On Lukasiewicz logic with truth constants

CIGNOLI, ROBERTO LEONARDO OSCAR; ESTEVA, FRANCESC; GODO, LLUIS

Cancun, Méjico

Congreso; International Fuzzy Systems Association World Congress; 2007

International Fuzzy Systems Association

Canonical completeness results for ¨©(C), the expansion of ¨©ukasiewicz logic ¨© with a countable set of truth-constants C, have been recently proved in [5] for the case when the algebra of truth constants C is a subalgebra of the rational interval [0, 1] ¡û Q. The case when(C), the expansion of ¨©ukasiewicz logic ¨© with a countable set of truth-constants C, have been recently proved in [5] for the case when the algebra of truth constants C is a subalgebra of the rational interval [0, 1] ¡û Q. The case whenC, have been recently proved in [5] for the case when the algebra of truth constants C is a subalgebra of the rational interval [0, 1] ¡û Q. The case whenC is a subalgebra of the rational interval [0, 1] ¡û Q. The case when C ¡ö [0, 1] ¡û Q was left as an open problem. In this paper we solve positively this open problem by showing that ¨©(C) is strongly canonical complete for finite theories for any countable subalgebra C of the standard ¨©ukasiewicz chain [0, 1]¨©.¡ö [0, 1] ¡û Q was left as an open problem. In this paper we solve positively this open problem by showing that ¨©(C) is strongly canonical complete for finite theories for any countable subalgebra C of the standard ¨©ukasiewicz chain [0, 1]¨©.(C) is strongly canonical complete for finite theories for any countable subalgebra C of the standard ¨©ukasiewicz chain [0, 1]¨©.C of the standard ¨©ukasiewicz chain [0, 1]¨©. Keywords: ¨©ukasiewicz logic, truth-constants, canonical standard completeness.¨©ukasiewicz logic, truth-constants, canonical standard completeness.