Predicative logical matrices

In this paper the procedure is presented that allows to determine in finite number of steps if consequence relations in two finite-valued logical matrices for propostional language L are equal.

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On the Problem of Extending Matrix Semantics Sdequate to Classical Implicative Logic to Matrix Xemantics Adequate to Classical Conjunctive-Implicative Logic

Логико-философские штудии ◽

10.52119/lphs.2021.25.58.001 ◽

2021 ◽

pp. 1-11

Author(s):

Владимир Михайлович Попов

Keyword(s):

Binary Operation ◽

Matrix Semantics ◽

Logical Matrices

В (Попов 2019) дан перечень всех логических матриц, носитель каждой из которых есть {1, 1/2, 0} и выделенное множество каждой из которых есть {1}, адекватных классической импликативной логике. В частности, этому перечню принадлежат логические матрицы ⟨{1, 1/2, 0}, {1}, ⊃ (1, 0, 0, 1)⟩ и ⟨{1, 1/2, 0}, {1}, ⊃ (1/2, 0, 0, 1/2)⟩. Настоящая статья содержит построение бинарной операции & на {1, 1/2, 0} и доказательство того, что ⟨{1, 1/2, 0}, {1}, &, ⊃ (1, 0, 0, 1)⟩ есть L&⊃ -матрица, адекватная классической конъюнктивно-импликативной логике, а также доказательство того, что не существует операции ψ, для которой ⟨{1, 1/2, 0}, {1}, ψ, ⊃ (1/2, 0, 0, 1/2)⟩ есть L&⊃ -матрица, адекватная классической конъюнктивно-импликативной логике. In (Popov 2019), a list of all logical matrices is given, the carrier of each of which is {1, 1/2, 0} and the designated set of each of which is {1}, adequate to classical implicative logic. In particular, to this list belong the logical matrices ⟨{1, 1/2, 0}, {1}, ⊃ (1, 0, 0, 1)⟩ and ⟨{1, 1/2, 0}, {1}, ⊃ (1/2, 0, 0, 1/2)⟩. This article contains the construction of the binary operation & on {1, 1/2, 0} and the proof that ⟨{1, 1/2, 0}, {1}, &, ⊃ (1, 0, 0, 1)⟩ there is an L&⊃ -matrix adequate to the classical conjunctive-implicative logic, as well as a proof that there is no operation ψ for which ⟨{1, 1/2, 0}, {1}, ψ, ⊃ (1/2, 0, 0, 1/2)⟩ is an L&⊃ -matrix that is adequate to the classical conjunctive-implicative logic.

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Algebraic Valuations as Behavioral Logical Matrices

Logic, Language, Information and Computation - Lecture Notes in Computer Science ◽

10.1007/978-3-642-02261-6_2 ◽

2009 ◽

pp. 13-25 ◽

Cited By ~ 1

Author(s):

Carlos Caleiro ◽

Ricardo Gonçalves

Keyword(s):

Logical Matrices

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Novel Approach to Geological Modeling with Combination of Machine Learning

10.5194/egusphere-egu2020-21739 ◽

2020 ◽

Author(s):

Stanislav Ursegov ◽

Armen Zakharian

Keyword(s):

Machine Learning ◽

Oil And Gas ◽

The Novel ◽

Geological Modeling ◽

Oil And Gas Fields ◽

Novel Approach ◽

The Matrix ◽

Gas Fields ◽

Logical Matrices ◽

Fuzzy Logical

This work shows that the traditional version of geological models of oil and gas fields obtained by a computer approach is not the only possible one and it prevents the development of modeling as a whole, since it is not truly mathematical.Given that computers do not work with images, but with numbers, a novel approach is presented for the construction of truly mathematical geological models. The proposed model has an unusual appearance and is not intended for visual analysis, but it is more effective for forecasting. The mathematical basis of the novel approach is the cascades of fuzzy-logical matrices, which are formed from spatial coordinates and considered geological parameters.Suppose that for each point in the geological grid there is a coordinate vector, in the simplest case these are the lateral coordinates X and Y, as well as the vertical coordinate Z. There is also a set of points (wells) at which the specified coordinates and the values of considered geological parameter, for example, porosity or oil saturation are determined. If some seismic parameter is added to them, which can be taken from grids constructed according to seismic data at the points of the wells, then four coordinates become available.Preliminary, all considered geological parameters should be normalized in the range from -1.0 to + 1.0 in order to standardize and equalize them.Four coordinates give six independent pairs. A matrix is constructed for each of these pairs. The matrix size can be different - from 100 per 100 to 1000 per 1000.Next, the values of the considered geological parameter at the well points determined by four coordinates are applied to these matrices. Certainly, such points are much smaller than the points in the matrix, therefore, to fill the entire polygon of the matrix, the interpolation method is used, based on the idea of the lattice Boltzmann equations.The number of fuzzy-logical matrices in one geological model can reach several hundreds.Using the obtained matrices, one can construct membership functions and predict the values of the selected geological parameters, as well as the distribution of initial hydrocarbon reserves or the effectiveness of new drilling at the field.The novel approach to geological modeling based on the cascades of fuzzy-logical matrices may seem complicated. However, the calculation of these cascades is carried out completely automatically, since they are the truly mathematical functions, and not the illustrations of the geological structure of the filed, and they are directly used in forecasting calculations.The cascades of fuzzy-logical matrices can be considered as a new form of machine learning algorithms, for which it is advisable to use big data sets. It opens up the additional possibilities for the application of machine learning methods in geological modeling of oil and gas fields with conventional and unconventional reserves.

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