The Thue problem and logical specifications of derivation in formal systems

1999 ◽  
Vol 35 (6) ◽  
pp. 860-866
Author(s):  
A. I. Provotar ◽  
Alhi Adnan
Keyword(s):  
Formal Systems ◽  
Logical Specifications

Modality and folk psychology

2019 ◽  
Vol 28 (1) ◽  
pp. 19-27
Author(s):  
Ja. O. Petik
Keyword(s):  
Modal Logic ◽  
Brain Activity ◽  
Formal System ◽  
Philosophy Of Logic ◽  
Psychological States ◽  
Formal Systems ◽  
Modern Psychology ◽  
Philosophical Interpretation ◽  
Important Direction

The connection of the modern psychology and formal systems remains an important direction of research. This paper is centered on philosophical problems surrounding relations between mental and logic. Main attention is given to philosophy of logic but certain ideas are introduced that can be incorporated into the practical philosophical logic. The definition and properties of basic modal logic and descending ones which are used in study of mental activity are in view. The defining role of philosophical interpretation of modality for the particular formal system used for research in the field of psychological states of agents is postulated. Different semantics of modal logic are studied. The hypothesis about the connection of research in cognitive psychology (semantics of brain activity) and formal systems connected to research of psychological states is stated.

A generalization of the concept of ω-completeness

1957 ◽  
Vol 22 (1) ◽  
pp. 1-14 ◽  
Author(s):  
Leon Henkin
Keyword(s):  
Number Theory ◽  
Functional Calculus ◽  
General Setting ◽  
Con A ◽  
Formal Systems ◽  
Individual Variable ◽  
Free Variables

The concepts of ω-consistency and ω-completeness are closely related. The former concept has been generalized to notions of Γ-consistency and strong Γ-consistency, which are applicable not only to formal systems of number theory, but to all functional calculi containing individual constants; and in this general setting the semantical significance of these concepts has been studied. In the present work we carry out an analogous generalization for the concept of ω-completeness.Suppose, then, that F is an applied functional calculus, and that Γ is a non-empty set of individual constants of F. We say that F is Γ-complete if, whenever B(x) is a formula (containing the single free individual variable x) such that ⊦ B(α) for every α in Γ, then also ⊦ (x)B(x). In the paper “Γ-con” a sequence of increasingly strong concepts, Γ-consistency, n = 1,2, 3,…, was introduced; and it is possible in a formal way to define corresponding concepts of Γn-completeness, as follows. We say that F is Γn-complete if, whenever B(x1,…, xn) is a formula (containing exactly n distinct free variables, namely x1…, xn) such that ⊦ B(α1,…,αn) for all α1,…,αn in Γ, then also ⊦ (X1)…(xn)B(x1,…,xn). However, unlike the situation encountered in the paper “Γ-con”, these definitions are not of interest – for the simple reason that F is Γn-complete if and only if it is Γ-complete, as one easily sees.

Recognition of Music Therapy in Europe

2015 ◽  
Author(s):  
Monika Nöcker-Ribaupierre
Keyword(s):  
Music Therapy ◽  
Formal Systems ◽  
Professional Recognition

The development of formal systems of professional recognition for music therapy within Europe has taken many decades and is still not complete. The European Music Therapy Confederation (EMTC) was established in 1990 with a primary goal being the pursuit of recognition for the profession. This ambition is complicated by the fact that there are so many associations across Europe and not all are in the EMTC. In this chapter the quest for formal professional recognition is outlined. The process by which some countries have achieved recognition, that is in Latvia, UK, and Netherlands, is presented.

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