Kripke Semantics for Intuitionistic Lukasiewicz Logic

被引:2
|
作者
Lewis-Smith, A. [1 ]
Oliva, P. [1 ]
Robinson, E. [1 ]
机构
[1] Queen Mary Univ London, Sch Elect Engn & Comp Sci, Mile End Rd, London E1 4NS, England
基金
英国工程与自然科学研究理事会;
关键词
Lukasiewicz logic; Intuitionistic Lukasiewicz logic; Kripke semantics; GBL algebras; URQUHARTS C;
D O I
10.1007/s11225-020-09908-z
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
This paper proposes a generalization of the Kripke semantics of intuitionistic logic IL appropriate for intuitionistic Lukasiewicz logicILL -a logic in the intersection between IL and (classical) Lukasiewicz logic. This generalised Kripke semantics is based on the poset sum construction, used in Bova and Montagna (Theoret Comput Sci 410(12):1143-1158, 2009). to show the decidability (and PSPACE completeness) of the quasiequational theory of commutative, integral and bounded GBL algebras. The main idea is that w & x22a9;psi-which for ILis a relation between worlds w and formulas psi, and can be seen as a function taking values in the booleans (w & x22a9;psi)is an element of B-becomes a function taking values in the unit interval (w & x22a9;psi)is an element of[0,1]. An appropriate monotonicity restriction (which we call sloping functions) needs to be put on such functions in order to ensure soundness and completeness of the semantics.
引用
收藏
页码:313 / 339
页数:27
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