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106
Universal coalgebra: a theory of systems
, 2000
"... In the semantics of programming, nite data types such as finite lists, have traditionally been modelled by initial algebras. Later final coalgebras were used in order to deal with in finite data types. Coalgebras, which are the dual of algebras, turned out to be suited, moreover, as models for certa ..."
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Cited by 408 (42 self)
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the notion of coalgebra homomorphism, the definition of bisimulation on coalgebras can be shown to be formally dual to that of congruence on algebras. Thus, the three basic notions of universal algebra: algebra, homomorphism of algebras, and congruence, turn out to correspond to coalgebra, homomorphism
UNIVERSAL COALGEBRAS AND THEIR LOGICS
, 2009
"... ABSTRACT. We survey coalgebras as models of state based systems together with their global and local logics. We convey some useful intuition regarding Setfunctors which leads naturally to coalgebraic modal logic where modalities are validity patterns for the successor object of a state. 1. ..."
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ABSTRACT. We survey coalgebras as models of state based systems together with their global and local logics. We convey some useful intuition regarding Setfunctors which leads naturally to coalgebraic modal logic where modalities are validity patterns for the successor object of a state. 1.
A Calculus of Transition Systems (towards Universal Coalgebra)
 IN ALBAN PONSE, MAARTEN DE RIJKE, AND YDE VENEMA, EDITORS, MODAL LOGIC AND PROCESS ALGEBRA, CSLI LECTURE NOTES NO
, 1995
"... By representing transition systems as coalgebras, the three main ingredients of their theory: coalgebra, homomorphism, and bisimulation, can be seen to be in a precise correspondence to the basic notions of universal algebra: \Sigmaalgebra, homomorphism, and substitutive relation (or congruence). ..."
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Cited by 30 (1 self)
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By representing transition systems as coalgebras, the three main ingredients of their theory: coalgebra, homomorphism, and bisimulation, can be seen to be in a precise correspondence to the basic notions of universal algebra: \Sigmaalgebra, homomorphism, and substitutive relation (or congruence
Algebras and Coalgebras
 Handbook of Modal Logic
, 2007
"... This chapter 1 sketches some of the mathematical surroundings of modal logic. First, we discuss the algebraic perspective on the field, showing how the theory of universal algebra, and more specifically, that of Boolean algebras with operators, can be used to prove significant results in modal logic ..."
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Cited by 28 (3 self)
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logic. In the second and last part of the chapter we describe how modal logic, and its model theory, provides many natural manifestations of the more general theory of universal coalgebra.
Automata and coinduction (an exercise in coalgebra
 LNCS
, 1998
"... The classical theory of deterministic automata is presented in terms of the notions of homomorphism and bisimulation, which are the cornerstones of the theory of (universal) coalgebra. This leads to a transparent and uniform presentation of automata theory and yields some new insights, amongst which ..."
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Cited by 86 (19 self)
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The classical theory of deterministic automata is presented in terms of the notions of homomorphism and bisimulation, which are the cornerstones of the theory of (universal) coalgebra. This leads to a transparent and uniform presentation of automata theory and yields some new insights, amongst
On Tree Coalgebras and Coalgebra Presentations
"... For deterministic systems, expressed as coalgebras over polynomial functors, every tree t (an element of the final coalgebra) turns out to represent a new coalgebra At. The universal property of these coalgebras, resembling freeness, is that for every state s of every system S there exists a unique ..."
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For deterministic systems, expressed as coalgebras over polynomial functors, every tree t (an element of the final coalgebra) turns out to represent a new coalgebra At. The universal property of these coalgebras, resembling freeness, is that for every state s of every system S there exists a unique
Coalgebraic algebra
 J. Pure Appl. Algebra
, 1998
"... Copyright & reuse City University London has developed City Research Online so that its users may access the research outputs of City University London's staff. Copyright © and Moral Rights for this paper are retained by the individual author(s) and / or other copyright holders. All materia ..."
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Cited by 18 (1 self)
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Copyright & reuse City University London has developed City Research Online so that its users may access the research outputs of City University London's staff. Copyright © and Moral Rights for this paper are retained by the individual author(s) and / or other copyright holders. All
Coalgebraic Models for Reactive Systems ⋆
"... Abstract. Reactive Systems à la Leifer and Milner allow to derive from a reaction semantics definition an LTS equipped with a bisimilarity relation which is a congruence. This theory has been extended by the authors (together with Barbara König) in order to handle saturated bisimilarity, a coarser e ..."
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equivalence that is more adequate for some interesting formalisms, such as logic programming and open picalculus. In this paper we recast the theory of Reactive Systems inside Universal Coalgebra. This construction is particularly useful for saturated bisimilarity, which can be seen as final semantics
Enlargements of Polynomial Coalgebras
 Proceedings of the 7th and 8th Asian Logic Conferences
"... This paper continues a series [GolOlc,a,b] of articles on the equational logic and model theory of coalgebras for certain functors T: Set  Set on the category of sets. A Tcoalgebra is a pair (A, () comprising a set A, thought of as a set of "states", and a function : A > TA called th ..."
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Cited by 3 (3 self)
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, streams, trees, automata, and classes in objectoriented programming languages  can be modelled as coalgebras for polynomial functors [Rei95, Jac96, Rut95, Rut00]. This has motivated the development of a theory of "universal coalgebra" [Rut95, Rut00], by analogy with, and categorically dual to
A coalgebraic theory of reactive systems
, 1999
"... In this report we study the connection between two well known models for interactive systems. Reactive Systems à la Leifer and Milner allow to derive an interactive semantics from a reduction semantics guaranteeing, semantics (bisimilarity). Universal Coalgebra provides a categorical framework where ..."
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Cited by 9 (1 self)
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In this report we study the connection between two well known models for interactive systems. Reactive Systems à la Leifer and Milner allow to derive an interactive semantics from a reduction semantics guaranteeing, semantics (bisimilarity). Universal Coalgebra provides a categorical framework
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