Most mathematicians think that first order arithmetic is objectively true in some sense. Stronger formal systems lead to increasing skepticism. Substituting the philosophical question of which mathematical statements are objective with the question of which mathematical statements are logically determined by events that could in theory occur in the physical universe, as we understand it, provid...

Kapur and Subramaniam [12] defined syntactical classes of equations where inductive validity can be decided automatically. However, these classes are quite restrictive, since defined function symbols with recursive definitions may only appear on one side of the equations. In this paper, we expand the decidable class of equations significantly by allowing both sides of equations to be expressed ...

Over 25 years ago, the first author conjectured in [15] that the existence of arbitrarily large primes is provable from the axioms IΔ0( ) + def( ), where (x) is the number of primes not exceeding x, IΔ0( ) denotes the theory of Δ0 induction for the language of arithmetic including the new function symbol , and def( ) is an axiom expressing the usual recursive definition of . We prove a modified...

We develop normalisation by evaluation (NBE) for dependent types based on presheaf categories. Our construction is formulated in the metalanguage of type theory using quotient inductive types. We use a typed presentation hence there are no preterms or realizers in our construction, and every construction respects the conversion relation. NBE for simple types uses a logical relation between the ...

Model integration extends the scope of model management to include the dimension of manipulation as well. This invariably leads to comparisons with database theory. Model integration is viewed from four perspectives: Organizational, definitional, procedural, and implementational. Strategic modeling is discussed as the organizational motivation for model integration. Schema and process integrati...