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TEMPORAL INTERPRETATION OF MONADIC INTUITIONISTIC QUANTIFIERS
| Content Provider | Scilit |
|---|---|
| Author | Bezhanishvili, Guram Carai, Luca |
| Copyright Year | 2021 |
| Description | We show that monadic intuitionistic quantifiers admit the following temporal interpretation: “always in the future” (for $\forall $ ) and “sometime in the past” (for $\exists $ ). It is well known that Prior’s intuitionistic modal logic ${\sf MIPC}$ axiomatizes the monadic fragment of the intuitionistic predicate logic, and that ${\sf MIPC}$ is translated fully and faithfully into the monadic fragment ${\sf MS4}$ of the predicate ${\sf S4}$ via the Gödel translation. To realize the temporal interpretation mentioned above, we introduce a new tense extension ${\sf TS4}$ of ${\sf S4}$ and provide a full and faithful translation of ${\sf MIPC}$ into ${\sf TS4}$ . We compare this new translation of ${\sf MIPC}$ with the Gödel translation by showing that both ${\sf TS4}$ and ${\sf MS4}$ can be translated fully and faithfully into a tense extension of ${\sf MS4}$ , which we denote by ${\sf MS4.t}$ . This is done by utilizing the relational semantics for these logics. As a result, we arrive at the diagram of full and faithful translations shown in Figure 1 which is commutative up to logical equivalence. We prove the finite model property (fmp) for ${\sf MS4.t}$ using algebraic semantics, and show that the fmp for the other logics involved can be derived as a consequence of the fullness and faithfulness of the translations considered. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/4C947B62161C0227DAA397AD822A0800/S1755020321000496a.pdf/div-class-title-temporal-interpretation-of-monadic-intuitionistic-quantifiers-div.pdf |
| ISSN | 17550203 |
| e-ISSN | 17550211 |
| DOI | 10.1017/s1755020321000496 |
| Journal | The Review of Symbolic Logic |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 2021-12-02 |
| Access Restriction | Open |
| Subject Keyword | The Review of Symbolic Logic |
| Content Type | Text |
| Resource Type | Article |
| Subject | Philosophy Logic |
