Formalizing Dijkstra's predicate transformer wp in weak second-order logic

Formalizing Dijkstra's Predicate Transformer wp in Weak Second-Order Logic

We present a purely syntactical but nevertheless handy definition of Dijkstra’s predicate transformer wp in weak second-order logic. This formalization allows us to prove a normal form theorem of wp, from which interesting properties can be inferred. In particular, it turns out that wp(P, .) is a homomorphism on the class of formulae in the formalism considered.

Quantifier Elimination in Second-Order Predicate Logic

An algorithm is presented which eliminates second–order quantifiers over predicate variables in formulae of type ∃P1, . . . , Pnψ where ψ is an arbitrary formula of first– order predicate logic. The resulting formula is equivalent to the original formula – if the algorithm terminates. The algorithm can for example be applied to do interpolation, to eliminate the second–order quantifiers in circ...

Extending models of second order predicate logic to models of second order dependent type theory

We describe a method for constructing a model of second order dependent type theory out of a model of classical second order predicate logic. Apart from the construction being of interest by itself, this also suggests a way of proving the completeness of the formulas-as-types embedding from second order predicate logic to second order dependent type theory. Under this embedding, formulas are in...

Predicate Construction in Higher-order Logic

Predicate construction is a guided search process: a space of predicates must be enumerated in some systematic way in order to find, according to some criterion, a suitable predicate for some purpose. Often the search space is large and heuristics are used to guide the search. Typically, predicate construction is studied and implemented in the context of first-order logic. In this paper, I outl...

Predicate Transformer Semantics of a Higher Order Imperative Language With . . .