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Wittgenstein's idea "the limits of my language mean the limits of my world" inspires us to ask ourselves if the means of communication and the code intervene in the construction of our world. This is the premise from which we started to develop this paper, considering that a formal system and formalization (a term used in an extended sense) not only have the role of solving specific problems but also radically modify the epistemic universe - "epistema", (from the perspective of the object and the subject) in which manifests. It is emphasized the idea of formalization is used broadly. This required a definition of the term, developed in the paper's first part. After, we underline the importance of writing, analyzing Plato's myth of Theuth. To support our point of view, we refer to some examples of the "epistema" metamorphosis that have as their cause the changes of a formal system, in this case, writing. The example from this article is Hangeul writing. In the framework of the paper, we analyze four directions of the epistema change: communicational, axiological, aesthetic, and socialpolitical, pointing out how these changes occurred within the Korean writing system. [ABSTRACT FROM AUTHOR]

The purpose of this work is the development of mathematical tools for formalizing decision-making problems in open expert real-time control systems. The goal was achieved by defining and formally describing all the elements of a formal system. The most significant result was the proposed approach to formalization. With its help, within the framework of a single formalism, the dynamic properties of the subject area and the logical-analytical activity of the power system dispatcher, presented in different classes of formal logics, were described. The significance of the results obtained lies in the possibility of a rigorous description of various aspects of knowledge within the framework of a single formal apparatus with further pragmatic interpretation in the management process. The proposed approach was distinguished by using the axioms of aletic and deontic logics and the development of axioms that reflect the specifics of the problems being solved. The introduced system of basic concepts and relations makes it possible to classify many decision-making problems for the power systems management. The goals were described within the framework of a single formalism form the basis of the apparatus for formalizing the decision-making problems of the class under consideration. The formalization apparatus provides a description of the dynamic properties of the system within each aspect of knowledge of the content paradigm. The direction of further research is the construction of an appropriate formal theory based on the proposed formal system.

We define a class of formal systems inspired by Prawitz's theory of grounds. The latter is a semantics that aims at accounting for epistemic grounding, namely, at explaining why and how deductively valid inferences have the power to epistemically compel to accept the conclusion. Validity is defined in terms of typed objects, called grounds, that reify evidence for given judgments. An inference is valid when a function exists from grounds for the premises to grounds for the conclusion. Grounds are described by formal terms, either directly when the terms are in canonical form, or indirectly when they are in non-canonical form. Non-canonical terms must reduce to canonical form, and two terms may be said to be equal when they converge towards equivalent grounds. In our systems these properties can be proved through rules distinguished according to whether they concern types or logic. Type rules involve type introduction and elimination, equality for application of operational symbols, and re-writing equations for non-canonical terms. The logic amounts to a sort of intuitionistic system in a Gentzen format. To conclude, we show that each system of our class enjoys a normalization property. [ABSTRACT FROM AUTHOR]

Formal verification technology has been widely applied in the fields of mathematics and computer science. The formalization of fundamental mathematical theories is particularly essential. Axiomatic set theory is a foundational system of mathematics and has important applications in computer science. Most of the basic concepts and theories in computer science are described and demonstrated in terms of set theory. In this paper, we present a formal system of axiomatic set theory based on the Coq proof assistant. The axiomatic system used in the formal system refers to Morse-Kelley set theory which is a relatively complete and concise axiomatic set theory. In this formal system, we complete the formalization of the basic definitions of sets, functions, ordinal numbers, and cardinal numbers and prove the most commonly used theorems in Coq. Moreover, the non-negative integers are defined, and Peano's postulates are proved as theorems. According to the axiom of choice, we also present formal proofs of the Hausdorff maximal principle and Schröeder-Bernstein theorem. The whole formalization of the system includes eight axioms, one axiom schema, 62 definitions, and 148 corollaries or theorems. The “axiomatic set theory” formal system is free from the more apparent paradoxes, and a complete axiomatic system is constructed through it. It is designed to give a foundation for mathematics quickly and naturally. On the basis of the system, we can prove many famous mathematical theorems and quickly formalize the theories of topology, modern algebra, data structure, database, artificial intelligence, and so on. It will become an essential theoretical basis for mathematics, computer science, philosophy, and other disciplines.

While TVET literature focuses on the potential role of the sector in socio-economic development, seldom is attention given to how socio-economic conditions and policies affect the development of the sector. This paper endeavours to contribute to filling this gap. It argues that examining the factors that influence access, equity and outcomes of TVET and education may not be possible without being embedded in their socio-economic context. A main finding of the paper is that cluttered socio-economic conditions and the public governance system in Sudan have resulted in a weak TVET system – severely deficient finance, contraction, inadequacy and irrelevance of provision, and uncoordinated institutional governance. Industrial employers' response is to rely largely on informal apprenticeship, which, while helping the poor and creating employment, may not be a replacement for formal TVET provision. A further finding is that the sector is neglecting rural and conflict-ridden regions and girls. [ABSTRACT FROM AUTHOR]

A theoretical discussion of units in linguistic theory would be, in a sense, incomplete without a discussion of the systems, whether overt or implied, that the units are associated with. This paper traces conceptualizations of units and their accompanying systems in several disciplines. We identify some important problems with rule-based accounts (Parsons 1937) of social action and discuss the transition to non-rule-based theory afforded by ethnomethodology (e.g. Garfinkel 1963, 1967; Heritage 1984, 2011). We draw direct parallels between these issues and analogous developments in mathematical logic (Gödel 1992) and philosophy of mind (Fodor 1968, 1983; Lucas 1961; Putnam 1960, 1967 etc.), and argue that these stem directly from fundamental properties of a class of all formal systems which permit self-reference. We argue that, since these issues are architectural in nature, linguistic theory which postulates that linguistic units are the outputs of a consistent, self-referential, rule-based formal systems (e.g. Hauser, Chomsky & Fitch 2002) will inevitably run into similar problems. This is further supported by examples from actual language use which, as a class, will elude any theoretical explanation grounded in such a system. [ABSTRACT FROM AUTHOR]

There are many important issues in informatics and many agree that algorithms and programming are most important issues that need to be included in informatics education (Dagiene and Jevsikova, 2012). In this paper, we propose how some of these issues can be easily taught using the notion of a formal system which consists of axioms and inference rules by which theorems can be proved. As is argued in (Dagiene and Jevsikova, 2012), we can introduce important topics in informatics using puzzle-like examples and students do not need to have prerequisites for learning. The materials presented in this paper have been used in a college-level elective class titled Hypertext and Computability in our university since the fall semester of 2008 and we believe that the contents proposed in this paper can be easily used to teach beginner students without technical backgrounds.

The standard theory of languages has two levels, one centering on the study, teaching, and application of natural languages, and the other on formal languages and formal systems as applied throughout the mathematical and empirical sciences, in analytic philosophy, and for computer programming, software engineering, artificial intelligence, and related technologies. On both of these levels, standard language theory is dualistic, defining languages in isolation from their domains of discourse and treating attributes in isolation from their objective instances while omitting important properties and functions ordinarily provided or executed by language users, automata, or physical systems on which they appear to supervene. This decoupling of languages from their universes, and from necessary linguistic functions such as display, processing, interpretation, and communication, has profound epistemological bearing, limiting scientific knowledge by precluding the linguistic formulation of any verifiable comprehensive description of reality. This paper proposes that in addition to the two existing levels of standard language theory involving natural and formal languages and systems, the theory of language be recognized to possess a third "metaformal" level on which languages and their universes are "wrapped" in a uniquely structured, totally self-contained metalanguage, the Metaformal System, which restores missing linguistic functionality while using a supertautological intelligibility criterion to generically couple languages with their universes on a fundamental level of shared structure and dynamics, thereby restoring the potential for a verifiable comprehensive and fully connected understanding of the reality we share. [ABSTRACT FROM AUTHOR]