Computer Science > Logic in Computer Science
[Submitted on 11 Jan 2021]
Title:Mechanisation of Model-theoretic Conservative Extension for HOL with Ad-hoc Overloading
View PDFAbstract:Definitions of new symbols merely abbreviate expressions in logical frameworks, and no new facts (regarding previously defined symbols) should hold because of a new definition. In Isabelle/HOL, definable symbols are types and constants. The latter may be ad-hoc overloaded, i.e. have different definitions for non-overlapping types. We prove that symbols that are independent of a new definition may keep their interpretation in a model extension. This work revises our earlier notion of model-theoretic conservative extension and generalises an earlier model construction. We obtain consistency of theories of definitions in higher-order logic (HOL) with ad-hoc overloading as a corollary. Our results are mechanised in the HOL4 theorem prover.
Submission history
From: EPTCS [view email] [via EPTCS proxy][v1] Mon, 11 Jan 2021 10:51:17 UTC (28 KB)
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