The deenition of a class C of functions is predicative if it doesn't use a class containing C; and is decidable if membershipto C can be decided syntactically, from the construction of its elements. Decidable and predicative characterizations of Poly-time functions are known. We present here such a characterization for the following classes of languages: P, p n ; p n , PH and PSPACE. It is obta...

Luo’s Extended Calculus of donstructions (ECC) is a higher order functional calculus based on Coquand’s and Huet’s Calculus of Constructions, but has in addition strong sums and a predicative cumulative type hierarchy. In this paper I introduce inductive types on the predicative type levels of ECC. I also show how the o-Set model for ECC can be extended to a model for this augmented calculus. '...

We present a formulation of the polyadic-calculus featuring a syntactic category for agents, together with a typing system assigning polymorphic types to agents. The new presentation introduces an operator to express recursion, and an ML-style let-constructor allowing to associate an agent to an agent-variable, and use the latter several times in a program. The essence of the monomorphic type s...

Predicative mathematics in the sense originating with Poincaré and Weyl begins by taking the natural number system for granted, proceeding immediately to real analysis and related fields. On the other hand, from a logicist or set-theoretic standpoint, this appears problematic, for, as the story is usually told, impredicative principles seem to play an essential role in the foundations of arithm...

The axiom of choice is shown to hold in the predicative logic of any locally cartesian closed category. A predicative form of excluded middle is then shown to be equivalent to the usual form of choice in topoi. The logic of topoi is a version of higher-order, intuitionistic logic (see 3]). In this setting, Diaconescu 2] has shown that the axiom of choice (AC) entails the law of excluded middle ...

Both the constructive and predicative approaches to mathematics arose during the period of what was felt to be a foundational crisis in the early part of this century. Each critiqued an essential logical aspect of classical mathematics, namely concerning the unrestricted use of the law of excluded middle on the one hand, and of apparently circular \impredicative" de nitions on the other. But th...

In the present paper, based on the previous work (Part I), we present a game semantics for the intensional variant of intuitionistic type theory that refutes the principle of uniqueness of identity proofs and validates the univalence axiom, though we do not interpret non-trivial higher propositional equalities. Specifically, following the historic groupoid interpretation by Hofmann and Streiche...

We give a construction of coequalisers in formal topology, a predicative version of locale theory. MSC: 03F65, 06D22, 54B15.

This paper studies some newly observed phenomena with indefinite descriptions when they appear as complements of prepositional phrases (PPs). We show that in many such cases the indefinite does not receive the traditional existential interpretation, and its quantificational force is sensitive to the identity of the preposition. Such cases of quantificational variability are explained by elabora...

We show that the diierence between indeenites and deenites with respect to their syntactic behaviour, in particular scrambling, follows from a diierence in their semantics. In general, deenites can be viewed as a special type of indeenites: they are restricted indeenites in all semantic types. This inherent restriction of deenites makes them insensitive to processes of semantic incorporation. T...