On strictly arithmetical completeness in logics of programs

Andrzej Szalas
1991 Theoretical Computer Science  
Szalas, A., On strictly arithmetical comp:eteness in logics of programs. Theoretical Computer Science 79 (1991) 341-355. We introduce and discuss a notion of strictly arithmetical completeness r&ted 10 relative compl&zness of Cook ( 1978) and arithmetical completeness of Hare1 (1978). We present a powerful technique of obtaining strictly arithmetical axiomatizations of logics of programs. Given a modeltheoretic semantics of' a logic and a set of formulae defining (in a metalanguagei its
more » ... ical connectives, we automatically derive strictly arithmetically complete and sound proof systems for this logic. As examples of applicdion of the technique we obtain new aGomatiz.ations ofalgorithmic logic, (concurrent) dynamic logic and :empozd logic.
doi:10.1016/0304-3975(91)90336-z fatcat:7jgtoukpircqxkuu5h3x4pyddi