arXiv subjects

Apostolos Syropoulos

Publications and source records attributed to Apostolos Syropoulos.

16 recordsLinked to original sources

arXiv2024

Fuzzy Aristotelian Diagrams

After a concise introduction to the square of opposition, in particular, and, Aristotelian Diagrams, in general, I describe how one can create a mathematical universe to host these objects. Since these objects assume that the underlying logic is the bivalent logic, I have used these objects as a starting point to introduce fuzzy Aristotelian Diagrams and describe a mathematical formulation of them. In addition, I outline the characteristrics of a mathematical universe that hosts them.

cs.LO↗

arXiv2020

Dialectica Fuzzy Petri Nets

Brown and Gurr have introduced a model of Petri Nets that is based on de~Paiva's Dialectica categories. This model was refined in an unpublished technical report, where Petri nets with multiplicities, instead of {\em elementary} nets (i.e., nets with multiplicities zero and one only) were considered. In this note we expand this modelling to deal with {\em fuzzy} petri nets. The basic idea is to use as the dualizing object in the Dialectica categories construction, the unit interval that has all the properties of a {\em lineale} structure.

cs.LO↗

arXiv2019

Fuzzy Bigraphs: An Exercise in Fuzzy Communicating Agents

Bigraphs and their algebra is a model of concurrency. Fuzzy bigraphs are a generalization of birgraphs intended to be a model of concurrency that incorporates vagueness. More specifically, this model assumes that agents are similar, communication is not perfect, and, in general, everything is or happens to some degree.

cs.LO↗

arXiv2018

Computing with P Systems

P systems are computing conceptual computing devices that are at least as powerful as Turing machines. However, until recently it was not known how one can encode any recursive function as a P~system. Here we propose a new encoding of recursive as P~systems with graph-like structure, which is the main difference with previous documented attempts. The consequence of this and other such efforts is that they provide a solid ground for the implementation of real programming languages in existing hardware.

cs.FL↗

arXiv2018

Robots That Do Not Avoid Obstacles

The motion planning problem is a fundamental problem in robotics, so that every autonomous robot should be able to deal with it. A number of solutions have been proposed and a probabilistic one seems to be quite reasonable. However, here we propose a more adoptive solution that uses fuzzy set theory and we expose this solution next to a sort survey on the recent theory of soft robots, for a future qualitative comparison between the two.

cs.RO↗

arXiv2016

On Vague Computers

Vagueness is something everyone is familiar with. In fact, most people think that vagueness is closely related to language and exists only there. However, vagueness is a property of the physical world. Quantum computers harness superposition and entanglement to perform their computational tasks. Both superposition and entanglement are vague processes. Thus quantum computers, which process exact data without "exploiting" vagueness, are actually vague computers.

cs.OH↗

arXiv2016

Ideograms for Physics and Chemistry

Ideograms (symbols that represent a word or idea) have great communicative value. They refer to concepts in a simple manner, easing the understanding of related ideas. Moreover, ideograms can simplify the often cumbersome notation used in the fields of Physics and physical Chemistry. Nonetheless only a few specific ideograms for these fields have been defined to date. In this work we propose that the scientific community follows the example of Mathematics -as well as that of oriental languages- and bestows a more important role upon ideograms. To support this thesis we propose ideograms for essential concepts in Physics and Chemistry. They are designed to be intuitive, and their goal is to make equations easier to read and understand. Our symbols are included in a publicly available Latex package (svrsymbols).

physics.ed-ph↗

arXiv2016

A (Basis for a) Philosophy of a Theory of Fuzzy Computation

Vagueness is a linguistic phenomenon as well as a property of physical objects. Fuzzy set theory is a mathematical model of vagueness that has been used to define vague models of computation. The prominent model of vague computation is the fuzzy Turing machine. This conceptual computing device gives an idea of what computing under vagueness means, nevertheless, it is not the most natural model. Based on the properties of this and other models of vague computing, it is aimed to formulate a basis for a philosophy of a theory of fuzzy computation.

cs.OH↗

arXiv2014

Fuzzy Categories

Since categories are graphs with additional "structure", one should start from fuzzy graphs in order to define a theory of fuzzy categories. Thus is makes sense to introduce categories whose morphisms are associated with a plausibility degree that determines to what extend it is possible to "go" from one object to another one. These categories are called {\em fuzzy categories}. Of course, the basic properties of these categories are similar but not identical to their ordinary counterparts. Thus, it is necessary to introduce notion like fuzzy commutative diagrams, fuzzy initial and fuzzy terminal objects, etc.

cs.LO↗

arXiv2014

Using Scripting Languages to Teach Programming

Nowadays, scripting programming languages like Python, Perl and Ruby are widely used in system programming, scientific computing, etc. Although solving a particular problem in these languages requires less time, less programming effort, and less concepts to be taught to achieve the desired goal, still they are not used as teaching tools. Therefore, the use of scripting languages as a teaching vehicle for programming course is very promising. On the other hand, GUI programming, when performed with such languages, is easy and rewarding, since one sees the result of her work immediately. Thus, we are sure that scripting languages combined with GUI toolkits will be the next big thing in computer education.

cs.CY↗

arXiv2012

On Generalized Fuzzy Multisets and their Use in Computation

An orthogonal approach to the fuzzification of both multisets and hybrid sets is presented. In particular, we introduce L-multi-fuzzy and L-fuzzy hybrid sets, which are general enough and in spirit with the basic concepts of fuzzy set theory. In addition, we study the properties of these structures. Also, the usefulness of these structures is examined in the framework of mechanical multiset processing. More specifically, we introduce a variant of fuzzy P systems and, since simple fuzzy membrane systems have been introduced elsewhere, we simply extend previously stated results and ideas.

cs.LO↗

arXiv2011

Fuzzy Topological Systems

Dialectica categories are a very versatile categorical model of linear logic. These have been used to model many seemingly different things (e.g., Petri nets and Lambek's calculus). In this note, we expand our previous work on fuzzy petri nets to deal with fuzzy topological systems. One basic idea is to use as the dualizing object in the Dialectica categories construction, the unit real interval [0,1], which has all the properties of a {\em lineale}. The second basic idea is to generalize Vickers's notion of a topological system.

cs.LO↗

arXiv2011

Generalizing Topology via Chu Spaces

By using the representational power of Chu spaces we define the notion of a generalized topological space (or GTS, for short), i.e., a mathematical structure that generalizes the notion of a topological space. We demonstrate that these topological spaces have as special cases known topological spaces. Furthermore, we develop the various topological notions and concepts for GTS. Moreover, since the logic of Chu spaces is linear logic, we give an interpretation of most linear logic connectives as operators that yield topological spaces.

cs.LO↗

arXiv2009

Can we debug the Universe?

Roughly, the Church-Turing thesis is a hypothesis that describes exactly what can be computed by any real or feasible conceptual computing device. Generally speaking, the computational metaphor is the idea that everything, including the universe itself, has a computational nature. However, if the Church-Turing thesis is not valid, then does it make sense to expect the construction of a computer program capable of simulating the whole Universe? In the lights of hypercomputation, the scientific discipline that is about computing beyond the Church-Turing barrier, the most natural answer to this question is: No. This note is a justification of this answer and its deeper meaning based on arguments from physics, the philosophy of the mind, and, of course, (hyper)computability theory.

cs.OH↗

arXiv2009

Some Thoughts on Hypercomputation

Hypercomputation is a relatively new branch of computer science that emerged from the idea that the Church--Turing Thesis, which is supposed to describe what is computable and what is noncomputable, cannot possible be true. Because of its apparent validity, the Church--Turing Thesis has been used to investigate the possible limits of intelligence of any imaginable life form, and, consequently, the limits of information processing, since living beings are, among others, information processors. However, in the light of hypercomputation, which seems to be feasibly in our universe, one cannot impose arbitrary limits to what intelligence can achieve unless there are specific physical laws that prohibit the realization of something. In addition, hypercomputation allows us to ponder about aspects of communication between intelligent beings that have not been considered before

cs.OH↗

arXiv2009

Fuzzy Chemical Abstract Machines

Fuzzy set theory opens new vistas in computability theory and here I show this by defining a new computational metaphor--the fuzzy chemical metaphor. This metaphor is an extension of the chemical metaphor. In particular, I introduce the idea of a state of a system as a solution of fuzzy molecules, that is molecules that are not just different but rather similar, that react according to a set of fuzzy reaction rules. These notions become precise by introducing fuzzy labeled transition systems. Solutions of fuzzy molecules and fuzzy reaction rules are used to define the general notion of a fuzzy chemical abstract machine, which is a {\em realization} of the fuzzy chemical metaphor. Based on the idea that these machines can be used to describe the operational semantics of process calculi and algebras that include fuzziness as a fundamental property, I present a toy calculus that is a fuzzy equivalent of the $π$-calculus.

cs.FL↗