On Theses Without Iterated Modalities of Modal Logics Between C1 and S5. Part 1

Andrzej Pietruszczak

Bulletin of the Section of Logic (2017)

  • Volume: 46, Issue: 1/2
  • ISSN: 0138-0680

Abstract

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This is the first, out of two papers, in which we identify all logics between C1 and S5 having the same theses without iterated modalities. All these logics canbe divided into certain groups. Each such group depends only on which of thefollowing formulas are theses of all logics from this group: (N), (T), (D), ⌜(T)∨ ☐q⌝,and for any n > 0 a formula ⌜(T) ∨ (altn)⌝, where (T) has not the atom ‘q’, and(T) and (altn) have no common atom. We generalize Pollack’s result from [12],where he proved that all modal logics between S1 and S5 have the same theseswhich does not involve iterated modalities (i.e., the same first-degree theses).

How to cite

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Andrzej Pietruszczak. "On Theses Without Iterated Modalities of Modal Logics Between C1 and S5. Part 1." Bulletin of the Section of Logic 46.1/2 (2017): null. <http://eudml.org/doc/295574>.

@article{AndrzejPietruszczak2017,
abstract = {This is the first, out of two papers, in which we identify all logics between C1 and S5 having the same theses without iterated modalities. All these logics canbe divided into certain groups. Each such group depends only on which of thefollowing formulas are theses of all logics from this group: (N), (T), (D), ⌜(T)∨ ☐q⌝,and for any n > 0 a formula ⌜(T) ∨ (altn)⌝, where (T) has not the atom ‘q’, and(T) and (altn) have no common atom. We generalize Pollack’s result from [12],where he proved that all modal logics between S1 and S5 have the same theseswhich does not involve iterated modalities (i.e., the same first-degree theses).},
author = {Andrzej Pietruszczak},
journal = {Bulletin of the Section of Logic},
keywords = {first-degree theses of modal logics; theses without iterated modalities; Pollack’s theory of Basic Modal Logic; basic theories for modal logics between C1 and S5},
language = {eng},
number = {1/2},
pages = {null},
title = {On Theses Without Iterated Modalities of Modal Logics Between C1 and S5. Part 1},
url = {http://eudml.org/doc/295574},
volume = {46},
year = {2017},
}

TY - JOUR
AU - Andrzej Pietruszczak
TI - On Theses Without Iterated Modalities of Modal Logics Between C1 and S5. Part 1
JO - Bulletin of the Section of Logic
PY - 2017
VL - 46
IS - 1/2
SP - null
AB - This is the first, out of two papers, in which we identify all logics between C1 and S5 having the same theses without iterated modalities. All these logics canbe divided into certain groups. Each such group depends only on which of thefollowing formulas are theses of all logics from this group: (N), (T), (D), ⌜(T)∨ ☐q⌝,and for any n > 0 a formula ⌜(T) ∨ (altn)⌝, where (T) has not the atom ‘q’, and(T) and (altn) have no common atom. We generalize Pollack’s result from [12],where he proved that all modal logics between S1 and S5 have the same theseswhich does not involve iterated modalities (i.e., the same first-degree theses).
LA - eng
KW - first-degree theses of modal logics; theses without iterated modalities; Pollack’s theory of Basic Modal Logic; basic theories for modal logics between C1 and S5
UR - http://eudml.org/doc/295574
ER -

References

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  13. [13] G. Priest, An Introduction to Non-Classical Logic, 2th edition, Cambridge University Press, 2008. DOI: 10.1017/CBO9780511801174 
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