## Relational Framework and its Applications

### BibTeX

@MISC{Obojska_relationalframework,

author = {Lidia Obojska},

title = {Relational Framework and its Applications},

year = {}

}

### OpenURL

### Abstract

primitive notions of quality and relation. With the introduction of a unary relation, we develop a system totally based on the sole primitive notion of relation. Such a modification enables a definition of the concept of dynamic unary relation. In this way we construct a simple language capable to express other well known theories such as Robinson’s arithmetic or a piece of a theory of concatenation. A key role in this system plays an abstract relation designated by “ ()”, which can be interpreted in different ways, but in this paper we will focus on the case when we can perform computations and obtain results. Keywords—language, unary relations, arithmetic, computability I.

### Citations

41 | Arithmetices principia, nova methodo exposita. Fratres Bocca - Peano |

2 |
G.Lenzi - Verso i sistemi assiomatici del 2000
- Giorgi
- 1996
(Show Context)
Citation Context ... define everything in frames of mathematics in terms of sets and membership relation. In this paper we would like to encode some of the well known concepts in terms of a primitive relation “( )” [6], =-=[2]-=-, [4]. Hence, we propose a kind of a calculus on unary relations. The most important thing is how we interpret the main operator of a system – “( )”. Let us begin with several examples. Examples: 1) L... |

2 |
Foundations of Mathematics: Questions of Analysis, Geometry and Algorithmics
- Engeler
- 1993
(Show Context)
Citation Context ...e from the axioms of M, and the proof is complete. IV. CALCULUS ON RELATIONS AND THEORY OF CONCATENATION Besides the theory Q we will consider another weak theory, a theory of concatenation — TC [1], =-=[3]-=-. Its language is composed of a binary function symbol, three constants: { ⌢ ,ǫ, α, β} and the following six axioms: (C1) ∀x : x ⌢ ǫ = ǫ ⌢ x = x (C2) ∀x∀y∀z : x ⌢ [y ⌢ z] = [x ⌢ y] ⌢ z (C3) ∀x∀y∀u∀v :... |

2 |
A general axiomatic framework for the foundations of mathematics, logic and computer science", Memorie di Matematica e Applicazioni
- Forti, Lenzi
- 1997
(Show Context)
Citation Context ...ne everything in frames of mathematics in terms of sets and membership relation. In this paper we would like to encode some of the well known concepts in terms of a primitive relation “( )” [6], [2], =-=[4]-=-. Hence, we propose a kind of a calculus on unary relations. The most important thing is how we interpret the main operator of a system – “( )”. Let us begin with several examples. Examples: 1) Let “(... |

1 |
Andrzej Mostowski and foundational studies
- Grzegorczyk, Zdanowski, et al.
- 2008
(Show Context)
Citation Context ...er strings that are mutually different. The axiom (C3) is called an editor axiom and describes what happens if two editors independently suggest splitting a large text into two volumes. It was proved =-=[5]-=- the undecidability of the theory TC. In the previous Section we showed that Q is interpretable within DGSS when multiplication is defined in classical recursive way and “( )” is interpretable as a un... |

1 |
Primary relations” in a new foundational axiomatic framework
- Obojska
- 2007
(Show Context)
Citation Context ...l. We define everything in frames of mathematics in terms of sets and membership relation. In this paper we would like to encode some of the well known concepts in terms of a primitive relation “( )” =-=[6]-=-, [2], [4]. Hence, we propose a kind of a calculus on unary relations. The most important thing is how we interpret the main operator of a system – “( )”. Let us begin with several examples. Examples:... |