Pseudocomplements of closure operators on posets

Authors:
Francesco Ranzato
Affiliations:
Dipartimento di Matematica Pura ed Applicata, Universita di Padova, Via Belzoni 7, 35131 Padova, Italy
Venue:
Discrete Mathematics
Year:
2002

Citing 4
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Complementation in abstract interpretation

ACM Transactions on Programming Languages and Systems (TOPLAS)
Closures on CPOs form complete lattices

Information and Computation
Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints

POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Principles of Program Analysis

Principles of Program Analysis

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Abstract

Some recent results provide sufficient conditions for complete lattices of closure operators on complete lattices, ordered pointwise, to be pseudocomplemented. This paper gives results of pseudocomplementation in the more general setting of closure operators on mere posets. The following result is first proved: closure operators on a meet-continuous meet-semilattice form a pseudocomplemented complete lattice. Furthermore, the following orthogonal result (actually, a slightly more general result) is proved: Closure operators on a directed-complete poset which is transfinitely generated by maximal lower bounds from its set of completely meet-irreducible elements-any poset satisfying the ascending chain condition belongs to this class-form a pseudocomplemented complete lattice.