Programming Paradigms in Computer Science Education

Main styles, or paradigms of programming – imperative, functional, logic, and object-oriented – are shortly described and compared, and corresponding programming techniques are outlined. Programming languages are classified in accordance with the main style and techniques supported. It is argued that profound education in computer science should include learning base programming techniques of all main programming paradigms.

Representing "Recursive" Default Logic in Modal Logic

The "recursive" definition of Default Logic is shown to be representable in a monotonic Modal Quantificational Logic whose modal laws are stronger than S5. Specifically, it is proven that a set of sentences of First Order Logic is a fixed-point of the "recursive" fixed-point equation of Default Logic with an initial set of axioms and defaults if and only if the meaning of the fixed-point is logically equivalent to a particular modal functor of the meanings of that initial set of sentences and of the sentences in those defaults. This is important because the modal representation allows the use of powerful automatic deduction systems for Modal Logic and because unlike the original "recursive" definition of Default Logic, it is easily generalized to the case where quantified variables may be shared across the scope of the components of the defaults.

Representing Reflective Logic in Modal Logic

The nonmonotonic logic called Reflective Logic is shown to be representable in a monotonic Modal Quantificational Logic whose modal laws are stronger than S5. Specifically, it is proven that a set of sentences of First Order Logic is a fixed-point of the fixed-point equation of Reflective Logic with an initial set of axioms and defaults if and only if the meaning of that set of sentences is logically equivalent to a particular modal functor of the meanings of that initial set of sentences and of the sentences in those defaults. This result is important because the modal representation allows the use of powerful automatic deduction systems for Modal Logic and because unlike the original Reflective Logic, it is easily generalized to the case where quantified variables may be shared across the scope of the components of the defaults thus allowing such defaults to produce quantified consequences. Furthermore, this generalization properly treats such quantifiers since all the laws of First Order Logic hold and since both the Barcan Formula and its converse hold.

Representing Default Logic in Modal Logic

The nonmonotonic logic called Default Logic is shown to be representable in a monotonic Modal Quantificational Logic whose modal laws are stronger than S5. Specifically, it is proven that a set of sentences of First Order Logic is a fixed-point of the fixed-point equation of Default Logic with an initial set of axioms and defaults if and only if the meaning or rather disquotation of that set of sentences is logically equivalent to a particular modal functor of the meanings of that initial set of sentences and of the sentences in those defaults. This result is important because the modal representation allows the use of powerful automatic deduction systems for Modal Logic and because unlike the original Default Logic, it is easily generalized to the case where quantified variables may be shared across the scope of the components of the defaults thus allowing such defaults to produce quantified consequences. Furthermore, this generalization properly treats such quantifiers since both the Barcan Formula and its converse hold.

Representing Autoepistemic Logic in Modal Logic

The nonmonotonic logic called Autoepistemic Logic is shown to be representable in a monotonic Modal Quantificational Logic whose modal laws are stronger than S5. Specifically, it is proven that a set of sentences of First Order Logic is a fixed-point of the fixed-point equation of Autoepistemic Logic with an initial set of axioms if and only if the meaning or rather disquotation of that set of sentences is logically equivalent to a particular modal functor of the meaning of that initial set of sentences. This result is important because the modal representation allows the use of powerful automatic deduction systems for Modal Logic and unlike the original Autoepistemic Logic, it is easily generalized to the case where quantified variables may be shared across the scope of modal expressions thus allowing the derivation of quantified consequences. Furthermore, this generalization properly treats such quantifiers since both the Barcan formula and its converse hold.

Methodology for Language Analysis and Generation in Closed Domains: Pharmaceutical Leaflet

The best results in the application of computer science systems to automatic translation are obtained in word processing when texts pertain to specific thematic areas, with structures well defined and a concise and limited lexicon. In this article we present a plan of systematic work for the analysis and generation of language applied to the field of pharmaceutical leaflet, a type of document characterized by format rigidity and precision in the use of lexicon. We propose a solution based in the use of one interlingua as language pivot between source and target languages; we are considering Spanish and Arab languages in this case of application.

Towards New Teaching in Mathematics How to Realize Inquiry Based and Problem Oriented Mathematics Lessons?

Дагмар Рааб Математиката е вълнуваща и забавна. Можем ли да убедим учениците, че това може да стане действителност. Задачите са най-важните инструменти за учителите по математика, когато планират уроците си. Планът трябва да съдържа идеи как да се очертае и как да се жалонира пътят, по който учениците ще стигнат до решението на дадена задача. Учителите не трябва да очакват от учениците си просто да кажат кой е отговорът на задачата, а да ги увлекат в процеса на решаване с подходящи въпроси. Ролята на учителя е да помогне на учениците • да бъдат активни и резултатни при решаването на задачи; • самите те да поставят задачи; • да модифицират задачи; • да откриват закономерности; • да изготвят стратегии за решаване на задачи; • да откриват и изследват различни начини за решаване на задачи; • да намират смислена връзка между математическите си знания и проблеми от ежедневието. В доклада са представени избрани и вече експериментирани примери за това как учители и ученици могат да намерят подходящ път към нов тип преживявания в преподаването и изучаването на училищната математика.

Scaling and Multiscaling Exponents in Networks and Flows

The main focus of this paper is on mathematical theory and methods which have a direct bearing on problems involving multiscale phenomena. Modern technology is refining measurement and data collection to spatio-temporal scales on which observed geophysical phenomena are displayed as intrinsically highly variable and intermittant heirarchical structures,e.g. rainfall, turbulence, etc. The heirarchical structure is reflected in the occurence of a natural separation of scales which collectively manifest at some basic unit scale. Thus proper data analysis and inference require a mathematical framework which couples the variability over multiple decades of scale in which basic theoretical benchmarks can be identified and calculated. This continues the main theme of the research in this area of applied probability over the past twenty years.