Some Papers and books of P.J. Scott
Final published (and expanded) versions of the preprints below have copyrights
mostly owned by the publisher. Preprints are available here for personal
and nonprofit use. Redistribution and commercial use is not allowed
without expressed permission of the copyright holder.
Unfortunately I do not have downloadable versions of all my papers.
Preprints are in a mixture of .ps and .pdf formats. Where possible, public domain versions of publisher's pdfs are included.
- Some Edited Books
- Feasible Mathematics (Editors: Samuel Buss, Philip Scott), Birkhauser/Springer, 1990.
- Linear Logic in Computer Science (Editors: T. Ehrhard, J-Y Girard, P. Ruet, P. Scott),
LMS Lecture Series, Cambridge U. Press, 2004.
Language & Grammar (Editors: C. Casadio, P.J. Scott, R.A.G. Seely),
CSLI Publications, No. 168, Stanford University, 2005.
- Models, Logics, and Higher-Dimensional Categories: A tribute
to M. Makkai (Editors: B. Hart, T. G. Kucera, A. Pillay, P.J. Scott, R.A.G. Seely),
CRM Proceedings v. 53, Am. Math Soc.,2011.
- Joachim Lambek: The Interplay of Mathematics, Logic, and Linguistics (Editors: C. Casadio, P.J. Scott),
Springer-Verlag, Outstanding Contributions to Logic Series, 2021.
- Some early work in Categorical Logic
- Various Research Papers in Logic and Theoretical Computer Science (1990-)
- Functorial Polymorphism (with E.S. Bainbridge, P. Freyd,
& A. Scedrov) Theoretical Computer Science,v. 70 (1990), pp. 35-64.
- Bounded Linear Logic
(with J.Y. Girard & A. Scedrov), Theoretical Computer Science,v. 97 (1992), pp. 1-66.
- Normal Forms and Cut-Free Proofs as Natural
Transformations (with J.Y. Girard & A. Scedrov), appeared in:
Logic from Computer Science, MSRI publications, V. 21, Springer-Verlag (1992),
pp. 217-241. (.ps version)
- On the
Pi-Calculus and Linear Logic (with G. Bellin) appeared in:
Theoretical Computer Science, 135 (1994), pp. 11-65.
- Linear Lauchli Semantics (with R.F. Blute)
appeared in: Ann. Pure & Applied Logic, 77 (1996), pp. 101-142. (.pdf)
- The Shuffle Hopf Algebra and Noncommutative
Full Completeness (with R.F. Blute) appeared in:
J. Symbolic Logic, v. 63, No.4, 1998, pp. 1413-1436.(.pdf version) also available
gzipped .ps version ; also
The Shuffle Hopf Algebra and Noncommutative
Full Completeness (A4-version)
- Normalization and the Yoneda Embedding
(with D. Cubric and P. Dybjer) appeared in: Math. Structures in
Computer Science, V. 8, No.2, 1998, pp. 153-192. (.ps version) (Here's a .pdf version):
Normalization and the Yoneda Embedding (.pdf version)
A Note on Rewriting Theory for Uniqueness of Iteration
(with M. Okada) appeared in: Theory and Applications of Categories, Vol. 6, 1999, No. 4, pp. 47-64.
- Normalization by evaluation for typed lambda calculus
with coproducts (with T. Altenkirch, P. Dybjer, M. Hofmann), appeared in:
LICS 2001, IEEE Press. pp. 303-310. (.ps version)
- Realizability models for BLL-like languages
(with M. Hofmann ) appeared in: Theoretical Comp. Science, V.318, 2004, pp. 121-137.
- Softness of hypercoherences
and MALL full completeness (with R. Blute and M. Hamano)
appeared in: Ann. Pure and Applied Logic, 131 (2005), pp. 1-63.
- An exactification of the monoid of primitive recursive functions (with J. Lambek)
and also .ps version . Appeared in:
Studia Logica 81,2005, pp. 1--18
A categorical semantics for Polarized MALL (with M. Hamano), appeared in: Ann. Pure & Applied Logic, 145 (2007), pp. 276-313. (.pdf version)
Reflections on a Categorical Foundations
of Mathematics (with J. Lambek) (2009), published in: Foundational Theories of
Classical and Constructive Mathematics, G. Sommaruga, ed., Springer Western Ontario Series in Philosophy
of Science, 2011, pp. 171-185.
- Survey Articles
- Geometry of Interaction
- Geometry of Interaction and Linear Combinatory Algebras
(with S. Abramsky and E. Haghverdi). Appeared in: Math. Structures in Computer Science, V. 12 (2002), pp. 1-40. (.ps version)
- A Categorical Model for the Geometry of Interaction (with Esfandiar Haghverdi) ICALP 2004, SLNCS 3142, pp. 708-720.
and also .ps version
- A Categorical Model for the Geometry of Interaction (full paper) (with
Esfandiar Haghverdi), Theoretical Computer Science, Volume 350, Issues 2-3 , Feb 2006, pp. 252-274 (.pdf version).
- From Geometry of Interaction to Denotational Semantics (with Esfandiar Haghverdi),
in CTCS 2004. In ENTCS, vol. 122, pp. 67-87. Elsevier (.ps version)
- P. Scott: Tutorial on Geometry of Interaction (from FMCS 2004)
- Towards a Typed Geometry of Interaction
(with Esfandiar Haghverdi),
CSL2005 (Computer Science Logic), Luke Ong, Ed. SLNCS 3634, pp. 216-231.
- Proofs as Polynomials (with Esfandiar Haghverdi)
published in Springer's ENTCS,
Volume 218, 22 October 2008, Pages 53-72.)(Proc. MFPS XXIV)
- Geometry of Interaction and the dynamics
of proof reduction: a tutorial
(with Esfandiar Haghverdi) (in Springer Lecture Notes in Physics 813 (2011) pp.
- Towards a Typed Geometry of Interaction
(with Esfandiar Haghverdi) (MSCS 20(3), 2010, pp. 1--49. )
- Partially Traced Categories,
(with Octavio Malherbe and Peter Selinger).
J. Pure and Applied Algebra, V.216 (12), December 2012, pp. 2563-2585.
- Lecture: Partially Traced Categories
- On geometry of interaction for polarized linear logic (with M. Hamano) Preliminary version. Final version to appear in:
Mathematical Structures in CS, Cambridge U. Press, 28 September 2017.
- Quantum Computing
- Presheaf models of quantum computation: an outline
(with Octavio Malherbe and Peter Selinger) (arXiv, Feb. 24, 2013).
In Bob Coecke, Luke Ong, Prakash Panangaden, editors, Computation, Logic, Games, and Quantum Foundations. The Many Facets of Samson Abramsky. Lecture Notes in Computer Science 7860:178-194, Springer, 2013.
- Categorical traces from single-photon linear optics.
(with P. Hines). In: Mathematical Foundations of Information Flow, Proceedings of
Symposia in Applied Mathematics, Vol. 71, American Math. Soc., 2012, pp. 89-123.
- MV and Effect Algebras (and Inverse Semigroups)
- AF inverse monoids and the structure of countable MV-algebras
(with Mark Lawson) (arXiv, Aug. 6, 2014).
- Published (shorter) version of above:
M. Lawson , P. Scott, AF Inverse Monoids and the structure of
Countable MV Algebras, J. Pure and Applied Algebra 221 (Issue 1) (2017), pp. 45--74.
- FMCS(2017): Lectures on MV and Effect Algebras (extended versions) June, 2017:
Lecture 1: MV Algebras and Lecture 2: Effect Algebras and Coordinatization.
- Coordinatizing some Concrete MV Algebras and a Decomposition Theorem , W. Lu and P. Scott, Semigroup Forum,
April 2019, Volume 98, Issue 2, pp 213-233.
- Characterizations of classes of countable Boolean inverse monoids (with Mark Lawson) (arXiv, May 23, 2022).
- Recursion Theory and Formal Methods
- From Gödel to Lambek. Talk at CRM, U. Montreal, Sept, 2013 in honour
of J. Lambek's 91st birthday.
- Formalizing Abstract Computability: Turing Categories in Coq,
(with P.Vinogradova, A. Felty) in: Proceedings of the 12th Workshop on Logical and Semantic Frameworks
with Applications (LSFA 2017), in :
Springer Electronic Notes in Theoretical Computer Science, Volume
338, 203-218, 2018.
- Aspects of Categorical Recursion Theory (with P. Hofstra), preprint, Jan. 2020. Final Version appeared in J. Lambek book (edited above).
- Towards Formal Verification of Program Obfuscation, (with Bahman Sistany,
Amy Felty, Weiyun Lu). Workshop on Software Attacks and
Defenses (SAD), in Proceedings of the 2020 IEEE European Symposium on
Security and Privacy Workshops, September 2020, to appear.
- Categorical Algebra and Categorical Logic
- Finiteness spaces and generalized power series, with R. Blute, R. Cockett, and
P-A Jacqmin, in Springer Electronic Notes in Theoretical Computer Science,
Proceedings MFPS (2018), 341 (2018) 5-22 (Open Access).
- Isotropy of Algebraic Theories , with P. Hofstra and J. Parker, in Springer Electronic Notes in Theoretical Computer Science,
Proceedings MFPS (2018), 341 (2018) 201-217 (Open Access).
- Polymorphic Automorphisms and the Picard Group , with P. Hofstra and J. Parker,
published in: LIPIcs, Volume 195, FSCD 2021 (for full volume, see https://www.dagstuhl.de/dagpub/978-3-95977-191-7)