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Rewriting Logic as a Semantic Framework for Concurrency: a Progress Report
, 1996
"... . This paper surveys the work of many researchers on rewriting logic since it was first introduced in 1990. The main emphasis is on the use of rewriting logic as a semantic framework for concurrency. The goal in this regard is to express as faithfully as possible a very wide range of concurrency mod ..."
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Cited by 82 (22 self)
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. This paper surveys the work of many researchers on rewriting logic since it was first introduced in 1990. The main emphasis is on the use of rewriting logic as a semantic framework for concurrency. The goal in this regard is to express as faithfully as possible a very wide range of concurrency models, each on its own terms, avoiding any encodings or translations. Bringing very different models under a common semantic framework makes easier to understand what different models have in common and how they differ, to find deep connections between them, and to reason across their different formalisms. It becomes also much easier to achieve in a rigorous way the integration and interoperation of different models and languages whose combination offers attractive advantages. The logic and model theory of rewriting logic are also summarized, a number of current research directions are surveyed, and some concluding remarks about future directions are made. Table of Contents 1 In...
Categorybased Semantics for Equational and Constraint Logic Programming
, 1994
"... This thesis proposes a general framework for equational logic programming, called categorybased equational logic by placing the general principles underlying the design of the programming language Eqlog and formulated by Goguen and Meseguer into an abstract form. This framework generalises equation ..."
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Cited by 24 (10 self)
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This thesis proposes a general framework for equational logic programming, called categorybased equational logic by placing the general principles underlying the design of the programming language Eqlog and formulated by Goguen and Meseguer into an abstract form. This framework generalises equational deduction to an arbitrary category satisfying certain natural conditions; completeness is proved under a hypothesis of quantifier projectivity, using a semantic treatment that regards quantifiers as models rather than variables, and regards valuations as model morphisms rather than functions. This is used as a basis for a model theoretic categorybased approach to a paramodulationbased operational semantics for equational logic programming languages. Categorybased equational logic in conjunction with the theory of institutions is used to give mathematical foundations for modularisation in equational logic programming. We study the soundness and completeness problem for module imports i...
Formal Interoperability
, 1998
"... this paper I briefly sketch recent work on metalogical foundations that seems promising as a conceptual basis on which to achieve the goal of formal interoperability. Specificaly, I will briefly discuss: ..."
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Cited by 13 (3 self)
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this paper I briefly sketch recent work on metalogical foundations that seems promising as a conceptual basis on which to achieve the goal of formal interoperability. Specificaly, I will briefly discuss:
Higherdimensional categories with finite derivation type
"... We study convergent (terminating and confluent) presentations of ncategories. Using the notion of polygraph (or computad), we introduce the homotopical property of finite derivation type for ncategories, generalising the one introduced by Squier for word rewriting systems. We characterise this pr ..."
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Cited by 12 (3 self)
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We study convergent (terminating and confluent) presentations of ncategories. Using the notion of polygraph (or computad), we introduce the homotopical property of finite derivation type for ncategories, generalising the one introduced by Squier for word rewriting systems. We characterise this property by using the notion of critical branching. In particular, we define sufficient conditions for an ncategory to have finite derivation type. Through examples, we present several techniques based on derivations of 2categories to study convergent presentations by 3polygraphs.
Foundations of Behavioural Specification in Rewriting Logic
, 1996
"... We extend behavioural specification based on hidden sorts to rewriting logic by constructing a hybrid between the two underlying logics. This is achieved by defining a concept of behavioural satisfaction for rewriting logic. Our approach is semantic in that it is based on a general construction on m ..."
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Cited by 9 (2 self)
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We extend behavioural specification based on hidden sorts to rewriting logic by constructing a hybrid between the two underlying logics. This is achieved by defining a concept of behavioural satisfaction for rewriting logic. Our approach is semantic in that it is based on a general construction on models, called behaviour image, which uses final models in an essential way. However we provide syntactic characterisations for the for the behavioural satisfaction relation, thus opening the door for shifting recent advanced proof techniques for behavioural satisfaction to rewriting logic. We also show that the rewriting logic behavioural satisfaction obeys the socalled "satisfaction condition" of the theory of institutions, thus providing support for OBJ style modularisation for this new paradigm. 1 Introduction This research aims at integrating two different semantic approaches on objects and concurrency by internalising behavioural specification [12] to [conditional] rewriting logic (abb...
Worytkiewicz: A model category for local pospaces
 Homology, Homotopy and Applications
, 506
"... Abstract. Locally partialordered spaces (local pospaces) have been used to model concurrent systems. We provide equivalences for these spaces by ..."
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Cited by 7 (2 self)
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Abstract. Locally partialordered spaces (local pospaces) have been used to model concurrent systems. We provide equivalences for these spaces by
Every homotopy theory of simplicial algebras admits a proper model
 Topology Appl. 119
, 2002
"... Abstract. We show that any closed model category of simplicial algebras over an algebraic theory ..."
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Cited by 5 (0 self)
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Abstract. We show that any closed model category of simplicial algebras over an algebraic theory
Simplicial monoids and Segal categories
 Contemp. Math
"... Abstract. Much research has been done on structures equivalent to topological or simplicial groups. In this paper, we consider instead simplicial monoids. ..."
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Cited by 4 (3 self)
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Abstract. Much research has been done on structures equivalent to topological or simplicial groups. In this paper, we consider instead simplicial monoids.
I.Kriz: Laplaza sets, or how to select coherence diagrams for pseudo algebras
"... Abstract. We define a general concept of pseudo algebras over theories and 2theories. A more restrictive such notion was introduced in [5], but as noticed by M. Gould, did not capture the desired examples. The approach taken in this paper corrects the mistake by introducing a more general concept, ..."
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Cited by 3 (1 self)
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Abstract. We define a general concept of pseudo algebras over theories and 2theories. A more restrictive such notion was introduced in [5], but as noticed by M. Gould, did not capture the desired examples. The approach taken in this paper corrects the mistake by introducing a more general concept, allowing more flexibility in selecting coherence diagrams for pseudo algebras. 1.
FirstOrder Logical Duality
, 2008
"... Generalizing Stone duality for Boolean algebras, an adjunction between Boolean coherent categories—representing firstorder syntax—and certain topological groupoids—representing semantics—is constructed. The embedding of a Boolean algebra into a frame of open sets of a space of 2valued models is re ..."
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Cited by 3 (2 self)
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Generalizing Stone duality for Boolean algebras, an adjunction between Boolean coherent categories—representing firstorder syntax—and certain topological groupoids—representing semantics—is constructed. The embedding of a Boolean algebra into a frame of open sets of a space of 2valued models is replaced by an embedding of a Boolean coherent category, B, into a topos of equivariant sheaves on a topological groupoid of setvalued models and isomorphisms between them. The latter is a groupoid representation of the topos of coherent sheaves on B, analogously to how the Stone space of a Boolean algebra is a spatial representation of the ideal completion of the algebra, and the category B can then be recovered from its semantical groupoid, up to pretopos completion. By equipping the groupoid of sets and bijections with a particular topology, one obtains a particular topological groupoid which plays a role analogous to that of the discrete space 2, in being the dual of the object classifier and the object one ‘homs into ’ to recover a Boolean coherent category from its semantical groupoid. Both parts of the adjunction, then, consist of ‘homming into sets’, similarly to how both parts of the equivalence between Boolean algebras and Stone spaces consist of ‘homming into 2’. By slicing over this groupoid (modified to display an alternative setup), Chapter 3 shows how the adjunction specializes to the case of firstorder single sorted logic to yield an adjunction between such theories and an independently characterized slice category of topological groupoids such that the counit component at a theory is an isomorphism. Acknowledgements I would like, first and foremost, to thank my supervisor Steve Awodey. I would like to thank the members of the committee: Jeremy Avigad, Lars