We construct a sound, complete, and terminating tableau system for the interval temporal logic 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 -structures, and show that every formula satisfiable in is satisfiable in such pseudo-models, thereby proving small-model property and decidability in PSPACE of , a result established earlier by Shapirovsky and Shehtman by means of filtration. We also show how to extend our results to the interval logic interpreted over dense interval structures with proper (irreflexive) subinterval relation, which differs substantially from and is generally more difficult to analyze. Up to our knowledge, no complete deductive systems and decidability results for 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)