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### A New Approach to Operations on Bipolar Neutrosophic Soft Sets and Bipolar Neutrosophic Soft Topological Spaces

Taha Yasin Ozturk, Tugba Han Dizman (Simsekler)
2019 Zenodo
In this study, we re-define some operations on bipolar neutrosophic soft sets differently from the studies [2]. On this operations are given interesting examples and them basic properties.  ...  Finally, we introduce basic definitions and theorems on bipolar neutrosophic soft topological spaces  ...  In addition, basic properties of these operations was presented. ( ))⟩: ∈ ): ∈ } for = 1,2 be two bipolar neutrosophic soft sets over .  ...

### Some interconnections between modern algebra and mathematical logic

Leon Henkin
1953 Transactions of the American Mathematical Society
Thus, every finite subset of A is satisfied by some model from the complement of P, and hence every finite subset drawn from the union of A and T is satisfied (by a model of 0).  ...  Higher order languages contain constants denoting, and variables ranging over, sets whose elements may be sets or functions of model elements, as well as functions and relations defined over sets or functions  ...

### Some Interconnections Between Modern Algebra and Mathematical Logic

Leon Henkin
1953 Transactions of the American Mathematical Society
Basic sentences are formed by placing an equality sign between two terms, and further sentences are built up from these basic ones in the following ways.  ...  First we provide two symbols, " + " and " ■," to be used as names of the operations. Next we wish to have symbols (called individual constants) which can be used as names of particular elements in D.  ...  Thus, every finite subset of A is satisfied by some model from the complement of P, and hence every finite subset drawn from the union of A and T is satisfied (by a model of 0).  ...

### Infinite behaviour and fairness in concurrent constraint programming [chapter]

Marta Kwiatkowska
1993 Lecture Notes in Computer Science
It allows the actions ask and tell, the pre x operator !, the (angelic) non-deterministic choice operator , the procedure call p(X), and the concurrency operator k.  ...  Subsequently, we provide semantic, topological de nitions of safety, liveness and fairness properties in a given constraint system.  ...  ACKNOWLEDGEMENTS The author would like to acknowledge the AP1 group at CWI, especially Jaco de Bakker, Jan Rutten, Katuscia Palamidessi, Frank de Boer and Jeroen Warmerdam for a stimulating environment  ...

### Topology and Epistemic Logic [chapter]

Rohit Parikh, Lawrence S. Moss, Chris Steinsvold
2007 Handbook of Spatial Logics
In the former area, we would like to present the basic ideas and results of topologic, the study of two-sorted bimodal logical systems interpreted on subset spaces; these are arbitrary sets with collections  ...  of subsets called opens.  ...  We thank Guram Bezhanishvili, Bernhard Heinemann, Eric Pacuit and Johan van Benthem for comments.  ...

### Representing Temporal Knowledge in the Semantic Web: The Extended 4D Fluents Approach [chapter]

Sotiris Batsakis, Euripides G. M. Petrakis
2011 Smart Innovation, Systems and Technologies
Representing information that evolves in time in ontologies, as well as reasoning over static and dynamic ontologies are the areas of interest in this work.  ...  Existing approaches allow for representations of temporal information, but do not support representation of qualitative relations and reasoning.  ...  TOQL follows an SQL-like syntax (SELECT-FROM-WHERE) and supports SQL operators and constructs such as LIMIT, OFFSET, AND, OR,MINUS, UNION, UNION ALL, INTERSECT, EXISTS, ALL, ANY, IN.  ...

### A metamodeling language supporting subset and union properties

Marcus Alanen, Ivan Porres
2007 Journal of Software and Systems Modeling
The Meta Object Facility (MOF) 2.0 and the Unified Modeling Language Infrastructure introduce new language features such as subsets, (derived) unions and redefinitions, but without a precise semantics.  ...  We give our understanding of these new language features by formalizing the structural constraints imposed by subsets and unions on metamodels and models using Liskov substitutability as the main criterion  ...  Coral is open source and available at http://mde.abo.fi. The basic model operations over models containing subset properties are defined in [2] .  ...

### Some Fundamental Operations on Interval Valued Neutrosophic Hypersoft Set with Their Properties

2021 Zenodo
We also developed some basic operations on IVNHSS such as union, intersection, addition, difference, Truth-favorite, and False-favorite, etc. with their desirable properties.  ...  Finally, the necessity and possibility operations on IVNHSS with properties are presented in the following research  ...  We present different operators on IVNHSS such as union, intersection, addition, difference, extended union, extended intersection, truth-favorite, and false-favorite operations in section 3 with properties  ...

### Page 21 of Mathematical Reviews Vol. 51, Issue 1 [page]

1976 Mathematical Reviews
Intersection distributes over union and vice versa.  ...  The properties of union, intersection, difference, and symmetric difference are studied.  ...

### VAlloy — Virtual Functions Meet a Relational Language [chapter]

Darko Marinov, Sarfraz Khurshid
2002 Lecture Notes in Computer Science
Models in VAlloy are automatically translated into Alloy and can be automatically checked using the existing Alloy Analyzer.  ...  Alloy is suitable for modeling structural properties of object-oriented software. However, Alloy lacks support for dynamic dispatch, i.e., function invocation based on actual parameter types.  ...  We would like to thank Manu Sridharan and Ang-Chih Kao for comments on an earlier draft of this paper. This work was funded in part by ITR grant #0086154 from the National Science Foundation.  ...

### Interpreter fr topologists [article]

Jindrich Zapletal
2017 arXiv   pre-print
Let M be a transitive model of set theory.  ...  , functional analysis, and dynamics.  ...  To find the spaceX , consider the union B of all interpretations of ground model Borel subsets of P(ω <ω ) containing only illfounded trees.  ...

### Measures and forking

H.Jerome Keisler
1987 Annals of Pure and Applied Logic
Methods from ordinary forking theory and the Loeb measure construction from nonstandard analysis are used.  ...  This allows us to extend the method of forking from the class of stable theories to the larger class of theories which do not have the independence property.  ...  By taking unions of basic subsets of X~, we may restrict our consideration to finite subsets of P which mention at most one basic subset Zi of X/for finitely many i e I and are such that Ii increases as  ...

### Granular Computing using Neighborhood Systems [chapter]

Y. Y. Yao
Operations on neighborhood systems, such as complement, intersection, and union, are defined by extending set-theoretic operations.  ...  Using this framework, we examine the notions of rough sets and qualitative fuzzy sets.  ...  If a binary operation g is distributive over f , g + may not be distributive over f + . A neighborhood system is a family of subsets of the universe U .  ...

### A Semantical Approach to Rough Sets and Dominance-Based Rough Sets [chapter]

Lynn D'eer, Chris Cornelis, Yiyu Yao
2016 Communications in Computer and Information Science
In this paper, we focus on a semantically sound approach of Pawlak's rough set model and covering-based rough set models.  ...  There exist two formulations of rough sets: the conceptual and computational one.  ...  This work was partially supported by the Spanish Ministry of Science and Technology under the Project TIN2014-57251-P and the Andalusian Research Plans P10-TIC-6858, P11-TIC-7765 and P12-TIC-2958.  ...

### Logics for hybrid systems

J.M. Davoren, A. Nerode
2000 Proceedings of the IEEE
The high-profile and safety-critical nature of the application areas has fostered a large and growing body of work on formal methods for hybrid systems: mathematical logics, computational models and methods  ...  Such mathematical models have proved fruitful in a great diversity of engineering applications, including air-traffic control, automated manufacturing, and chemical process control.  ...  ACKNOWLEDGMENT The authors' view of hybrid systems and logics for reasoning about them has benefited from fruitful conversations and exchanges with many people; in particular, they would like to thank  ...
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