Distribution Laws in Weak Positional Logics

Marcin Tkaczyk

doi:10.18290/rf.2018.66.3-8

Published : 2018-09-24

Vol. 66 No. 3 (2018)

Distribution Laws in Weak Positional Logics

Marcin Tkaczyk

DOI: https://doi.org/10.18290/rf.2018.66.3-8

Abstract

A formal language is positional if it involves a positional connecitve, i.e. a connective of realization to relate formulas to points of a kind, like points of realization or points of relativization. The connective in focus in this paper is the connective “R”, first introduced by Jerzy Łoś. Formulas “R_αφ” involve a singular name α and a formula φ to the effect that ϕ is satisfied (true) relative to the position designated by α In weak positional calculi no nested occurences of the connective “R” are allowed. The distribution problem in weak positional logics is actually the problem of distributivity of the connective “R” over classical connectives, viz. the problem of relation between the occurences of classical connectives inside and outside the scope of the positional connective“R”.

Keywords:

positional logic, weak positional logic, distribution, distributive law, realization connective, completeness

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Tkaczyk, M. (2018). Distribution Laws in Weak Positional Logics. Roczniki Filozoficzne, 66(3), 163–179. https://doi.org/10.18290/rf.2018.66.3-8

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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

References

The comprehensive bibliography of positional logics up to 2015 may be found in the book by Jarmużek and Tkaczyk (2015). In what follows only works referred to in the present paper are listed.

Jarmużek, Tomasz, & Andrzej Pietruszczak. 2004. “Completeness of Minimal Positional Calculus.” Logic and Logical Philosophy 13: 147–62.

Jarmużek, Tomasz, & Marcin Tkaczyk. 2015. Normalne logiki pozycyjne. Metateoria i zastosowania. Lublin: Wydawnictwo KUL.

Karczewska, Anna. 2018. “Maximality of Minimal Logic and Logical Philosophy 27: 193–203.

Rescher, Nicolas, & James Garson. 1968. “Topological Logic.” The Journal of Symbolic Logic. 33: 534–48.

Rescher, Nicolas, & Alasdair Urquhart. 1971. Temporal Logic. Wien & New York: Springer Verlag.

Tkaczyk, Marcin. 2009. Logika czasu empirycznego. Funktor realizacji czasowej w językach teorii fizykalnych. Lublin: Wydawnictwo KUL.

Tkaczyk, Marcin. 2013. “Negation in Weak Positional Calculi.” Logic and Logical Philosophy 22: 3–19