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7,098
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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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
An axiomatic basis for computer programming
 COMMUNICATIONS OF THE ACM
, 1969
"... In this paper an attempt is made to explore the logical foundations of computer programming by use of techniques which were first applied in the study of geometry and have later been extended to other branches of mathematics. This involves the elucidation of sets of axioms and rules of inference w ..."
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Cited by 1754 (4 self)
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In this paper an attempt is made to explore the logical foundations of computer programming by use of techniques which were first applied in the study of geometry and have later been extended to other branches of mathematics. This involves the elucidation of sets of axioms and rules of inference
Premotor cortex and the recognition of motor actions
 Cognitive Brain Research
, 1996
"... In area F5 of the monkey premotor cortex there are neurons that discharge both when the monkey performs an action and when he observes a similar action made by another monkey or by the experimenter. We report here some of the properties of these 'mirror' neurons and we propose that their a ..."
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Cited by 742 (44 self)
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that their activity 'represents ' the observed action. We posit, then, that this motor epresentation is at the basis of the understanding of motor events. Finally, on the basis of some recent data showing that, in man, the observation of motor actions activate the posterior part of inferior frontal gyrus
GRASP  A New Search Algorithm for Satisfiability
, 1996
"... This paper introduces GRASP (Generic seaRch Algorithm for the Satisjiability Problem), an integrated algorithmic framework for SAT that un.$es several previously proposed searchpruning techniques and facilitates ident$cation of additional ones. GRASP is premised on the inevitability of confzicts dur ..."
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Cited by 449 (34 self)
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portions of the search space. In addition, by “recording ” the causes of conflicts, GRASP can recognize andpreempt the occurrence of similar conficts later on in the search. Finally, straightjwward bookkeeping of the causality chains leading up to conflicts allows GRASP to identifi assignments
Coalgebraic Logic
 Annals of Pure and Applied Logic
, 1999
"... We present a generalization of modal logic to logical systems which are interpreted on coalgebras of functors on sets. The leading idea is that infinitary modal logic contains characterizing formulas. That is, every modelworld pair is characterized up to bisimulation by an infinitary formula. The ..."
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Cited by 110 (0 self)
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logics. We then apply the characterization result to get representation theorems for final coalgebras in terms of maximal elements of ordered algebras. The end result is that the formulas of coalgebraic logics can be viewed as approximations to the elements of the final coalgebra. Keywords: infinitary
The age distribution of cancer and a multistage theory of carcinogenesis.
 Br J Cancer
, 1954
"... Attempts to drive theoretical laws from changes in the death rate with age have a long history. They have not, in general, been very fruitful and there has been some hesitation in applying the technique to the study of cancer. Recently, however, two hypotheses about the mechanism of carcinogenesis ..."
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Cited by 270 (1 self)
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in youth might be affected by special factors which were unlikely to operate at later ages and they, therefore, felt justified in basing their hypotheses on the data recorded for adults. Nordling i.e., log rate = 6log t + a constant. In contrast to Fisher and Hollomon's (1951) hypothesis this leads
Continuous functions on final coalgebras
, 2007
"... In a previous paper we have given a representation of continuous functions on streams, both discretevalued functions, and functions between streams. the topology on streams is the ‘Baire ’ topology induced by taking as a basic neighbourhood the set of streams that share a given finite prefix. We ga ..."
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Cited by 12 (1 self)
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gave also a combinator on the representations of stream processing functions that reflects composition. Streams are the simplest example of a nontrivial final coalgebras, playing in the coalgebraic realm the same role as do the natural numbers in the algebraic realm. Here we extend our previous
Simulations in Coalgebra
 THEOR. COMP. SCI
, 2003
"... A new approach to simulations is proposed within the theory of coalgebras by taking a notion of order on a functor as primitive. Such an order forms a basic building block for a "lax relation lifting", or "relator" as used by other authors. Simulations appear as coalgebras of thi ..."
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Cited by 28 (2 self)
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coincide. Also, suitable conditions are identified which ensures that similarity on a final coalgebra forms an (algebraic) dcpo structure. This involves a close investigation of the iterated applications F (#) and F (1) of a functor F with an order to the initial and final sets.
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
Similarity Quotients as Final Coalgebras
"... Abstract. We give a general framework relating a branching time relation on nodes of a transition system to a final coalgebra for a suitable endofunctor. Examples of relations treated by our theory include bisimilarity (a well known example), similarity, upper and lower similarity for transition sys ..."
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Cited by 8 (0 self)
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Abstract. We give a general framework relating a branching time relation on nodes of a transition system to a final coalgebra for a suitable endofunctor. Examples of relations treated by our theory include bisimilarity (a well known example), similarity, upper and lower similarity for transition
Results 1  10
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7,098