Andreas Nonnengart

Elimination of Predicate Quantifiers

Formulae of higher-order predicate logic are difficult to handle with automated inference systems. Some of these formulae, however, are equivalent to formulae of first-order predicate logic or even propositional logic. For example the formula of second-order predicate logic P (P P) is trivially equivalent to the propositional constant false. In applications where formulae of higher-order predicate logic occur naturally it is very useful to determine whether the given formula is in fact equivalent to a simpler formula of first-order or propositional logic. Typical applications where this occurs are predicate minimization by circumscription, correspondence theory in non-classical logic, and simple versions of set theory. In these areas we are faced with formulae of second-order predicate logic with existentially or universally quantified predicate variables and we want to simplify them by computing equivalent first-order formulae.

Hybrid Systems Verification by Location Elimination

In this paper we propose a verification method for hybrid systems that is based on a successive elimination of the various system locations involved. Briefly, with each such elimination we compute a weakest precondition (strongest postcondition) on the predecessor (successor) locations such that the property to be proved cannot be violated. Experiments show that this approach is particularly interesting in cases where a standard reachability analysis would require to travel often through some of the given system locations.