Existential Quantifiers in Predicate-Fact-Nets

Abstract

It is well known that every formula of first-order predicate logic in prenex form can be represented as a strict predicate transition net (PrT-net) in which all transitions are seen to be dead. Nets wherein all predicates can carry only one specimen of an n-tuple are called strict [Ge]. In this net representation of predicate logic Skolem functions are used to get descriptions for existential quantifiers [Th].

In PrT-systems given by PrT-nets and an initial marking, the dead transitions specify the facts about that system. S-invariants are a very useful means to prove transitions of a PrT-system to be facts. In those predicate fact nets (PrF-nets) derived from S-invariants, Skolem functions do not occur.

The question arises, whether existential quantifiers do not exist in those fact nets, or whether nets carry another more natural representation for them. Sums seem to yield such an appropriate net description for existential quantifiers. But some derivation problems remain, in which sums cannot replace the Skolem functions.