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Universal Algebraic Geometry: Syntax and Semantics
In this paper, we give a general insight into the ideas that make ground for the develo** of universal algebraic geometry and logical geometry. We...
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A Joint Logic of Problems and Propositions
AbstractIn a 1985 commentary to his collected works, Kolmogorov informed the reader that his 1932 paper On the interpretation of intuitionistic logic ...
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Robust Feedback Set Stabilization of Logic Networks with State-Dependent Uncertain Switching and Control Constraints
This study investigates the robust feedback set stabilization of switched logic control networks (SLCNs) with state-dependent uncertain switching and...
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Bernoullicity of lopsided principal algebraic actions
We show that the principal algebraic actions of countably infinite groups associated to lopsided elements in the integral group ring satisfying some...
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Logic, Spatial Algorithms and Visual Reasoning
Spatial and diagrammatic reasoning is a significant part not only of logical abilities, but also of logical studies. The authors of this paper...
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Fields of Algebraic Numbers Computable in Polynomial Time. II
This paper is a continuation of [Algebra and Logic, 58, No. 6, 447-469 (2019)] where we constructed polynomial-time presentations for the field of...
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Soft Logic as an Extension of Pascal’s Work
AbstractPascal was a great mathematician and scientist, who contributed to many fields in mathematics and science. When he was 19 years old, he...
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Logic
The terms logic and mathematics are often paired in the historiography of the latter. But, as discussed in this book, logic is not a monolithic...
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Algebraic Machine Learning: Emphasis on Efficiency
AbstractA survey of the state of the art in research on algebraic machine learning is presented. The main emphasis is on computational complexity....
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Algebraic Geometry over Algebraic Structures. VIII. Geometric Equivalences and Special Classes of Algebraic Structures
This paper belongs to our series of works on algebraic geometry over arbitrary algebraic structures. In this one, there will be investigated seven...
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A brief history of Tarskian algebraic logic with new perspectives and innovations
We take a magical tour in algebraic logic, which is the natural interface between universal algebra and mathematical logic, starting from classical...
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Elements of Algebraic Geometry
Here we present the algebraic geometry background for the study of PAC fields. The central result is a descent argument which associates to each...
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A Matrix Method for Detecting Formal Solutions to the Problem of Algebraic Synthesis of a Finite-State Machine with a Datapath of Transitions
For a finite-state machine with a datapath of transitions, a new method for detecting formal solutions to an algebraic synthesis problem is proposed....
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Features of a Multivalued Generalization of Binary Logic Operations in Linear Algebra for Problems of Digital Processing of Current-Output Sensor Signals
AbstractWe discuss the problems of transition to the logic synthesis of multivalued digital structures for computer technology and automatic control...
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Algebraic Operations on Fuzzy Sets and Relations in Automata Interpretation Implemented by Logical Hardware
Algebraic operations on fuzzy sets and relations and their implementation by hardware in automata interpretation are considered. Two ways of...
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Bridge between logic and algebra
The algebraic counterpart of classical sentential logic LS is the variety BA of Boolean algebras. Why is this so important? The answer lies in the...
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Algebraic Surgery
The main purpose of this chapter is to introduce a chain complex version of the L-groups and of the surgery obstructions and to identify them with...
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A Universal Algebraic Set Theory Built on Mereology with Applications
Category theory is often treated as an algebraic foundation for mathematics, and the widely known algebraization of ZF set theory in terms of this...
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On Algebraic-Geometric and Universal Theories of Abelian Groups
This paper is of an overview nature, accumulating results on algebraic geometry over Abelian groups and close to them model-theoretic results related...
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Logic in the History and Philosophy of Mathematical Practice
Mathematical logic is the study of reasoning about mathematical objects and the degree to which mathematical and scientific reasoning can be...