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Document Details : Title: Natural Deduction for First-Order Pure Imperative Logic Author(s): VRANAS, Peter B.M. Journal: Logique et Analyse Volume: 258 Date: 2022 Pages: 167-188 DOI: 10.2143/LEA.258.0.3291675 Abstract : First-Order Pure Imperative Logic (FOPIL) deals with arguments from imperative premises to imperative conclusions (i.e., pure imperative arguments) that may contain quantifiers and identity. FOPIL can be used to symbolize, for example, the reasoning from 'close the door of every office in the basement' to 'if your office is in the basement, close its door'. I present a natural deduction system for FOPIL that consists of replacement and inference rules that represent natural patterns of reasoning. I prove that two imperative formulas are logically equivalent exactly if one of them can be derived from the other by means of replacement rules, and that a pure imperative argument is valid exactly if its conclusion can be derived from its premises by means of replacement or inference rules. |
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