Relational systems with involution

We investigate relational systems endowed with an involution inverting couples of related elements. The concept of a so-called complemented or orthomodular relational system is introduced as a generalization of a complemented or orthomodular lattice, respectively. To every one of the mentioned relational systems [Formula: see text] there is assigned certain algebra [Formula: see text] which can be considered as an algebraic counterpart to [Formula: see text]. The paper is devoted to the relations between these relational systems and the assigned algebras. It is shown that these algebras have some congruence properties.

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Co-quasiordered residuated systems: An introduction

Asian-European Journal of Mathematics ◽

10.1142/s1793557119500736 ◽

2019 ◽

Vol 12 (05) ◽

pp. 1950073

Author(s):

Daniel A. Romano

Keyword(s):

Constructive Mathematics ◽

Relational System ◽

Philosophical Orientation ◽

Relational Systems ◽

Bishop’S Constructive Mathematics

In this paper, we introduce and discuss a concept of co-quasiordered residuated relational systems. The setting of this research is Bishop’s constructive mathematics — a mathematics based on the Intuitionisic logic and particular principle-philosophical orientation of this attitude. Moreover, we introduce the concept of co-filters in such relational system. Additionally, some of the fundamentals properties of these substructures we have been shown.

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An axiomatic system for the first order language with an equi-cardinality quantifier

Journal of Symbolic Logic ◽

10.2307/2269698 ◽

1966 ◽

Vol 31 (4) ◽

pp. 633-640 ◽

Cited By ~ 3

Author(s):

Mitsuru Yasuhara

Keyword(s):

Rational Numbers ◽

Axiomatic System ◽

Universal Quantifier ◽

Real Numbers ◽

Relational System ◽

First Order ◽

Order Language ◽

Relational Systems ◽

Finite Domains ◽

The Universe

The equi-cardinality quantifier1 to be used in this article, written as Qx, is characterised by the following semantical rule: A formula QxA(x) is true in a relational system exactly when the cardinality of the set consisting of these elements which make A(x) true is the same as that of the universe. For instance, QxN(x) is true in 〈Rt, N〉 but false in 〈Rl, N〉 where Rt, Rl, and N are the sets of rational numbers, real numbers, and natural numbers, respectively. We notice that in finite domains the equi-cardinality quantifier is the same as the universal quantifier. For this reason, all relational systems considered in the following are assumed infinite.

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On the algorithmic theory of stacks1

Fundamenta Informaticae ◽

10.3233/fi-1980-3305 ◽

1980 ◽

Vol 3 (3) ◽

pp. 311-331

Author(s):

Andrzej Salwicki

Keyword(s):

Programming Language ◽

Representation Theorem ◽

Relational System ◽

Finite Sequences ◽

Relational Systems

The algorithmic theory of stacks, ATS, formalizes properties of relational systems of stacks. It turns out that apart from previously known axioms a new axiom of algorithmic nature, while ¬ empty (s) do s: = pop (s) true is in place. The representation theorem stating that every relational system of stacks is isomorphic to a system of finite sequences of elements is proved. The connections between ATS and a type STACKS declaration (written in LOGLAN programming language) are shown.

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Programmability and P = N P conjecture

Fundamenta Informaticae ◽

10.3233/fi-1978-2106 ◽

1979 ◽

Vol 2 (1) ◽

pp. 71-82

Author(s):

Stanisław Radziszowski

Keyword(s):

Time Complexity ◽

Sufficient Conditions ◽

Turing Machines ◽

Relational System ◽

Relational Systems

We define the time-complexity of programs (FS-expressions) in an arbitrary relational system. We extend these notions to nondeterministic programs (NFS-expressions). There are some sufficient conditions for a relational system which ensure the equivalence of the P = N P problem in that system to the classical P = N P problem for Turing machines. This implies that the P = N P problem can be solved in thc theory of programs in some relational systems.

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Sheffer operation in relational systems

Soft Computing ◽

10.1007/s00500-021-06466-x ◽

2021 ◽

Author(s):

Ivan Chajda ◽

Helmut Länger

Keyword(s):

Binary Relation ◽

Boolean Algebras ◽

Variety Of Algebras ◽

Binary Relations ◽

Orthomodular Lattices ◽

Relational System ◽

Distributive Variety ◽

Congruence Distributive Variety ◽

Relational Systems ◽

Congruence Distributive

AbstractThe concept of a Sheffer operation known for Boolean algebras and orthomodular lattices is extended to arbitrary directed relational systems with involution. It is proved that to every such relational system, there can be assigned a Sheffer groupoid and also, conversely, every Sheffer groupoid induces a directed relational system with involution. Hence, investigations of these relational systems can be transformed to the treatment of special groupoids which form a variety of algebras. If the Sheffer operation is also commutative, then the induced binary relation is antisymmetric. Moreover, commutative Sheffer groupoids form a congruence distributive variety. We characterize symmetry, antisymmetry and transitivity of binary relations by identities and quasi-identities satisfied by an assigned Sheffer operation. The concepts of twist products of relational systems and of Kleene relational systems are introduced. We prove that every directed relational system can be embedded into a directed relational system with involution via the twist product construction. If the relation in question is even transitive, then the directed relational system can be embedded into a Kleene relational system. Any Sheffer operation assigned to a directed relational system $${\mathbf {A}}$$ A with involution induces a Sheffer operation assigned to the twist product of $${\mathbf {A}}$$ A .

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A counterexample to a conjecture of Scott and Suppes

Journal of Symbolic Logic ◽

10.2307/2964569 ◽

1959 ◽

Vol 24 (1) ◽

pp. 15-16 ◽

Cited By ~ 25

Author(s):

W. W. Tait

Keyword(s):

Functional Calculus ◽

Relational System ◽

First Order ◽

Universal Sentence ◽

Relational Systems ◽

Identity Symbol

In [1], it is conjectured that if S is a sentence in the first-order functional calculus with identity, and every subsystem of every finite relational system which satisfies S also satisfies S, then S is finitely equivalent to a universal sentence. (Two sentences are finitely equivalent if and only if they are satisfied by the same finite relational systems.) The following sentence S refutes that conjecture, and moreover S is satisfied by all finite subsystems of all (finite or infinite) relational systems which satisfy it.1S contains as predicate letters only the two-place predicate letters ≦, R (and the identity symbol =).

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Limit ultraproducts

Journal of Symbolic Logic ◽

10.2307/2270135 ◽

1965 ◽

Vol 30 (2) ◽

pp. 212-234 ◽

Cited By ~ 11

Author(s):

H. Jerome Keisler

Keyword(s):

Order Logic ◽

First Order Logic ◽

Relational System ◽

First Order ◽

Relational Systems ◽

Result Theorem ◽

General Limit

This paper is a sequel to our earlier paper, “Limit Ultrapowers”, [6]. In that paper we introduced the limit ultrapower construction and proved that is isomorphic to a limit ultrapower of if and only if every PCΔ class which contains also contains . In Section 1 of this paper we introduce the more general limit ultraproduct construction, and in Section 2 we prove that, for any class K of relational systems, a relational system is isomorphic to a limit ultraproduct of members of K if and only if every PCΔ class which includes K also contains . As a consequence, the property of K being an intersection of PCΔ classes is characterized purely set-theoretically by the property of K being closed under isomorphisms and limit ultraproducts.In Section 3 we apply limit ultraproducts to obtain model-theoretic conditions equivalent to the set-theoretic condition that every α-complete ultrafilter is γ+-complete. The first result, Theorem 3.7, was announced in the abstract [8], and it is also closely related to a result which was stated without proof in [10], namely Theorem 2 of that paper.In Sections 4 and 5 we apply our results in order to improve a theorem of Craig in [2]. Craig considered the logic L(Q), where Q is a set of cardinals, obtained from ordinary first order logic by adding for each α ϵ Q the quantifier “there exist at least α”.

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BRIDGING TO ANOTHER DIMENSION: THE RELATIONAL SYSTEM OF SHAMANISM AND RELIGIOUS ENCOUNTER AMONGST THE TEMIAR SENOI OF MALAYA

Jurnal Ilmiah Ilmu Ushuluddin ◽

10.18592/jiiu.v20i1.5051 ◽

2021 ◽

Vol 20 (1) ◽

pp. 72

Author(s):

Riza Saputra ◽

Husnul Khotimah

Keyword(s):

Religious Conversion ◽

World View ◽

Case Analysis ◽

Physical World ◽

Relational System ◽

Library Research ◽

Healing Ritual ◽

Relational Systems ◽

Cross Case Analysis ◽

Subjective Space

This paper aims at finding the relational system, religious encounter, and modernity of the Temiar community in Malaysia. The form of this research has focused on literature research (library research) by using literature as a source of research. The method used is an analysis of documents by conducting content analysis. This within-case analysis is followed by a thematic analysis across the case. The data patterns emerging from the within-case and cross-case analysis of theme, the information of Temiar’s world view is compared from several documents. Having discussed the relational systems in shamanic society and religious encounters and modernity amongst Temiar, this paper concludes that: Firstly. Shaman creates the cultural experience in the inter-subjective space of the ritual as the flow of the spirit guide through the healing ritual. The shaman is the spirit medium, a person who can receive songs from the spirit guide during dreams. Secondly, singing and dancing is an activity that in itself bridges the gulf between the physical world and the metaphysical. Thirdly, Temiars have begun to incorporate representations of varying spirit entities associated with religious conversion and modernization into their cosmology.

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