On Tarski algebras with a finite set of free generators

2017 ◽  
Vol 11 (01) ◽  
pp. 1850003
Author(s):  
Aldo V. Figallo
Keyword(s):  
Free Generators ◽  
Finite Set ◽  
Tarski Algebras ◽  
Tarski Algebra

In this paper, we describe a method to determine the structure of the Tarski algebra with a finite set of free generators which is different to that given by Iturrioz and Monteiro in [Les algèbres de Tarski avec un nombre fini de générateurs libres, in Informe Técnico, Vol. 37 (Instituto de Matemática de la Universidad Nacional del Sur, Bahía Blanca, 1994)].

Cn algebras with Moisil possibility operators

2020 ◽  
Author(s):  
Aldo V Figallo ◽  
Gustavo Pelaitay ◽  
Jonathan Sarmiento
Keyword(s):  
Free Generators ◽  
Finite Set ◽  
Tarski Algebras ◽  
Phd Thesis

Abstract In this paper, we continue the study of the Łukasiewicz residuation algebras of order $n$ with Moisil possibility operators (or $MC_n$-algebras) initiated by Figallo (1989, PhD Thesis, Universidad Nacional del Sur). More precisely, among other things, a method to determine the number of elements of the $MC_n$-algebra with a finite set of free generators is described. Applying this method, we find again the results obtained by Iturrioz and Monteiro (1966, Rev. Union Mat. Argent., 22, 146) and by Figallo (1990, Rep. Math. Logic, 24, 3–16) for the case of Tarski algebras and $I\varDelta _{3}$-algebras, respectively.

Implicational formulas in intuitionistic logic

1974 ◽  
Vol 39 (4) ◽  
pp. 661-664 ◽  
Author(s):  
Alasdair Urquhart
Keyword(s):  
Propositional Calculus ◽  
Modus Ponens ◽  
Equivalence Classes ◽  
Alternative Proof ◽  
Hilbert Algebra ◽  
Hilbert Algebras ◽  
Free Generators ◽  
Finite Set ◽  
Image Position ◽  
The Right

In [1] Diego showed that there are only finitely many nonequivalent formulas in n variables in the positive implicational propositional calculus P. He also gave a recursive construction of the corresponding algebra of formulas, the free Hilbert algebra In on n free generators. In the present paper we give an alternative proof of the finiteness of In, and another construction of free Hilbert algebras, yielding a normal form for implicational formulas. The main new result is that In is built up from n copies of a finite Boolean algebra. The proofs use Kripke models [2] rather than the algebraic techniques of [1].Let V be a finite set of propositional variables, and let F(V) be the set of all formulas built up from V ⋃ {t} using → alone. The algebra defined on the equivalence classes , by settingis a free Hilbert algebra I(V) on the free generators . A set T ⊆ F(V) is a theory if ⊦pA implies A ∈ T, and T is closed under modus ponens. For T a theory, T[A] is the theory {B ∣ A → B ∈ T}. A theory T is p-prime, where p ∈ V, if p ∉ T and, for any A ∈ F(V), A ∈ T or A → p ∈ T. A theory is prime if it is p-prime for some p. Pp(V) denotes the set of p-prime theories in F(V), P(V) the set of prime theories. T ∈ P(V) is minimal if there is no theory in P(V) strictly contained in T. Where X = {A1, …, An} is a finite set of formulas, let X → B be A1 →····→·An → B (ϕ → B is B). A formula A is a p-formula if p is the right-most variable occurring in A, i.e. if A is of the form X → p.

Non-repetitive sequences

1970 ◽  
Vol 68 (2) ◽  
pp. 267-274 ◽  
Author(s):  
P. A. B. Pleasants
Keyword(s):  
Repetitive Sequences ◽  
Finite Set ◽  
Infinite Sequences

This note is concerned with infinite sequences whose terms are chosen from a finite set of symbols. A segment of such a sequence is a set of one or more consecutive terms, and a repetition is a pair of finite segments that are adjacent and identical. A non-repetitive sequence is one that contains no repetitions.

The inverse problem of recovering the coefficients of a differential equations on a graph

2020 ◽  
Vol 28 (5) ◽  
pp. 727-738
Author(s):  
Victor Sadovnichii ◽  
Yaudat Talgatovich Sultanaev ◽  
Azamat Akhtyamov
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Finite Number ◽  
Characteristic Equation ◽  
Arbitrary Number ◽  
New Class ◽  
Finite Set

AbstractWe consider a new class of inverse problems on the recovery of the coefficients of differential equations from a finite set of eigenvalues of a boundary value problem with unseparated boundary conditions. A finite number of eigenvalues is possible only for problems in which the roots of the characteristic equation are multiple. The article describes solutions to such a problem for equations of the second, third, and fourth orders on a graph with three, four, and five edges. The inverse problem with an arbitrary number of edges is solved similarly.

scholarly journals A Novel Simplified Implementation of Finite-Set Model Predictive Control for Power Converters

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Jose J. Silva ◽  
Jose R. Espinoza ◽  
Jaime A. Rohten ◽  
Esteban S. Pulido ◽  
Felipe A. Villarroel ◽  
...  
Keyword(s):  
Model Predictive Control ◽  
Predictive Control ◽  
Power Converters ◽  
Finite Set

scholarly journals Robust Universal Inference

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 773
Author(s):  
Amichai Painsky ◽  
Meir Feder
Keyword(s):  
Robust Estimation ◽  
Minimax Estimator ◽  
Worst Case ◽  
Capacity Theory ◽  
Alternative Approach ◽  
True Model ◽  
Finite Set ◽  
Universal Prediction ◽  
Estimation Scheme

Learning and making inference from a finite set of samples are among the fundamental problems in science. In most popular applications, the paradigmatic approach is to seek a model that best explains the data. This approach has many desirable properties when the number of samples is large. However, in many practical setups, data acquisition is costly and only a limited number of samples is available. In this work, we study an alternative approach for this challenging setup. Our framework suggests that the role of the train-set is not to provide a single estimated model, which may be inaccurate due to the limited number of samples. Instead, we define a class of “reasonable” models. Then, the worst-case performance in the class is controlled by a minimax estimator with respect to it. Further, we introduce a robust estimation scheme that provides minimax guarantees, also for the case where the true model is not a member of the model class. Our results draw important connections to universal prediction, the redundancy-capacity theorem, and channel capacity theory. We demonstrate our suggested scheme in different setups, showing a significant improvement in worst-case performance over currently known alternatives.

scholarly journals Finite representability of semigroups with demonic refinement

2021 ◽  
Vol 82 (2) ◽  
Author(s):  
Robin Hirsch ◽  
Jaš Šemrl
Keyword(s):  
Partial Order ◽  
Turing Machines ◽  
Binary Relations ◽  
Finite Representation ◽  
First Order ◽  
Finite Structures ◽  
Finite Base ◽  
Finite Set ◽  
Finite Representability ◽  
Representation Class

AbstractThe motivation for using demonic calculus for binary relations stems from the behaviour of demonic turing machines, when modelled relationally. Relational composition (; ) models sequential runs of two programs and demonic refinement ($$\sqsubseteq $$ ⊑ ) arises from the partial order given by modeling demonic choice ($$\sqcup $$ ⊔ ) of programs (see below for the formal relational definitions). We prove that the class $$R(\sqsubseteq , ;)$$ R ( ⊑ , ; ) of abstract $$(\le , \circ )$$ ( ≤ , ∘ ) structures isomorphic to a set of binary relations ordered by demonic refinement with composition cannot be axiomatised by any finite set of first-order $$(\le , \circ )$$ ( ≤ , ∘ ) formulas. We provide a fairly simple, infinite, recursive axiomatisation that defines $$R(\sqsubseteq , ;)$$ R ( ⊑ , ; ) . We prove that a finite representable $$(\le , \circ )$$ ( ≤ , ∘ ) structure has a representation over a finite base. This appears to be the first example of a signature for binary relations with composition where the representation class is non-finitely axiomatisable, but where the finite representation property holds for finite structures.

On procrustean mean shapes and the shape of the means

1996 ◽  
Vol 28 (2) ◽  
pp. 336-337
Author(s):  
Hulling Le
Keyword(s):  
Statistical Models ◽  
Nuisance Parameters ◽  
Finite Set

Two sets of k labelled points, or configurations, in ℝm are defined to have the same shape if they differ only in translation, rotation and scaling. An important matter in practice is the estimation of the shape of the means; the shape determined by the means of data on the vertices of configurations. However, statistical models for vertices-based shapes always involve some unknown samplewise nuisance parameters associated with ambiguity of location, rotation and scaling. The use of procrustean mean shapes for a finite set of configurations, which are usually formulated directly in terms of their vertices, will enable one to eliminate these nuisance parameters.

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