Hybrid tense logic for Reichenbach’s tense theory with time reference operators

Prior (1967) claims that his classical tense logic has destroyed Reichenbach’s distinction between the simple past and the present perfect. In this paper, we first reveal the following surprising result: Prior’s classical tense logic can restore Reichenbach’s distinction between the simple past and the present perfect. This result is obtained from formalizing what we refer to as ‘effect inference’ in the present perfect and in the past perfect in Prior’s classical tense logic, where the past perfect is symbolized as a special (complex) case of the simple past. Second, we show that Blackburn and Jørgensen (Blackburn & Jørgensen, 2016)’s basic hybrid tense logic can reformulate this inferentialistic distinction between the simple past and the present perfect in a more faithful manner to Reichenbach’s terminology. Third, however, we find out a common limitation of Prior’s tense logic and Blackburn and Jørgensen (2016)’s hybrid tense logic: neither of them can smoothly slide effect inference in the present perfect into the future perfect in the context of branching time. We then demonstrate that Hosokawa (2023)’s version of hybrid tense logic with time reference operators can overcome this limitation naturally, while preserving the inferentialistic distinction between the simple past and the present perfect in a refined manner.