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10
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 45 (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 25 (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 20 (6 self)
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We investigate the development of theories of types and computability via realizability.
Constructive algebraic integration theory without choice. Dagstuhl proceedings
 Mathematics, Algorithms, Proofs, number 05021 in Dagstuhl Seminar Proceedings. 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
, 1997
"... This paper is an exercise in formal and philosophical logic. I will show how intuitionistic 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). T ..."
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Cited by 3 (0 self)
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This paper is an exercise in formal and philosophical logic. I will show how intuitionistic 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
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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Cited by 1 (0 self)
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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
Part II Local Realizability Toposes and a Modal Logic for
"... 5.1 Definition and Examples 5.1.1 Definition and Definability Results A tripos is a weak tripos with disjunction which has a (weak) generic object. Explicitly we define: ..."
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5.1 Definition and Examples 5.1.1 Definition and Definability Results A tripos is a weak tripos with disjunction which has a (weak) generic object. Explicitly we define:
PROPOSITIONAL LOGIC
, 2008
"... Intuitionistic logic is an important variant of classical logic, but it is not as wellunderstood, even in the propositional case. In this thesis, we describe a faithful representation of intuitionistic propositional formulas as tree automata. This representation permits a number of consequences, inc ..."
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Intuitionistic logic is an important variant of classical logic, but it is not as wellunderstood, even in the propositional case. In this thesis, we describe a faithful representation of intuitionistic propositional formulas as tree automata. This representation permits a number of consequences, including a characterization theorem for free Heyting algebras, which are the intutionistic analogue of free Boolean algebras, and a new algorithm for solving equations over intuitionistic propositional logic. BIOGRAPHICAL SKETCH
1.1.2 Cartesian Product...................... 5
"... 1.1.1 Categories........................... 4 ..."