Subalgebras of closure algebras

1992 ◽  
Vol 25 (3) ◽  
pp. 205-219 ◽  
Author(s):  
G. Hansoul ◽  
L. Vrancken-Mawet
Keyword(s):  
Closure Algebras

On Closed Elements in Closure Algebras

1946 ◽  
Vol 47 (1) ◽  
pp. 122 ◽  
Author(s):  
J. C. C. McKinsey ◽  
Alfred Tarski
Keyword(s):  
Closure Algebras

scholarly journals On subvarieties of symmetric closure algebras

2001 ◽  
Vol 108 (1-3) ◽  
pp. 137-152
Author(s):  
J.P. Dı́az Varela
Keyword(s):  
Closure Algebras

Closure Algebras and T1-Spaces

1977 ◽  
Vol 23 (1-6) ◽  
pp. 91-92 ◽  
Author(s):  
G. J. Logan
Keyword(s):  
Closure Algebras

Complexity of interpolation and related problems in positive calculi

2002 ◽  
Vol 67 (1) ◽  
pp. 397-408 ◽  
Author(s):  
Larisa Maksimova
Keyword(s):  
Modal Logic ◽  
Heyting Algebras ◽  
Logical System ◽  
Complexity Bounds ◽  
Np Completeness ◽  
Interpolation Problems ◽  
Finite Set ◽  
Modal Logic S4 ◽  
Closure Algebras ◽  
Logical Calculi

AbstractWe consider the problem of recognizing important properties of logical calculi and find complexity bounds for some decidable properties. For a given logical system L, a property P of logical calculi is called decidable over L if there is an algorithm which for any finite set Ax of new axiom schemes decides whether the calculus L + Ax has the property P or not. In [11] the complexity of tabularity, pre-tabularity. and interpolation problems over the intuitionistic logic Int and over modal logic S4 was studied, also we found the complexity of amalgamation problems in varieties of Heyting algebras and closure algebras.In the present paper we deal with positive calculi. We prove NP-completeness of tabularity, DP-hardness of pretabularity and PSPACE-completeness of interpolation problem over Int+. In addition to above-mentioned properties, we consider Beth's definability properties. Also we improve some complexity bounds for properties of superintuitionistic calculi.

scholarly journals Dimension Theory in Closure Algebras

1951 ◽  
Vol 38 ◽  
pp. 153-166
Author(s):  
Roman Sikorski
Keyword(s):  
Dimension Theory ◽  
Closure Algebras

Products of Closure Algebras and Their Dual Spaces

1977 ◽  
Vol 23 (27-30) ◽  
pp. 439-441
Author(s):  
G. J. Logan
Keyword(s):  
Dual Spaces ◽  
Closure Algebras

A problem in connected finite closure algebras

1947 ◽  
Vol 14 (2) ◽  
pp. 289-296 ◽  
Author(s):  
William T. Puckett
Keyword(s):  
Closure Algebras

Some theorems about the sentential calculi of Lewis and Heyting

1948 ◽  
Vol 13 (1) ◽  
pp. 1-15 ◽  
Author(s):  
J. C. C. McKinsey ◽  
Alfred Tarski
Keyword(s):  
Main Interest ◽  
Sentential Calculus ◽  
Closure Algebras

In this paper we shall prove theorems about some systems of sentential calculus, by making use of results we have established elsewhere regarding closure algebras and Brouwerian albegras. We shall be concerned mostly with the Lewis system and the Heyting system. Some of the results here are new (in particular, Theorems 2.4, 3.1, 3.9, 3.10, 4.5, and 4.6); others have been stated without proof in the literature (in particular, Theorems 2.1, 2.2, 4.4, 5.2, and 5.3).The proofs to be given here will be found to be mostly very simple; generally speaking, they amount to drawing conclusions from the theorems established in McKinsey and Tarski [10] and [11]. We have thought it might be worth while, however, to publish these rather elementary consequences of our previous work—so as to make them readily available to those whose main interest lies in sentential calculus rather than in topology or algebra.

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