Monotonic and nonmonotonic gentzen deduction systems for L3-valued propositional logic
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 L 3 -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...
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Veröffentlicht in: | Frontiers of Computer Science 2021-06, Vol.15 (3), p.153401, Article 153401 |
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Sprache: | eng |
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Zusammenfassung: | 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
L
3
-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. |
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ISSN: | 2095-2228 2095-2236 |
DOI: | 10.1007/s11704-020-9076-2 |