Predicate Logic with Definitions (PLD or D-logic) is a modification of first-order logic intended mostly for practical formalization of mathematics. The main syntactic constructs of D-logic are terms, formulas and definitions. A definition is a definition of variables, a definition of constants, or a composite definition (D-logic has also abbreviation definitions called abbreviations). Definiti...

We give conclusive answers to some questions about definability in analytic languages that arose shortly after the work by Denef and van den Dries, [DD], on p-adic subanalytic sets, and we continue the study of nonarchimedean fields with analytic structure of [LR3], [CLR1] and [CL1]. We show that the language LK consisting of the language of valued fields together with all strictly convergent p...

AIMS Redefinition of myocardial infarction (MI) based on specific cardiac troponins (cTn) was universally accepted in 2007. The new definition has been widely discussed for including a large spectrum of quantitative myocardial necrosis and their clinical implications remain under debate. Our aim was to assess the impact of the universal definition of MI on mortality at 10 years. METHODS AND R...

The distribution of indefinite singular generics is much more restricted than that of bare plural generics. The former, unlike the latter, seem to require that the property predicated of their subject be, in some sense, “definitional”. Moreover, the two constructions exhibit different scopal behavior, and differ in their felicity in conjunctions, questions, and expressions describing the speake...

A fragment with the same provably recursive functions as n iterated inductive definitions is obtained by restricting second order arithmetic in the following way. The underlying language allows only up to n + 1 nested second order quantifications and those are in such a way, that no second order variable occurs free in the scope of another second order quantifier. The amount of induction on ari...

How to define the security of undeniable signature schemes is a challenging task. This paper presents two security definitions of undeniable signature schemes which are more useful or natural than the existing definition. It then proves their equivalence. We first define the UC-security, where UC means universal composability. We next show that there exists a UC-secure undeniable signature sche...

One of the most widespread approaches to reactive planning is Schoppers’ universal plans. We propose a stricter definition of universal plans which guarantees a weak notion of soundness not present in the original definition. Furthermore, we isolate three different types of completeness which capture different behaviours exhibited by universal plans. We show that universal plans which run in po...