A Simple Embedding of T into Double S

Notre Dame Journal of Formal Logic 45 (1):13-18 (2004)
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Abstract

The system obtained by adding full propositional quantification to S5 is known to be decidable, while that obtained by doing so for T is known to be recursively intertranslatable with full second-order logic. Recently it was shown that the system with two S5 operators and full propositional quantification is also recursively intertranslatable with second-order logic. This note establishes that the map assigning [1][2]p to \squarep provides a validity and satisfaction preserving translation between the T system and the double S5 system, thus providing an easier proof of the recent result

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Steve Kuhn
Georgetown University

Citations of this work

Propositional Quantification in Bimodal S5.Peter Fritz - 2020 - Erkenntnis 85 (2):455-465.
On the Logic of Belief and Propositional Quantification.Yifeng Ding - 2021 - Journal of Philosophical Logic 50 (5):1143-1198.
Some Formal Semantics for Epistemic Modesty.Christopher Steinsvold - 2020 - Logic and Logical Philosophy 29 (3):381-413.

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References found in this work

Propositional quantifiers in modal logic.Kit Fine - 1970 - Theoria 36 (3):336-346.
Propositional Quantifiers in Modal Logic.Kit Fine - 1970 - Journal of Symbolic Logic 38 (2):329-329.

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