The recent discovery of an interpretation of constructive type theory into abstract homotopy theory suggests a new approach to the foundations of mathematics with intrinsic geometric content and a computational implementation. Voevodsky has proposed such a program, including a new axiom with both geometric and logical significance: the Univalence Axiom. It captures the familiar aspect of inform...

the effective and efficient understanding of the past, which is useful for present time, will transform the history into a dynamic science when it becomes an essential concern for historians. history, as a science, is the result of historian’s insights and perceptions; and philosophical hermeneutics with emphasizing on ontology of understanding and especially on importance of interpretation, ha...

Let q ≥ 1 be an integer, S denote the unit sphere embedded in the Euclidean space Rq+1, and μq be its Lebesgue surface measure. We establish upper and lower bounds for sup f∈B p,ρ ∣∣∣∣ ∫ Sq fdμq − M ∑ k=1 wkf(xk) ∣∣∣∣ , xk ∈ S , wk ∈ R, k = 1, · · · ,M, where B p,ρ is the unit ball of a suitable Besov space on the sphere. The upper bounds are obtained for choices of xk and wk that admit exact q...

This is the first of two papers describing how properties of open continuous maps between locales (which are the lattice-theoretic generalisation of topological spaces) can be used to give very straight-forward, constructive proofs of certain properties of first-order intuitionistic theories. The properties we have in mind are those of stability of a conservative interpretation of theories unde...

Coordinate, plural and predicative constructions of noun phrases are common and highly productive in natural languages. They are also related in intricate ways: conjunctive coordination is one of the simple means to form plural NP’s from singular ones; many coordinate and plural NP’s appear naturally in predicative positions. Any theory of grammar and semantic interpretation should account for ...

In the state of the art on the ramification problem, it is acknowledged that ramifications of actions are not logical consequences of state constraints and require explicit representation through causal laws. Yet, causal laws are still tightly coupled with state constraints in that their syntactic form is derived from state constraints or in that they merely serve to restore integrity of state ...

The main mathematical result of this work is a quite simple formulation and proof of a Rasiowa-Sikorski-like theorem for countable lattices. Then the paper suggests an interpretation of this mathematical result as a completeness theorem for the formal topologies introduced by G. Sambin in order to provide a constructive approach to topology which is expressible within Martin Löf’s intuitionisti...