Monotonic and nonmonotonic gentzen deduction systems for L3-valued propositional logic
| Autor: | Yuefei Sui, Lanxi Hu, Cungen Cao |
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| Rok vydání: | 2021 |
| Předmět: |
Discrete mathematics
General Computer Science Computer science 0202 electrical engineering electronic engineering information engineering 020207 software engineering 020201 artificial intelligence & image processing Monotonic function 02 engineering and technology Sequent Propositional calculus Theoretical Computer Science |
| Zdroj: | Frontiers of Computer Science. 15 |
| ISSN: | 2095-2236 2095-2228 |
| Popis: | A sequent is a pair (Γ, Δ), which is true under an assignment if either some formula in Γ is false, or some formula in Δ is true. In L3-valued propositional logic, a multisequent is a triple Δ|Θ|Γ, which is true under an assignment if either some formula in Δ has truth-value t, or some formula in Θ has truth-value m, or some formula in Γ has truth-value f. Correspondingly there is a sound and complete Gentzen deduction system G for multisequents which is monotonic. Dually, a co-multisequent is a triple Δ: Θ: Γ, which is valid if there is an assignment v in which each formula in Δ has truth-value ≠ t, each formula in Θ has truth-value ≠ m, and each formula in Γ has truth-value ≠ f. Correspondingly there is a sound and complete Gentzen deduction system G− for co-multisequents which is nonmonotonic. |
| Databáze: | OpenAIRE |
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