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Rules admissible in transitive temporal logic $$\mathrm{T}_{\mathrm{S}4}$$, sufficient condition. (English) Zbl 1209.03011
Summary: The paper develops a technique for computing inference rules admissible in temporal logic $$\text{T}_{\text{S}4}$$. The problem whether there exists an algorithm recognizing inference rules admissible in $$\text{T}_{\text{S}4}$$ is a long-standing open problem. The logic $$\text{T}_{\text{S}4}$$ has neither the extension property nor the co-cover property which previously were central instruments for constructing decision algorithms for admissibility in modal logics (e.g., reflexive and transitive modal logic $$\text{S}4$$). Our paper uses a linear-compression property, a zigzag-ray property and a zigzag stretching property which hold for $$\text{T}_{\text{S}4}$$. The main result of the paper is a sufficient condition for admissibility of inference rules in $$\text{T}_{\text{S}4}$$. It is shown that all rules which are valid in special finite models (with an effective upper bound on size) must be admissible in $$\text{T}_{\text{S}4}$$.

##### MSC:
 03B44 Temporal logic
##### Keywords:
temporal logic; inference rules; admissible rules
Full Text:
##### References:
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