reasoning from analogy, which can lead at best to a probable conclusion - these two are the only means employed to settle the dispute concerning the existence of the other-world. The Jain version of the same duologue-cum-parable, though varying in minor details regarding the name and identity of the monk refuting the king/governor, contains the same contrast, namely, perception versus analogical reasoning. There can be little doubt that the original parable was conceived with a view to asserting the existence of the other-world. In the Kaṭha Upaniṣad (sixth century BCE), an earlier Brahmanical text, however, instead of argument by analogy, verbal testimony (śabda) was invoked to settle the same point. Naciketas is assailed by doubt about the existence of a person after his or her death. The authority of Yama, the Pluto of Indian mythology, is invoked to convince him that the other-world does exist. Thus, the three parables taken together exhibit three means of knowledge in operation: verbal testimony and argument by analogy pitted against perception.

Remarks on an algebraic semantics for paraconsistent Nelson's logic

In the paper Busaniche and Cignoli (2009) we presented a quasivariety of commutative residuated lattices, called NPc-lattices, that serves as an algebraic semantics for paraconsistent Nelson's logic. In the present paper we show that NPc-lattices form a subvariety of the variety of commutative residuated lattices, we study congruences of NPc-lattices and some subvarieties of NPc-lattices.

Matrix- based logic for avoiding paradoxes and its paraconsistent alternative

The present article shows that there are consistent and decidable many- valued systems of propositional logic which satisfy two or all the three criteria for non- trivial inconsistent theories by da Costa (1974). The weaker one of these paraconsistent system is also able to avoid a series of paradoxes which come up when classical logic is applied to empirical sciences. These paraconsistent systems are based on a 6- valued system of propositional logic for avoiding difficulties in several domains of empirical science (Weingartner (2009)).