We investigate a non-classical version of linear temporal logic whose propositional fragment is G\"odel--Dummett logic (which is well known both as a superintuitionistic logic and a t-norm fuzzy logic). We define the logic using two natural semantics, a real-valued semantics and a bi-relational semantics, and show that these indeed define one and the same logic. Although this G\"odel temporal logic does not have any form of the finite model property for these two semantics, we show that every falsifiable formula is falsifiable on a finite quasimodel, which yields decidability of the logic. We then strengthen this result by showing that this G\"odel temporal logic is PSPACE-complete.

翻译：我们调查的是非经典的线性时间逻辑版本,其理论碎片为 G\“odel-Dummett 逻辑(这是众所周知的超级理论逻辑和t-norm furzzy逻辑 ) 。 我们用两种自然语义、一种真实价值的语义和一种双关系语义来定义逻辑,并表明这些逻辑确实定义了一种逻辑和同一逻辑。 虽然这个G\“odel 时间逻辑”没有两种语义的有限模型属性,但我们显示,每一种可变公式都是用一个有限的准模型来伪造的,从而产生逻辑的可变性。 然后,我们通过显示G\'odel 时间逻辑是PACCE的完成性来强化这一结果。