A natural term rewriting framework for the Bellantoni Cook schemata of predicative recursion, which yields a canonical definition of the polynomial time computable functions, is introduced. In terms of an exponential function both, an upper bound and a lower bound are proved for the resulting derivation lengths of the functions in question. It is proved that any natural reduction strategy yield...

Instead of the half-century old foundational feud between set theory and category theory, this paper argues that they are theories about two different complementary types of universals. The set-theoretic antinomies forced naïve set theory to be reformulated using some iterative notion of a set so that a set would always have higher type or rank than its members. Then the universal uF = {x | F (...

We apply the predicative programming formal method of [2] in specifying and designing a solution to the invoicing case study. The method is used in an object-oriented style: first-class citizens of the descriptions are classes and objects. We discuss some of the advantages to using the predicative method in its object-oriented style, as well as its limitations in this problem domain.

This paper shows how to introduce predicative adjunction in a dependency grammar inspired from TAG, MTT and RG. The addition of predicative adjunction allows us to obtain a modular surface syntactic grammar, the derivation structures of which can be interpreted as semantic representations.

We apply the predicative programming formal method of [2] in specifying and designing a solution to the invoicing case study. The method is used in an object-oriented style: first-class citizens of the descriptions are classes and objects. We discuss some of the advantages to using the predicative method in its object-oriented style, as well as its limitations in this problem domain.

The syntax of intuitionistic propositional second-order logic PSOLi consists of a set of propositional constants P , Q, R, etc, a denumerable set of propositional variables F , G, H, etc, together with the primitive logical signs of the conditional and the universal propositional quantifier, and ponctuation signs (parenthesis). The formulas of PSOLi are the smallest class of expressions of the ...

Abstract Although there has been growing interest in the study of demonstratives, a number demonstrative categories remain largely unexplored. This article addresses one gap, presenting preliminary typological overview predicative type used primarily non-verbal predication constructions. The morphosyntax demonstratives is first briefly examined, followed by characterization based on semantic an...