Aczel, P., Replacement Systems and the axiomatisation of Situation Theory, Situation Theory and Applications, CSLI Lecture Notes No.22, Stanford University, 1990.  Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Process Structures - Honda (1997) (5 citations) (Correct)
....processes and the establishment of equivalence between the name based theory and the name free theory, together with the systematic way to turn the former into the latter (and back) are the original contributions of the present work. Theory of composita studied by Aczel, Nerode and others [3, 4, 52] is closest in motivations and gives a study of structured objects with some operations including substitution. Their theory differs in that variable less structures are not the target of the study (thus there is no analogue of our equivalence theorem) while deeper algebraic properties were ....
Aczel, P., Replacement Systems and the axiomatisation of Situation Theory, Situation Theory and Applications, CSLI Lecture Notes No.22, Stanford University, 1990.
Notes on P-Algebra (4): Algebra over Process Structure, Part I. - Honda (Correct)
....Two processes (corresponding to two elements) may be related in diverse ways, considering how interface points of processes are connected to each other. This was implicit in the study of process algebra [11, 6] embodied in the notion of free names, or study of composita and its generalisations [2, 3, 13], embodied in the notion of variables (of, say, open terms) and is made explicit by the study of process structure [7] as well as by such works as [1, 5, 12] Specifically what [7] showed is that a coherent theory of maps and relations, with which we manipulate processes collectively, can be ....
....on FinPerm is precisely a process structure in the sense of our preceding Notes. As proved in [7] this structure has an equivalent presentation which directly underlies many mathematical and computational structures studied so far. In this form, the structure relates to a series of study of Aczel [2, 3] and Nerode [13] where algebra of open terms involving general substitution is considered. We shall discuss their theory (especially that of [3] in comparison with our algebraic theory over process structures in Part II. iii) A process structure on Perm generalises the above to the case when ....
Aczel, P., Replacement Systems and the axiomatisation of Situation Theory, Situation Theory and Applications, CSLI Lecture Notes No.22, Stanford University, 1990.
Term Declaration Logic and Generalised Composita - Aczel (1991) (6 citations) Self-citation (Aczel) (Correct)
....for all, not necessarily finitary generalised composita. The original motivation for our interest in these ideas has been in connection with a long term program to develope a theory of structured objects, intended to be used as a tool in the development of a mathematical situation theory, See [1] and [2] Structured objects are like terms in that they may contain things called parameters and there is a notion of substitution for parameters. A good example of the kind of structured object that was our starting point may be found in [3] where a universe of possibly non well founded sets ....
Peter Aczel. Replacement Systems and the axiomatisation of Situation Theory, in: Situation Theory and its applications, CSLI Lecture Notes No. 22, Stanford University, 1990.
Elementary Structures in Process Theory (1) Sets with Renaming - Honda (1997) (Correct)
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Aczel, P., Replacement Systems and the axiomatisation of Situation Theory, Situation Theory and Applications, CSLI Lecture Notes No.22, Stanford University, 1990.
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