Abstract
Canonical completeness results for Ł\((\mathcal{C})\), the expansion of Łukasiewicz logic Ł with a countable set of truth-constants \(\mathcal{C}\), have been recently proved in [5] for the case when the algebra of truth constants \(\mathcal{C}\) is a subalgebra of the rational interval [0, 1] ∩ ℚ. The case when \(C \not \subseteq [0, 1] \cap \mathbb{Q}\) was left as an open problem. In this paper we solve positively this open problem by showing that Ł\((\mathcal{C})\) is strongly canonical complete for finite theories for any countable subalgebra \(\mathcal{C}\) of the standard Łukasiewicz chain [0,1]Ł.
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Cignoli, R., Esteva, F., Godo, L. (2007). On Łukasiewicz Logic with Truth Constants. In: Castillo, O., Melin, P., Ross, O.M., Sepúlveda Cruz, R., Pedrycz, W., Kacprzyk, J. (eds) Theoretical Advances and Applications of Fuzzy Logic and Soft Computing. Advances in Soft Computing, vol 42. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72434-6_88
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DOI: https://doi.org/10.1007/978-3-540-72434-6_88
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