Formal system

A formal system is an abstract structure used for inferring theorems from axioms according to a set of rules. These rules, which are used for carrying out the inference of theorems from axioms, are the logical calculus of the formal system. A formal system is essentially an "axiomatic system". In 1921, David Hilbert proposed to use such a system as the foundation for the knowledge in mathematics. A formal system may represent a well-defined system of abstract thought. The term formalism is sometimes a rough synonym for formal system, but it also refers to a given style of notation, for example, Paul Dirac's bra–ket notation. Background Logical form Each formal system is described by primitive symbols (which collectively form an alphabet) to finitely construct a formal language from a set of axioms through inferential rules of formation. The system thus consists of valid formulas built up through finite combinations of the primitive symbols—combinations that are formed fr

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EE-110: Logic systems (for MT)

Ce cours couvre les fondements des systèmes numériques. Sur la base d'algèbre Booléenne et de circuitscombinatoires et séquentiels incluant les machines d'états finis, les methodes d'analyse et de synthèse de systèmelogiques sont étudiées et appliquée

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This course gives an introduction to the fundamental concepts and methods of the Digital Humanities, both from a theoretical and applied point of view. The course introduces the Digital Humanities circle of processing and interpretation, from data acquisition to new understandings.

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Le but de ce cours est d'introduire et d'étudier les notions de base de l'algèbre abstraite.

Experience Catalysts And Architecture Towards a New Tradition

Jens Badura, Jeffrey Huang, Selena Savic, Andrew James Sempere

This paper describes two research projects in the field of interactive architecture, both examples of experience catalysts; Settings which allow new insights in the aesthetic constitution and perception of environments. This term can be thought of as somewhat synonymous with artistic intervention, but is used instead to recognize that the participants might not self-identify as artists. We are working with architectural notions of space and place, but are interested in the experience of place more than its formal structure. We wish to emphasize the dynamic and are interested in transitions not as the pauses between states but as destinations worth exploring. Quadricone by Selena Savic is an actual experience catalyst: a physical manifestation of a digital “material” (in this case network traffic.) The goal is less data visualization and more an attempt to understand what it means to physically experience something normally invisible. Inter-Actor by Andrew Sempere casts architecture as an ongoing event which might benefit from the flexibility of the digital. The idea is to create a combination of software and hardware that allows for “rapid prototyping” of interactive space. Inter-Actor is not an experience catalyst but a toolkit for creating them.

Porto: FAUP Publicações2013

Western listeners detect boundary hierarchy in Indian music: a segmentation study

Tudor Popescu, Martin Alois Rohrmeier

How are listeners able to follow and enjoy complex pieces of music? Several theoretical frameworks suggest links between the process of listening and the formal structure of music, involving a division of the musical surface into structural units at multiple hierarchical levels. Whether boundaries between structural units are perceivable to listeners unfamiliar with the style, and are identified congruently between naive listeners and experts, remains unclear. Here, we focused on the case of Indian music, and asked 65 Western listeners (of mixed levels of musical training; most unfamiliar with Indian music) to intuitively segment into phrases a recording of sitar alap of two different raga-modes. Each recording was also segmented by two experts, who identified boundary regions at section and phrase levels. Participant- and region-wise scores were computed on the basis of "clicks" inside or outside boundary regions (hits/false alarms), inserted earlier or later within those regions (high/low "promptness"). We found substantial agreement-expressed as hit rates and click densities-among participants, and between participants' and experts' segmentations. The agreement and promptness scores differed between participants, levels, and recordings. We found no effect of musical training, but detected real-time awareness of grouping completion and boundary hierarchy. The findings may potentially be explained by underlying general bottom-up processes, implicit learning of structural relationships, cross-cultural musical similarities, or universal cognitive capacities.

NATURE RESEARCH2021

The Socio-Economic Embeddedness of the Circular Economy: An Integrative Framework

Claudia Rebeca Binder Signer, Rafael Laurenti

Global economies have been characterised by a large dependency of material inflows from natural stocks, an exponential growth of material stock-in-use in the built environment, and the extensive disposal of waste material outflows to anthropogenic sinks. In this context, the concept of the circular economy has emerged, promising to circulate the stock-in-use of materials and transforming output waste material flows back into useful resources while promoting job and value creation. These promises have drawn the attention and interest of policymakers and industry, and gained popularity across society. Despite its apparent emergent legitimacy and diffusion, a few essential adjustments still need to be addressed so that circular economy initiatives can actually deliver on their promises without leading to negative unintended effects. First, a complete entanglement with the existing formal economy is fundamentally needed; this implies valuing the preservation of natural stocks and pricing material input flows adequately. Secondly, a recognition of its socio-economic embeddedness is essentially necessary. The decision-making of societal actors affects material configuration, which in turn affects societal actors; this important feedback loop needs to be explicitly taken into account in circular economy initiatives. The aim of this short communication paper is to explore these pervasive challenges in a broad context of sustainable physical resource management. An integrative framework for recognising the socio-economic embeddedness of the circular economy in practice and the role of the formal economic system in realising its ambitions is proposed.

2018

First-order logic

First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer

Mathematical logic

Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research i

Mathematics

Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These top