Related papers: Sierpinski Gaskets for Logic Functions Representat…
We study the extension problem on the Sierpinski Gasket ($SG$). In the first part we consider minimizing the functional $\mathcal{E}_{\lambda}(f) = \mathcal{E}(f,f) + \lambda \int f^2 d \mu$ with prescribed values at a finite set of points…
The paper presents a software tool for analysis and interactive engagement in various logical reasoning tasks. A first feature of the program consists in providing an interface for working with logic-specific repositories of formal…
We give an overview over the application of functional equations, namely the classical Poincar\'e and renewal equations, to the study of the spectrum of Laplace operators on self-similar fractals. We compare the techniques used to those…
We use spectral decimation to provide formulae for computing the harmonic gradients of Laplacian eigenfunctions on the Sierpinski Gasket. These formulae are given in terms of special functions that are defined as infinite products.
Traditional treatments of formal logic provide: 1. A syntax for formulas. 2. An inference relation between sets of formulas. 3. A rule for assigning meaning to formulas (semantics) that is sound with respect to the inference relation. First…
We give a mathematically rigorous construction of a magnetic Schr\"odinger operator corresponding to a field with flux through finitely many holes of the Sierpinski Gasket. The operator is shown to have discrete spectrum accumulating at…
The computation of the distance between any two points of the Sierpinski Gasket with respect to the intrinsic metric has already been investigated by several authors. In the literature there is not an explicit formula using the code space…
A Mazurkiewicz set is a plane subset that intersect every straight line at exactly two points, and a Sierpi\'{n}ski-Zygmund function is a function from $\mathbb{R}$ into $\mathbb{R}$ that has as little of the standard continuity as…
Underlying the theory of inferences, a primary task of logic is language analysis. Such a task can be understood as depending on a general theory of representation, taking as a starting point the idea that some entities (`` representations…
In traditional justification logic, evidence terms have the syntactic form of polynomials, but they are not equipped with the corresponding algebraic structure. We present a novel semantic approach to justification logic that models…
We explore a definition of complexity based on logic functions, which are widely used as compact descriptions of rules in diverse fields of contemporary science. Detailed numerical analysis shows that (i) logic complexity is effective in…
Synchrotron radiation plays a central role in astrophysical and high-energy processes. Its spectral description involves the synchrotron function, defined by a non-trivial integral of modified Bessel functions and commonly evaluated through…
One of the main claims of the paper is that Dirac's calculus and broader theories of physics can be treated as theories written in the language of Continuous Logic. Establishing its true interpretation (model) is a model theory problem. The…
In this paper, we establish an analogue of the classical mean value property for both the harmonic functions and some general functions in the domain of the Laplacian on the Sierpinski gasket. Furthermore, we extend the result to some other…
We present a new approach to the theory of k-forms on self-similar fractals. We work out the details for two examples, the standard Sierpinski gasket and the 3-dimensional Sierpinski gasket, but the method is expected to be effective for…
Ludics is a logical framework in which types/formulas are modelled by sets of terms with the same computational behaviour. This paper investigates the representation of inductive data types and functional types in ludics. We study their…
In everyday life it happens that a person has to reason about what other people think and how they behave, in order to achieve his goals. In other words, an individual may be required to adapt his behaviour by reasoning about the others'…
A semantics is given to possibilistic logic, a logic that handles weighted classical logic formulae, and where weights are interpreted as lower bounds on degrees of certainty or possibility, in the sense of Zadeh's possibility theory. The…
Memcomputing logic gates generalize the traditional Boolean logic gates for operation in the reverse direction. According to the literature, this functionality enables the efficient solution of computationally-intensive problems including…
Fractal geometry is the study of sets which exhibit the same pattern at multiple scales. Developing tools to study these sets is of great interest. One step towards developing some of these tools is recognizing the duality between…