Interpreting Negation: A Semantic Theory of Negation for Standard and Non-Standard Logics

I argue that there is a common core to the negation operators found in classical logic, quantum logic and some versions of three-valued logic--logics I refer to an 'valent' logics. In particular, each of these operators adheres to the following three constraints: (1) A proposition and its negation cannot intersect in a non-trivial way, (2) The law of contraposition holds, and (3) Negation maps propositions one-to-one and onto propositions. I further show that a logic consisting of an operator defined by just these constraints, i.e., a minimal negation operator, along with a standard disjunctive operator, is decidable. Finally, I argue that intuitionistic logic does not contain an operator which meets the constraints outlined above, but that it does contain an operator which provides a different form of negation.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Philosophy

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2014

Author dc:creator

• Hass, Marjorie

Contributors dc:contributor

• McCarthy, T.,

• Philosophy

Identifier

(UMI)AAI9314877

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/72601