This is the home page for the LFCS TPG course: Mathematical Structures for Semantics.
This half course covers a variety of mathematical structures used in semantics. The course is structured around a single weekly lecture in which a selected topic is reviewed. Reading lists are issued a week in advance of lectures, and lectures assume some acquaintance with this material. Each lecture covers a different topic, and aims to reach the frontier of research in that area.
Lectures: Thursdays 11-12, Room 4310
Course starts: Thursday 7th February
Course ends: Thursday 14th March
There will also be student-given lectures on miscellaneous topics in term 3.
Other reading: [Sco72], [Plo83, Ch.6], [Smy83], [Jun89], [Jun90], [AR94].
Other reading: [SP82], [Fre91], [Fre92], [Fio94], [Sim02], [Pit96].
Other reading: [Vic89], [Joh86], [Abr91].
Other reading: [Sco72], [GHK80], [MS02], [Bau00].
[Abr91] Samson Abramsky. Domain theory in logical form, Annals of Pure and Applied Logic, 51:1-77, 1991.
[AJ94] Samson Abramsky and Achim Jung, Domain theory, Handbook of Logic in Computer Science Vol. III, 1994.
[AR94] Jiri Adamek and Jiri Rosicky, Locally Presentable and Accessible Categories, London Mathematical Society Lecture Note Series, 189, CUP, 1994.
[Bau00] Andrej Bauer, The Realizability Approach to Computable Analysis and Topology, PhD Thesis, CMU, 2000.
[BBS02] Andrej Bauer, Lars Birkedal and Dana Scott, Equilogical spaces, to appear in Theoretical Computer Science, 2002.
[BES02] Andrej Bauer, Martín Escardó and Alex Simpson, Comparing Functional Paradigms for Exact Real-number Computation, draft paper, 2002.
[Fio94] Marcelo Fiore, Axiomatic Domain Theory in Categories of Partial Maps, PhD Thesis, University of Edinburgh, ECS-LFCS-94-307, 1994. (Published in Distinguished Dissertation Series, CUP, 1996.)
[Fre91] Peter Freyd, Algebraically complete categories, in Category Theory, Proceedings Como 1990, Springer LNM 1488, 1991.
[Fre92] Peter Freyd, Remarks on algebraically compact categories, in Applications of Categories in Computer Science, pages 95-106, LMS Lencture Notes 177, CUP, 1992.
[GHK80] Gerhard Gierz, Karl Heinrich Hofmann, Klaus Keimel, Jimmie D. Lawson, Michael W. Mislove, and Dana S. Scott, A Compendium of Continuous Lattices, Springer-Verlag, 1980
[Joh86] Peter Johnstone, Stone Spaces, CUP, 1986.
[Jun89] Achim Jung, Cartesian Closed Categories of Domains, PhD dissertation, Vol. 66 of CWI Tracts, 1989.
[Jun90] Achim Jung, The classification of continuous domains , Proc. 5th IEEE Symposium on Logic in Computer Science, 1990.
[MS02] Matías Menni and Alex Simpson,
Topological and Limit-space Subcategories
of Countably-based Equilogical Spaces,
To appear in Math. Struct. in Comp. Sci.
[Pit96] Andrew Pitts, Relational properties of domains, Information and Computation, 127:66-90, 1996.
[Plo83] Gordon Plotkin, Domains, the "Pisa notes", 1983.
[Sco72] Dana Scott, Continuous lattices, in Toposes, algebraic geometry and logic, pp. 97-136, Springer LNM 274, 1972.
[Sim02] Alex Simpson, Computational Adequacy for Recursive Types in Models of Intuitionistic Set Theory, draft paper, 2002.
[Smy83] Michael Smyth, The largest cartesian closed category of domains, Theoretical Computer Science, 27:109-119, 1983
[Smy92] Michael Smyth, Topology, Handbook of Logic in Computer Science Vol. I, 1992.
[SP82] Michael Smyth and Gordon Plotkin, The category-theoretic solution of recursive domain equations, SIAM Journal of Computing, 11:761-783, 1982.
[Vic89] Steve Vickers, Topology in Logical Form, CUP, 1989.