Erkenntnis 85 (2):455-465 (2020)

Authors
Peter Fritz
Australian Catholic University
Abstract
Propositional quantifiers are added to a propositional modal language with two modal operators. The resulting language is interpreted over so-called products of Kripke frames whose accessibility relations are equivalence relations, letting propositional quantifiers range over the powerset of the set of worlds of the frame. It is first shown that full second-order logic can be recursively embedded in the resulting logic, which entails that the two logics are recursively isomorphic. The embedding is then extended to all sublogics containing the logic of so-called fusions of frames with equivalence relations. This generalizes a result due to Antonelli and Thomason, who construct such an embedding for the logic of such fusions.
Keywords propositional quantifiers  bimodal logic  S5
Categories (categorize this paper)
Reprint years 2020
ISBN(s)
DOI 10.1007/s10670-018-0035-3
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Translate to english
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 56,999
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

A Completeness Theorem in Modal Logic.Saul A. Kripke - 1959 - Journal of Symbolic Logic 24 (1):1-14.
Possible Worlds.Robert Stalnaker - 1976 - Noûs 10 (1):65-75.
On the Logic of Demonstratives.David Kaplan - 1979 - Journal of Philosophical Logic 8 (1):81 - 98.
Symbolic Logic.C. I. Lewis & C. H. Langford - 1934 - Erkenntnis 4 (1):65-66.
Two-Dimensional Modal Logic.Krister Segerberg - 1973 - Journal of Philosophical Logic 2 (1):77 - 96.

View all 14 references / Add more references

Citations of this work BETA

Diamonds Are Forever.Cian Dorr & Jeremy Goodman - 2020 - Noûs 54 (3):632-665.

Add more citations

Similar books and articles

Logics for Propositional Contingentism.Peter Fritz - 2017 - Review of Symbolic Logic 10 (2):203-236.
A Simple Embedding of T Into Double S.Steven Kuhn - 2004 - Notre Dame Journal of Formal Logic 45 (1):13-18.
Defining Relevant Implication in a Propositionally Quantified S4.Philip Kremer - 1997 - Journal of Symbolic Logic 62 (4):1057-1069.
Expressivity of Second Order Propositional Modal Logic.Balder ten Cate - 2006 - Journal of Philosophical Logic 35 (2):209-223.
Propositional Quantification in the Topological Semantics for S.Philip Kremer - 1997 - Notre Dame Journal of Formal Logic 38 (2):295-313.

Analytics

Added to PP index
2018-07-27

Total views
69 ( #144,449 of 2,410,434 )

Recent downloads (6 months)
7 ( #101,554 of 2,410,434 )

How can I increase my downloads?

Downloads

My notes