Article thumbnail

Program Semantics and Classical Logic

By Reinhard Muskens


In the tradition of Denotational Semantics one usually lets program constructs take their denotations in reflexive domains, i.e. in domains where self-application is possible. For the bulk of programming constructs, however, working with reflexive domains is an unnecessary complication. In this paper we shall use the domains of ordinary classical type logic to provide the semantics of a simple programming language containing choice and recursion. We prove that the rule of {\em Scott Induction\/} holds in this new setting, prove soundness of a Hoare calculus relative to our semantics, give a direct calculus ${\cal C}$ on programs, and prove that the denotation of any program $P$ in our semantics is equal to the union of the denotations of all those programs $L$ such that $P$ follows from $L$ in our calculus and $L$ does not contain recursion or choice

Topics: Language, Logic
Year: 1997
OAI identifier:

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.

Suggested articles


  1. (1940). A Formulation of the Simple Theory of Types.
  2. (1969). A Theory of Programs,
  3. (1963). A Theory of Propositional Types.
  4. (1975). An Introduction to Mathematical Logic and Type Theory: to Truth through Proof.
  5. (1991). Anaphora and the Logic of Change.
  6. (1996). Combining Montague Semantics and Discourse Representation. Linguistics and Philosophy,
  7. (1950). Completeness in the Theory of Types.
  8. (1990). Denotational Semantics.
  9. Domains for Denotational Semantics.
  10. (1984). Dynamic Logic.
  11. (1990). Dynamic Montague Grammar.
  12. (1996). Exploring Logical Dynamics.
  13. (1986). Foundations and Applications of Montague Grammar.
  14. (1983). Higher-Order Logic. doi
  15. (1975). Intensional and Higher-Order Modal Logic.
  16. (1987). Logics of Time and Computation.
  17. (1980). Mathematical Theory of Program Correctness.
  18. (1994). Modal State Semantics,
  19. (1976). Semantical Considerations on Floyd-Hoare Logic.
  20. (1995). Tense and the Logic of Change. In
  21. (1973). The Proper Treatment of Quantification in Ordinary English.
  22. Toward a Mathematical Semantics for Computer Languages. In doi
  23. (1997). Typed Logics with States. doi
  24. (1970). Universal Grammar. In Formal Philosophy,