论文标题
时间和戈德尔：pspace中模糊的时间推理
Time and Gödel: Fuzzy temporal reasoning in PSPACE
论文作者
论文摘要
我们研究了线性时间逻辑的非古典版本，其命题片段是Gödel--dummett逻辑（这既被称为超级逻辑，又是T-norm模糊逻辑）。我们使用两种自然语义，一种实现的语义和双重关系语义来定义逻辑，并表明这些语义确实定义了一个和相同的逻辑。尽管此Gödel时间逻辑没有这两种语义的任何有限模型属性，但我们表明，每个可伪造的公式都是在有限的Quasimodel上伪造的，该公式可产生逻辑的可决定性。然后，我们通过表明该Gödel时间逻辑是Pspace complete来加强结果。
We investigate a non-classical version of linear temporal logic whose propositional fragment is Gödel--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 Gödel 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 Gödel temporal logic is PSPACE-complete.
