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THE LOGIC OF HYPERLOGIC. PART A: FOUNDATIONS

Published online by Cambridge University Press:  27 April 2022

ALEXANDER W. KOCUREK*
Affiliation:
SAGE SCHOOL OF PHILOSOPHY CORNELL UNIVERSITY ITHACA, NY14853, USA

Abstract

Hyperlogic is a hyperintensional system designed to regiment metalogical claims (e.g., “Intuitionistic logic is correct” or “The law of excluded middle holds”) into the object language, including within embedded environments such as attitude reports and counterfactuals. This paper is the first of a two-part series exploring the logic of hyperlogic. This part presents a minimal logic of hyperlogic and proves its completeness. It consists of two interdefined axiomatic systems: one for classical consequence (truth preservation under a classical interpretation of the connectives) and one for “universal” consequence (truth preservation under any interpretation). The sequel to this paper explores stronger logics that are sound and complete over various restricted classes of models as well as languages with hyperintensional operators.

Type
Research Article
Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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