An extended propositional logic
by
Mariano Giaquinta
Giuseppe Modica
Jiri Soucek
Vol. 10 No. 1 (2015) P.73~P.100
ABSTRACT
Motivated by quantum mechanics we discuss an extended propositional logic (EPL)
basing its syntax on partitions of sets. Every complete partition define a context and in
every context EPL reduces to a classical propositional logic. Partitions lead to a notion
of incompatibility expressing that knowledge cannot be refined without changing context.
We also deal with interpretations, tautologies and semantic consequences in EPL.
KEYWORDS
nonclassical propositional logic, foundations of quantum mechanics, contexts.
MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 03B60, 81P10, 81P16.
MILESTONES
Received: 2013-11-04
Revised : 2014-11-06
Accepted: 2014-11-04
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