# The ICICS/CS Reading Room

## UBC CS TR-91-31 Summary

- No on-line copy of this technical report is available.

- Solving Domain Equations in NaDSet, December 1991 Paul C. Gilmore and George K. Tsiknis, 23 pages
Solutions of systems of domain equations is the basis for what is called
the Strachey-Scott approach to providing a denotational semantics for
programming languages. The solutions offered by the mathematical
methods developed by Scott, however, do not provide a computational
basis for the semantics in the form of a proof theory. The purpose of
this paper is to provide such a theory using the logic and set theory
NaDSet.
\nThe development of NaDSet was motivated by the following three
principles:\\
1. Abstraction, along with truth functions and quantification, is one of
the three fundamental concepts of logic and should be formalized in the
same manner as the other two.\\
2. Natural deduction presentations of logic provide a transparent
formalization of Tarski's reductionist semantics.\\
3. Atomic formulas receive their truth values from a nominalist
interpretation.
\nThat these three principles lead to a successful resolution of the set
theoretic paradoxes and to a sound formulation of NaDSet has been
demonstrated elsewhere with proofs of consistency and completeness.
Applications of NaDSet to programming language semantics, category
theory, non-well-founded sets, and to foundational questions of
mathematics have also been demonstrated.
\nThe financial support of the Natural Science and Engineering Research
Council of Canada is gratefully acknowledged.

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