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Reactive Systems, (Semi)Saturated Semantics and Coalgebras on Presheaves
, 2009
"... The semantics of process calculi has traditionally been specified by labelled transition systems (ltss), but with the development of name calculi it turned out that reaction rules (i.e., unlabelled transition rules) are often more natural. This leads to the question of how behavioural equivalences ( ..."
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The semantics of process calculi has traditionally been specified by labelled transition systems (ltss), but with the development of name calculi it turned out that reaction rules (i.e., unlabelled transition rules) are often more natural. This leads to the question of how behavioural equivalences (bisimilarity, trace equivalence, etc.) defined for lts can be transferred to unlabelled transition systems. Recently, in order to answer this question, several proposals have been made with the aim of automatically deriving an lts from reaction rules in such a way that the resulting equivalences are congruences. Furthermore these equivalences should agree with the standard semantics, whenever one exists. In this paper we propose saturated semantics, based on a weaker notion of observation and orthogonal to all the previous proposals, and we demonstrate the appropriateness of our semantics by means of two examples: logic programming and open Petri nets. We also show that saturated semantics can be efficiently characterized through the so called semisaturated games. Finally, we provide coalgebraic models relying on presheaves.
The Syntax of Coherence
, 1999
"... This article tackles categorical coherence within a twodimensional generalization of Lawvere’s functorial semantics. 2theories, a syntactical way of describing categories with structure, are presented. From the perspective here afforded, many coherence results become simple statements about the qu ..."
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This article tackles categorical coherence within a twodimensional generalization of Lawvere’s functorial semantics. 2theories, a syntactical way of describing categories with structure, are presented. From the perspective here afforded, many coherence results become simple statements about the quasiYoneda lemma and 2theorymorphisms. Given two 2theories and a 2theorymorphism between them, we explore the induced relationship between the corresponding 2categories of algebras. The strength of the induced quasiadjoints are classified by the strength of the 2theorymorphism. These quasiadjoints reflect the extent to which one structure can be replaced by another. A twodimensional analogue of the Kronecker product is defined and constructed. This operation allows one to generate new coherence laws from old ones. 1
Talk given at the Conference on Topics in Geometry and Physics
, 1992
"... hepth/9304061 Closed string field theory, strong homotopy Lie algebras and the operad actions of moduli spaces ..."
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hepth/9304061 Closed string field theory, strong homotopy Lie algebras and the operad actions of moduli spaces