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21.
22.
Zdzisław Dywan 《Studia Logica》1980,39(1):1-4
In [2] A. Wroski proved that there is a strongly finite consequence C which is not finitely based i.e. for every consequence C
+ determined by a finite set of standard rules C C
+. In this paper it will be proved that for every strongly finite consequence C there is a consequence C
+ determined by a finite set of structural rules such that C(Ø)=C
+(Ø) and
=
(where
,
are consequences obtained by adding to the rules of C, C
+ respectively the rule of substitution). Moreover it will be shown that under certain assumptions C=C
+. 相似文献
23.
Wiesław Dziobiak 《Studia Logica》1981,40(3):249-252
We prove that each intermediate or normal modal logic is strongly complete with respect to a class of finite Kripke frames
iff it is tabular, i.e. the respective variety of pseudo-Boolean or modal algebras, corresponding to it, is generated by a
finite algebra.
The author wishes to thank the Editors for calling his attention to the fact that the result of this paper concerning the
intermediate logics was announced earlier by A. Wroński at the conference “Logical calculi”, Wrocław, October 5–7, 1975, though
without proof. Wroński's result has not been published. 相似文献
24.
The intuitionistic consequence operation restricted to the language with (equivalence) and (negation) as the only connectives is axiomatized by means of a finite set of sequential rules of inference.To the memory of Professor Roman Suszko 相似文献
25.
Wiesław Dziobiak 《Studia Logica》1982,41(1):67-73
The aim of this note is to show (Theorem 1.6) that in each of the cases: = {, }, or {, , }, or {, , } there are uncountably many -intermediate logics which are not finitely approximable. This result together with the results known in literature allow us to conclude (Theorem 2.2) that for each : either all -intermediate logics are finitely approximate or there are uncountably many of them which lack the property. 相似文献
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