The logic of isomorphism and its uses
(2014) In Preprint without journal information- Abstract
- We present a class of first-order modal logics, called transformational logics, which are designed for working with sentences that hold up to a certain type of transformation. An inference system is given, and com- pleteness for the basic transformational logic HOS is proved. In order to capture ‘up to isomorphism’, we express a very weak version of higher category theory in terms of first-order models, which makes tranforma- tional logics applicable to category theory. A category-theoretical concept of isomorphism is used to arrive at a modal operator nisoφ expressing ‘up to isomorphism, φ’, which is such that category equivalence comes out as literally isomorphism up to isomorphism.
In the final part of the paper, we explore the... (More) - We present a class of first-order modal logics, called transformational logics, which are designed for working with sentences that hold up to a certain type of transformation. An inference system is given, and com- pleteness for the basic transformational logic HOS is proved. In order to capture ‘up to isomorphism’, we express a very weak version of higher category theory in terms of first-order models, which makes tranforma- tional logics applicable to category theory. A category-theoretical concept of isomorphism is used to arrive at a modal operator nisoφ expressing ‘up to isomorphism, φ’, which is such that category equivalence comes out as literally isomorphism up to isomorphism.
In the final part of the paper, we explore the possibility of using trans- formational logics to define weak higher categories. We end with two informal comparisons: one between HOS and counterpart semantics, and one between isomorphism logic, as a transformational logic, and Homo- topy Type Theory. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/4393790
- author
- Angere, Staffan ^{LU}
- organization
- publishing date
- 2014
- type
- Contribution to journal
- publication status
- unpublished
- subject
- keywords
- isomorphism, higher category theory, Modal logic, equivalence
- in
- Preprint without journal information
- publisher
- Manne Siegbahn Institute
- ISSN
- 0348-7911
- language
- English
- LU publication?
- yes
- id
- 1461d658-05ac-4b39-beb0-c9d0c61484db (old id 4393790)
- date added to LUP
- 2014-04-28 12:04:42
- date last changed
- 2018-11-21 21:17:19
@article{1461d658-05ac-4b39-beb0-c9d0c61484db, abstract = {We present a class of first-order modal logics, called transformational logics, which are designed for working with sentences that hold up to a certain type of transformation. An inference system is given, and com- pleteness for the basic transformational logic HOS is proved. In order to capture ‘up to isomorphism’, we express a very weak version of higher category theory in terms of first-order models, which makes tranforma- tional logics applicable to category theory. A category-theoretical concept of isomorphism is used to arrive at a modal operator nisoφ expressing ‘up to isomorphism, φ’, which is such that category equivalence comes out as literally isomorphism up to isomorphism.<br/><br> In the final part of the paper, we explore the possibility of using trans- formational logics to define weak higher categories. We end with two informal comparisons: one between HOS and counterpart semantics, and one between isomorphism logic, as a transformational logic, and Homo- topy Type Theory.}, author = {Angere, Staffan}, issn = {0348-7911}, keyword = {isomorphism,higher category theory,Modal logic,equivalence}, language = {eng}, publisher = {Manne Siegbahn Institute}, series = {Preprint without journal information}, title = {The logic of isomorphism and its uses}, year = {2014}, }