On triangular norms and uninorms definable in ŁΠ12

AbstractIn this paper, we investigate the definability of classes of t-norms and uninorms in the logic ŁΠ12. In particular we provide a complete characterization of definable continuous t-norms, weak nilpotent minimum t-norms, conjunctive uninorms continuous on [0,1), and idempotent conjunctive uninorms, and give both positive and negative results concerning definability of left-continuous t-norms (and uninorms). We show that the class of definable uninorms is closed under construction methods as annihilation, rotation and rotation–annihilation. Moreover, we prove that every logic based on a definable uninorm is in PSPACE, and that any finitely axiomatizable logic based on a class of definable uninorms is decidable. Finally we show that the Uninorm Mingle Logic (UML) and the Basic Uninorm Logic (BUL) are finitely strongly standard complete w.r.t. the related class of definable left-continuous conjunctive uninorms

Generalized continuous and left-continuous t-norms arising from algebraic semantics for fuzzy logics

This paper focuses on the issue of how generalizations of continuous and left-continuous t-norms over linearly ordered sets should be from a logical point of view. Taking into account recent results in the scope of algebraic semantics for fuzzy logics over chains with a monoidal residuated operation, we advocate linearly ordered BL-algebras and MTL-algebras as adequate generalizations of continuous and left-continuous t-norms respectively. In both cases, the underlying basic structure is that of linearly ordered residuated lattices. Although the residuation property is equivalent to left-continuity in t-norms, continuous t-norms have received much more attention due to their simpler structure. We review their complete description in terms of ordinal sums and discuss the problem of describing the structure of their generalization to BL-chains. In particular we show the good behavior of BL-algebras over a finite or complete chain, and discuss the partial knowledge of rational BL-chains. Then we move to the general non-continuous case corresponding to left-continuous t-norms and MTL-chains. The unsolved problem of describing the structure of left-continuous t-norms is presented together with a fistful of construction-decomposition techniques that apply to some distinguished families of t-norms and, finally, we discuss the situation in the general study of MTL-chains as a natural generalization of left-continuous t-norms

Fitting aggregation operators to data

Theoretical advances in modelling aggregation of information produced a wide range of aggregation operators, applicable to almost every practical problem. The most important classes of aggregation operators include triangular norms, uninorms, generalised means and OWA operators.With such a variety, an important practical problem has emerged: how to fit the parameters/ weights of these families of aggregation operators to observed data? How to estimate quantitatively whether a given class of operators is suitable as a model in a given practical setting? Aggregation operators are rather special classes of functions, and thus they require specialised regression techniques, which would enforce important theoretical properties, like commutativity or associativity. My presentation will address this issue in detail, and will discuss various regression methods applicable specifically to t-norms, uninorms and generalised means. I will also demonstrate software implementing these regression techniques, which would allow practitioners to paste their data and obtain optimal parameters of the chosen family of operators.<br /

The Language of Paul Muldoon

This book interprets the multifarious writing of the Irish-American word wizard, Paul Muldoon, who has been described by The Times Literary Supplement as ‘the most significant English-language poet born since the second World War’. Readership: All interested in poetry and writing from Ireland and the English-speaking world, and in the enigma of language

On The Corporeal Exchange: Thai Boxing's Sacrificial Movement

This dissertation is an ethnographic study of Thai boxing (muay Thai) understood as sacrificial exchange, exploring the practice of this martial art in the context of contemporary Thai society. Drawing on two years of apprenticeship and participation research in Northeast Thailand and Bangkok, I consider the fighters’ integration in broader patterns of seasonal labor migration as they move between rural, regional tournaments and Bangkok stadiums. Focusing on the training of one particular boxer, I investigate interactions between trainers, managers, family, patrons and ancestral spirits. The boxers’ embodied actions as they unfold in time represent the sovereign relationship between living and dead, nature and culture, performatively establishing the boundaries between growth and decay. As the living move through a world of animate social relations, accruing debt, the boxer’s embodied patterns of repetition and exhaustion in training, and of destructive action in combat, create a possibility for shifting this balance, accruing merit for those otherwise occupied in handling materials which support the powerful, and transforming the established hierarchical order of everyday life. Against the background of the impermanent, closed, linear, cyclical or progressive temporalities of monasteries, factories, the military and the monarchy, the temporality of the ring remains open, giving fighters the elbow-room to performatively engage crucial symbols of life and death, male and female, human and animal, affording otherwise politically disempowered Northeastern Thai families the opportunity to create meaning and possibility in their lives. Acting as both victim and executioner, fighters accrue credit for the assembled audience, reinvesting each tier of the community with a degree of responsibility for life. I argue that these practices occur within a ‘deathworld’, in which the heightened attentiveness to the limited possibilities for action reaffirm the local position of the individual within the collective. With embodied motion that cuts across local categories of stillness and mobility, the living and the dead, with ever-greater stamina, Thai boxers become increasingly valuable and credit-able, paying the debts, material and spiritual, that their assembled supporters have incurred as they live their kinetically excessive lives, allowing men throughout the community to remain accountable to Kings, Buddha, ancestors, factories and patrons.Doctor of Philosoph

Quantum Mechanics for Thinkers

This book provides quick access to quantum mechanics without dealing with a true textbook that demands proper specialized studies in physics (and related mathematics) for about a couple of years. It consists of three parts: basic formalism, formal development, and ontological issues. The 70 figures are a crucial instrument for becoming acquainted in a "representative" way with abstract problems, and the 30 in-section boxes assist readers understand for difficult mathematical problems. The book offers a considerable number of clear and analytical treatments of what are considered the most difficult conceptual problems of the theory