Spontaneous language has rarely been subjected to neuroimaging studies. This study therefore introduces a newly developed method for the analysis of linguistic phenomena observed in continuous language production during fMRI. Most neuroimaging studies investigating language have so far focussed on single word or - to a smaller extent - sentence processing, mostly due to methodological considera...

We study different completeness definitions for two categories of lattice-valued Cauchy spaces and the relations between these definitions. We also show the equivalence of a so-called completion axiom and the existence of a completion.

Completeness Jasmin Christian Blanchette, Andrei Popescu, and Dmitriy Traytel

The Boolean ring $B$ of measurable subsets of the unit interval, modulo sets of measure zero, has proper radical ideals (for example, ${0})$ that are closed under the natural metric, but has no prime ideal closed under that metric; hence closed radical ideals are not, in general, intersections of closed prime ideals. Moreover, $B$ is known to be complete in its metric. Togethe...

We present a coalgebraic generalisation of Fischer and Ladner’s Propositional Dynamic Logic (PDL) and Parikh’s Game Logic (GL). In earlier work, we proved a generic strong completeness result for coalgebraic dynamic logics without iteration. The coalgebraic semantics of such programs is given by a monad T , and modalities are interpreted via a predicate lifting λ whose transpose is a monad morp...

In this paper we discuss two hybrid languages , L(∀) and L(↓), and provide them with complete axiomatizations. Both languages combine features of modal and classical logic. Like modal languages, they contain modal operators and have a Kripke semantics. Unlike modal languages, in these systems it is possible to ‘label’ states by using ∀ and ↓ to bind special state variables . This paper explores...

DEFINITION A relational query language Q is BP-complete if for each relational database D, the set of all relations defined by the queries of Q on D is equal to the set of all first-order definable relations over D. More formally, fix some infinite universe U of atomic data elements. A relational database schema S is a finite set of relation names, each with an associated arity. A relational da...

This is an exposition of Lambek’s strengthening and generalization of the deduction theorem in categories related to intuitionistic propositional logic. Essential notions of category theory are introduced so as to yield a simple reformulation of Lambek’s Functional Completeness Theorem, from which its main consequences can be readily drawn. The connections of the theoremwith combinatory logic, ...

The identity rule of the sequent calculus exhibits one connection between the judgments A left and A right : If we assume A left we can prove A right . In other words, the left rules of the sequent calculus are strong enough so that we can reconstitute a proof of A from the assumption A. So the identity theorem (see Section 5) is a global version of the local completeness property for the elimi...