Mathematical foundations for social computing

Economic Foundations of Practical Social Computing

Foundations for Mathematical Structuralism∗

We investigate the form of mathematical structuralism that acknowledges the existence of structures and their distinctive structural elements. This form of structuralism has been subject to criticisms recently, and our view is that the problems raised are resolved by proper, mathematics-free theoretical foundations. Starting with an axiomatic theory of abstract objects, we identify a mathematic...

Mathematical Foundations for Asymmetric

1.2 Algorithm for GCD The Euclidean algorithm is a simple algorithm for finding the gcd of two numbers. The basis of the algorithm is the fact that if a = qb+ c, a, q, b, c ∈ Z,⇒ (a, b) = (b, c). (4) This is very easy to see. Let s = (a, b)⇒ s|a, s|b⇒ a = sa1, b = sb1 t = (b, c)⇒ t|b, t|c⇒ b = tb2, c = tc2 Also c = a− qb = s(a1 − qb1)⇒ s|c Also as s|b (as s is the gcd of (a, b), s divides b and...

Mathematical Foundations for Participation Ontologies

The notion of participation as a relation between objects, activities, and time has been axiomatized in various ontologies. In this paper, we focus on three of these ontologies – PSL-Core, Gangemi’s axioms, and DOLCE. We provide a verification of these participation ontologies by introducing ontologies for new classes of mathematical structures known as incidence bundles and incidence foliation...

Astrogeometry: towards Mathematical Foundations

In image processing (e.g., in astronomy), the desired black-and-white image is, from the mathematical viewpoint, a set. Hence, to process images, we need to process sets. To deene a generic set, we need innnitely many parameters; therefore, if we want to represent and process sets in the computer, we must restrict ourselves to nite-parametric families of sets that will be used to approximate th...