Abstract
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.
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Acknowledgments
This work has been partially supported by FWO-FWF grant G030620N/I4513N (J.P.A. and D.F.D.), FWO grant 3E017319 (J.P.A.), the projects EL4HC and étoiles montantes CTASP at Région Pays de la Loire, France (M.D.), the COST action CA-17124 (M.D. and D.F.D.), and SNSF–FWO Lead Agency Grant 200021L_196176/G0E2121N (B.M. and D.F.D.).
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Aguilera, J.P., Diéguez, M., Fernández-Duque, D., McLean, B. (2022). Time and Gödel: Fuzzy Temporal Reasoning in PSPACE. In: Ciabattoni, A., Pimentel, E., de Queiroz, R.J.G.B. (eds) Logic, Language, Information, and Computation. WoLLIC 2022. Lecture Notes in Computer Science, vol 13468. Springer, Cham. https://doi.org/10.1007/978-3-031-15298-6_2
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