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| Content Provider | Springer Nature Link |
|---|---|
| Author | Beeson, Michael Veroff, Robert Wos, Larry |
| Copyright Year | 2005 |
| Abstract | This article answers two questions (posed in the literature), each concerning the guaranteed existence of proofs free of double negation. A proof is free of double negation if none of its deduced steps contains a term of the formn(n(t)) for some term t, where n denotes negation. The first question asks for conditions on the hypotheses that, if satisfied, guarantee the existence of a double-negation-free proof when the conclusion is free of double negation. The second question asks about the existence of an axiom system for classical propositional calculus whose use, for theorems with a conclusion free of double negation, guarantees the existence of a double-negation-free proof. After giving conditions that answer the first question, we answer the second question by focusing on the Lukasiewicz three-axiom system. We then extend our studies to infinite-valued sentential calculus and to intuitionistic logic and generalize the notion of being double-negation free. The double-negation proofs of interest rely exclusively on the inference rule condensed detachment, a rule that combines modus ponens with an appropriately general rule of substitution. The automated reasoning program Otter played an indispensable role in this study. |
| Starting Page | 195 |
| Ending Page | 234 |
| Page Count | 40 |
| File Format | |
| ISSN | 00393215 |
| Journal | Studia Logica |
| Volume Number | 80 |
| Issue Number | 2-3 |
| e-ISSN | 15728730 |
| Language | English |
| Publisher | Kluwer Academic Publishers |
| Publisher Date | 2005-01-01 |
| Publisher Place | Dordrecht |
| Access Restriction | One Nation One Subscription (ONOS) |
| Subject Keyword | Logic Mathematical Logic and Foundations Computational Linguistics |
| Content Type | Text |
| Resource Type | Article |
| Subject | Logic History and Philosophy of Science |
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