Hereditarily Structurally Complete Superintuitionistic Deductive Systems
Alex Citkin
TL;DR
This paper investigates the properties of hereditarily structurally complete superintuitionistic deductive systems, revealing that such systems do not have a general hereditary structurality criterion but can still define many standard superintuitionistic logics.
Contribution
It establishes that a hereditary structurality criterion does not exist for deductive systems, yet many standard superintuitionistic logics can be characterized by hereditarily structurally complete systems.
Findings
No general hereditary structurality criterion for deductive systems.
Many standard superintuitionistic logics can be defined by hereditarily structurally complete systems.
Hereditary structurality criteria similar to those for logics do not exist for deductive systems.
Abstract
The paper studies hereditarily complete superintuitionistic deductive systems, that is, the deductive system which logic is an extension of the intuitionistic propositional logic. It is proven that for deductive systems a criterion of hereditary structurality - similar to one that exists for logics - does not exists. Nevertheless, it is proven that many standard superintuitionistic logics (including Int) can be defined by a hereditarily structurally complete deductive system.
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Taxonomy
TopicsAdvanced Algebra and Logic · Logic, Reasoning, and Knowledge · Computability, Logic, AI Algorithms