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20
Presheaf Models for Concurrency
, 1999
"... In this dissertation we investigate presheaf models for concurrent computation. Our aim is to provide a systematic treatment of bisimulation for a wide range of concurrent process calculi. Bisimilarity is defined abstractly in terms of open maps as in the work of Joyal, Nielsen and Winskel. Their wo ..."
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Cited by 49 (19 self)
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In this dissertation we investigate presheaf models for concurrent computation. Our aim is to provide a systematic treatment of bisimulation for a wide range of concurrent process calculi. Bisimilarity is defined abstractly in terms of open maps as in the work of Joyal, Nielsen and Winskel. Their work inspired this thesis by suggesting that presheaf categories could provide abstract models for concurrency with a builtin notion of bisimulation. We show how
Variations on Algebra: monadicity and generalisations of equational theories
 Formal Aspects of Computing
, 2001
"... this paper the author was partially supported by an SERC/EPSRC Advanced Research Fellowship, EPSRC Research grant GR/L54639, and EU Working Group APPSEM ..."
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Cited by 24 (0 self)
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this paper the author was partially supported by an SERC/EPSRC Advanced Research Fellowship, EPSRC Research grant GR/L54639, and EU Working Group APPSEM
Developing Theories of Types and Computability via Realizability
, 2000
"... We investigate the development of theories of types and computability via realizability. ..."
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Cited by 23 (6 self)
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We investigate the development of theories of types and computability via realizability.
Constructive algebraic integration theory without choice”, in Mathematics, Algorithms and Proofs
 Dagstuhl Seminar Proceedings, 05021, Internationales Begegnungs und Forschungszentrum (IBFI), Schloss Dagstuhl
, 2005
"... Abstract. We present a constructive algebraic integration theory. The theory is constructive in the sense of Bishop, however we avoid the axiom of countable, or dependent, choice. Thus our results can be interpreted in any topos. Since we avoid impredicative methods the results may also be interpret ..."
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Cited by 9 (5 self)
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Abstract. We present a constructive algebraic integration theory. The theory is constructive in the sense of Bishop, however we avoid the axiom of countable, or dependent, choice. Thus our results can be interpreted in any topos. Since we avoid impredicative methods the results may also be interpreted in MartinL type theory or in a predicative topos in the sense of Moerdijk and Palmgren. We outline how to develop most of Bishop’s theorems on integration theory that do not mention points explicitly. Coquand’s constructive version of the Stone representation theorem is an important tool in this process. It is also used to give a new proof of Bishop’s spectral theorem.
Extending intuitionistic logic with subtraction. Unpublished note. Available at http://consequently.org/writing/extendingj
, 1977
"... This paper is an exercise in formal and philosophical logic. I will show howintuitionistic propositional logic can be extended with a new twoplace connective, not expressible in the traditional language of intuitionistic logic (the language of conjunction, disjunction, negation and implication). Th ..."
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This paper is an exercise in formal and philosophical logic. I will show howintuitionistic propositional logic can be extended with a new twoplace connective, not expressible in the traditional language of intuitionistic logic (the language of conjunction, disjunction, negation and implication). The new system will be shown to be a conservative extension of intuitionistic logic. After examining the formal properties of this extension, the task will be to consider whether this is an `acceptable ' extension of intuitionistic logic. It will turn out that on some intuitionistic considerations the extension is acceptable, and on others it is not. In this paper I presume that the reader has some idea both of the formal properties of intuitionistic logic, and some motivating philosophical principles which inform the development ofintuitionistic logic. Readers wanting such an introduction can do no better than look at some of the excellent, extensive literature on intuitionism [3, 5, 8, 12]. Other work has been done on extending intuitionistic propositional logic with new connectives. Gabbay [6] considers extending the logic with propositional
CATEGORIES OF COMPONENTS AND LOOPFREE CATEGORIES
"... Abstract. Given a groupoid G one has, in addition to the equivalence of categories E from G to its skeleton, a fibration F (Definition 1.11) from G to its set of connected components (seen as a discrete category). From the observation that E and F differ unless G[x, x] = {idx} for every object x of ..."
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Abstract. Given a groupoid G one has, in addition to the equivalence of categories E from G to its skeleton, a fibration F (Definition 1.11) from G to its set of connected components (seen as a discrete category). From the observation that E and F differ unless G[x, x] = {idx} for every object x of G, we prove there is a fibered equivalence (Definition 1.12) from C[Σ1] (Proposition 1.1) to C/Σ (Proposition 1.8) when Σ is a