The present study is a sequel to [3] and [5]. We further explore preservational properties of a class of implicational connectives. The implicational approach to preservation examines what happens when the implicational connective is required to preserve various properties. We focus on a particular class of properties, called meta-valuational properties, and the class of implicational connectiv...

An embedding of the implicational propositional intuitionistic logic (iil) into the nonmodal fragment of intuitionistic linear logic (imall) is given. The embedding preserves cut-free proofs in a proof system that is a variant of iil. The embedding is eecient and provides an alternative proof of the pspace-hardness of imall. It exploits several proof-theoretic properties of intuitionistic impli...

In a recently published paper J. C. C. McKinsey has pointed out some difficulties which arise from Axiom I of my theory of probability implication. This axiom states the unambiguity of the degree p of a given probability implication (03VP) for the case that the class 0 is not empty, a condition formulated by (o), but postulates ambiguity of p in case of an empty class 0, this condition being fo...

We review key constraints in the context of XML as introduced by Buneman et al. We show that one of the proposed inference rules is not sound in general, and the axiomatisation proposed for XML keys is incomplete even if key paths are simple. Therefore, the axiomatisation and also the implication problem for XML keys are still unsolved. We propose a set of inference rules that is indeed sound a...

In this paper we introduce the notion of generalized implication for lattices, as a binary function⇒ that maps every pair of elements of a lattice to an ideal. We prove that a bounded lattice A is distributive if and only if there exists a generalized implication ⇒ defined in A satisfying certain conditions, and we study the class of bounded distributive lattices A endowed with a generalized im...

The aim of this work is to introduce an approach for interval-valued R-implications, which satisfy some analogous properties of R-implications. We show that the best interval representation of an R-implication that is obtained from a left continuous tnorm coincides with the interval-valued R-implication obtained from the best interval representation of such t-norm, whenever this is an inclusion...

Implication problems occur in many areas of computer science. Examples include, of course, logic, but also database systems (constraints), data mining (association rules), and reasoning under uncertainty (conditional independence). We provide a general framework for implication problems based on the observation that many can be reduced to an implication problem for additive constraints on speci...

Motivational attitudes play an important role in investigations into intelligent agents. One of the key problems of representing and reasoning about motivational attitudes is which propositions are the desirable ones. The answer based on classical logic is that the propositions that logically imply the goal are desirable and the others are not. We argue that this criterion is inadequate for the...

Some recent works rely on the intuitionistic theory of Hereditary Harrop formulas to provide extensions for Horn clauses while preserving the logic paradigm. In particular, an intuitionistic implication is used to provide some form of scoping. However the lack of appropriate evaluation strategies, notably a strategy relying on a forward-chaining search, has limited its application. This paper i...

Main Outcome Measures: Clinical diagnosis of LOAD. Results: Thestrongestoverall findingwasat chromosome 19q13.32,confirmingtheeffectof theapolipoproteinEgene on LOAD risk in the family-based and case-control analyses. However, single-nucleotide polymorphisms at the following loci were also statistically significant in 1 or more of the analyses performed: 7p22.2, 7p21.3, and 16q21 in the linkage...