A Sequent Calculus for 3-Dimensional Space
A central issue for spatial reasoning in practice is to formalize reasoning about 3-dimensional space. In this paper, a spatial logic called 3-dimensional spatial logic (3SL), which can appropriately represent the 3-Cartesian product ω 3 of the set ω of natural numbers, is introduced as a Gentzen-type sequent calculus. 3SL is an extension and generalization of the linear-time temporal logic LTL in which the time domain is ω. The completeness and cut-elimination theorems for 3SL are proved.
KeywordsPropositional Variable Completeness Theorem Spatial Reasoning Classical Propositional Logic Satisfaction Relation
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