Logical Analysis of Demonic NonDeterministic Programs

Stéphane Demri (1, 2) , Ewa Orlowska (3)

1 LIFIA - Laboratoire d'Informatique Fondamentale et d'Intelligence Artificielle
2 CNRS - Centre National de la Recherche Scientifique
3 PAN - Polska Akademia Nauk = Polish Academy of Sciences = Académie polonaise des sciences

A logical framework is presented for representing and reasoning about nondeterministic programs that may not terminate. We propose a logic PDL(; ;, ||, d(*)) which is an extension of dynamic logic such that the program constructors related to demonic operations are introduced in its language. A complete and sound Hilbert-style proof system is given and it is shown that PDL(; ;, ||, d(*)) is decidable. In the second part of this paper, a translation is defined between PDL(; ;, ||, d(*)) and a relational logic. A sound and complete Rasiowa-Sikorski-style proof system for the relational logic is given. It provides a natural deduction-style method of reasoning for PDL(; ;, ||, d(*)).

Mots clés: propositional dynamic logic PDL; demonic operator; Hilbert-style proof system; Rasiowa-Sikorski-style proof system; axiomatisation

Domaines: Informatique [cs]; Logique en informatique [cs.LO]

Stéphane Demri, Ewa Orlowska. Logical Analysis of Demonic NonDeterministic Programs. Theoretical Computer Science, 1996, 166 (1-2), pp.173-202. ⟨10.1016/0304-3975(95)00190-5⟩. ⟨hal-03193705⟩