Modal Boolean Connexive Logics: Semantics and Tableau Approach

Tomasz Jarmużek; Jacek Malinowski

Bulletin of the Section of Logic (2019)

  • Volume: 48, Issue: 3, page 213-243
  • ISSN: 0138-0680

Abstract

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In this paper we investigate Boolean connexive logics in a language with modal operators: □, ◊. In such logics, negation, conjunction, and disjunction behave in a classical, Boolean way. Only implication is non-classical. We construct these logics by mixing relating semantics with possible worlds. This way, we obtain connexive counterparts of basic normal modal logics. However, most of their traditional axioms formulated in terms of modalities and implication do not hold anymore without additional constraints, since our implication is weaker than the material one. In the final section, we present a tableau approach to the discussed modal logics.

How to cite

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Tomasz Jarmużek, and Jacek Malinowski. "Modal Boolean Connexive Logics: Semantics and Tableau Approach." Bulletin of the Section of Logic 48.3 (2019): 213-243. <http://eudml.org/doc/295527>.

@article{TomaszJarmużek2019,
abstract = {In this paper we investigate Boolean connexive logics in a language with modal operators: □, ◊. In such logics, negation, conjunction, and disjunction behave in a classical, Boolean way. Only implication is non-classical. We construct these logics by mixing relating semantics with possible worlds. This way, we obtain connexive counterparts of basic normal modal logics. However, most of their traditional axioms formulated in terms of modalities and implication do not hold anymore without additional constraints, since our implication is weaker than the material one. In the final section, we present a tableau approach to the discussed modal logics.},
author = {Tomasz Jarmużek, Jacek Malinowski},
journal = {Bulletin of the Section of Logic},
keywords = {Boolean connexive logics; connexive logic; modal Boolean connexive logics; modal logics; normal modal logics; possible worlds semantics; relatedness; relating logic; relating semantics; tableau methods},
language = {eng},
number = {3},
pages = {213-243},
title = {Modal Boolean Connexive Logics: Semantics and Tableau Approach},
url = {http://eudml.org/doc/295527},
volume = {48},
year = {2019},
}

TY - JOUR
AU - Tomasz Jarmużek
AU - Jacek Malinowski
TI - Modal Boolean Connexive Logics: Semantics and Tableau Approach
JO - Bulletin of the Section of Logic
PY - 2019
VL - 48
IS - 3
SP - 213
EP - 243
AB - In this paper we investigate Boolean connexive logics in a language with modal operators: □, ◊. In such logics, negation, conjunction, and disjunction behave in a classical, Boolean way. Only implication is non-classical. We construct these logics by mixing relating semantics with possible worlds. This way, we obtain connexive counterparts of basic normal modal logics. However, most of their traditional axioms formulated in terms of modalities and implication do not hold anymore without additional constraints, since our implication is weaker than the material one. In the final section, we present a tableau approach to the discussed modal logics.
LA - eng
KW - Boolean connexive logics; connexive logic; modal Boolean connexive logics; modal logics; normal modal logics; possible worlds semantics; relatedness; relating logic; relating semantics; tableau methods
UR - http://eudml.org/doc/295527
ER -

References

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  3. T. Jarmużek, Tableau Metatheorem for Modal Logics, [in:] R. Ciuni, H. Wansing, C. Willkomennen (eds.), Recent Trends in Philosphical Logic, Trends in Logic, Springer Verlag 2013, pp. 105–128. 
  4. T. Jarmużek and B. Kaczkowski, On some logic with a relation imposed on formulae: tableau system F, Bulletin of the Section of Logic, Vol. 43, No. 1/2 (2014), pp. 53–72. 
  5. T. Jarmużek and M. Klonowski, On logic of strictly-deontic modalities, submitted to a review. 
  6. T. Jarmużek and J. Malinowski, Boolean Connexive Logics, Semantics and tableau approach, Logic and Logical Philosophy, Vol. 28, No. 3 (2019), pp. 427–448, DOI: http://dx.doi.org/10.12775/LLP.2019.003 
  7. A. Kapsner, Strong Connexivity, Thought, Vol. 1 (2012), pp. 141–145. 
  8. A. Kapsner, Humble Connexivity, Logic and Logical Philosophy, Vol. 28, No. 2 (2019), DOI: http://dx.doi.org/10.12775/LLP.2019.001 
  9. S. McCall, A History of Connexivity, [in:] D. M. Gabbay et al. (eds.), Handbook of the History of Logic, Vol. 11, pp. 415–449, Logic: A History of its Central Concepts, Amsterdam: Elsevier 2012. 
  10. H. Omori, Towards a bridge over two approaches in connexivelogics, Logic and Logical Philosophy, Vol. 28, No. 2 (2019), DOI: http://dx.doi.org/10.12775/LLP.2019.005 
  11. D. N. Walton, Philosophical basis of relatedness logic, Philosophical Studies, Vol. 36, No. 2 (1979), pp. 115–136. 
  12. H. Wansing and M. Unterhuber, Connexive conditional logic. Part 1, Logic and Logical Philosophy, Vol. 28, No. 2 (2019), DOI: http://dx.doi.org/10.12775/LLP.2018.018 

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