We construct a sound, complete, and terminating tableau system for the interval temporal logic D interpreted in interval structures over dense linear orderings endowed with strict subinterval relation (where both endpoints of the sub-interval are strictly inside the interval). In order to prove the soundness and completeness of our tableau construction, we introduce a kind of finite pseudo-models for our logic, called D -structures, and show that every formula satisfiable in D is satisfiable in such pseudo-models, thereby proving small-model property and decidability in PSPACE of D, a result established earlier by Shapirovsky and Shehtman by means of filtration. We also show how to extend our results to the interval logic D interpreted over dense interval structures with proper (irreflexive) subinterval relation, which differs substantially from D and is generally more difficult to analyze. Up to our knowledge, no complete deductive systems and decidability results for D have been proposed in the literature so far.
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机译:转换术语± Sup> [n i Sub>] f(+/-) min sup>的条件最小化结构的逻辑动态过程的方法Sub> AND ± Sup> [m i Sub>] f(+/-) min Sub>在功能添加结构中± Sup> f < Sub> 1 Sub>(Σ RU Sub>) min Sub>,不带纹波f 1 Sub>(± Sup>←←)和循环ΔtΣ Sub>→5∙f(&)-和5个条件逻辑函数f(&)-,并通过三元数系统的算术公理同时转换术语参数的过程f RU Sub>(+ 1,0,-1)及其实现其的功能结构(俄罗斯逻辑版本)