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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