Peter Aczel. Non-Well-Founded Sets. Center for the Study of Language and Information, Stanford University, 1988. CSLI Lecture Notes, Volume 14.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of a program with its environment, called its behaviour. Two programs are equivalent if we can t prove they have di erent behaviour. This equivalence is called bisimilarity or behavioural equivalence, and has its roots in concurrent communicating processes [Mil89] non well founded sets [Acz88,BM96] and coalgebra, which is becoming a popular theory of systems and in nite objects [Rut00,Kur01] Bisimilarity relations are de ned coinductively. OS Kernel Shared Memory Console Disk Network Other processes Process Environment Program Fig. 5: A program viewed as a process that ....

Peter Aczel. Non-Well-Founded Sets. Center for the Study of Language and Information, Stanford University, 1988. CSLI Lecture Notes, Volume 14.

....of a program with its environment, called its behaviour. Two programs are equivalent if we can t prove they have di#erent behaviour. This equivalence is called bisimilarity or behavioural equivalence, and has its roots in concurrent communicating processes [Mil89] non well founded sets [Acz88,BM96] and coalgebra, which is becoming a popular theory of systems and infinite objects [Rut00,Kur01] Bisimilarity relations are defined coinductively. OS Kernel Shared Memory Console Disk Network Other processes Process Environment Program Fig. 5: A program viewed as a process that ....

Peter Aczel. Non-Well-Founded Sets. Center for the Study of Language and Information, Stanford University, 1988. CSLI Lecture Notes, Volume 14.

....to the attention of researchers in differing fields such as mathematical logic, computer science, artificial intelligence, linguistics, cognitive science, and philosophy. Logicians first explored set theories whose universe contains what are called non wellfounded sets, or hypersets (cf. 17] [5]) But the area was considered rather exotic until these theories were put to use in developing rigorous accounts of circular notions in computer science (cf. 7] Instead of the Foundation Axiom these set theories adopt the so called Anti Foundation Axiom, AFA, which gives rise to a rich ....

P. Aczel: Non-well-founded sets.CSLI Lecture Notes 14 (CSLI Publications, Stanford, 1988).

....come to the attention of researchers in differing fields such as mathematical logic, computer science, artificial intelligence, linguistics, cognitive science, and philosophy. Logicians first explored set theories whose universe contains what are called non wellfounded sets, or hypersets (cf. 6] [2]) But the area was considered rather exotic until these theories were put to use in developing rigorous accounts of circular notions in computer science (cf. 4] Instead of the Foundation Axiom these set theories adopt the so called AntiFoundation Axiom, AFA, which gives rise to a rich universe ....

P. Aczel: Non-well-founded sets.CSLI Lecture Notes 14 (CSLI Publications, Stanford, 1988).

....Cohen) that it is independent of other, more widely accepted axioms of set theory. Still more recently, there has been debate about the Axiom of Foundation, which asserts that there is no infinite sequence of sets S 1 ; S 2 ; S 3 ; such that each S i 1 is an element of S i . In fact, Aczel [1] and others have used an Anti Foundation Axiom, which positively asserts the existence of such non well founded sets, to model various phenomena in computation, including communicating processes in the sense of Milner [54] I think it is fair to say that most mathematicians no longer believe in ....

Peter Aczel. Non-Well-Founded Sets. Center for the Study of Language and Information, Stanford University, 1988. CSLI Lecture Notes, Volume 14.

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