6,952 research outputs found
Information Flow under Budget Constraints
Although first proposed in the database theory as properties of functional dependencies between attributes, Armstrong\u27s axioms capture general principles of information flow by describing properties of dependencies between sets of pieces of information. This article generalizes Armstrong\u27s axioms to a setting in which there is a cost associated with information. The proposed logical system captures general principles of dependencies between pieces of information constrained by a given budget
Knowing Values and Public Inspection
We present a basic dynamic epistemic logic of "knowing the value". Analogous
to public announcement in standard DEL, we study "public inspection", a new
dynamic operator which updates the agents' knowledge about the values of
constants. We provide a sound and strongly complete axiomatization for the
single and multi-agent case, making use of the well-known Armstrong axioms for
dependencies in databases
Armstrong\u27s Axioms and Navigation Strategies
The paper investigates navigability with imperfect information. It shows that the properties of navigability with perfect recall are exactly those captured by Armstrong\u27s axioms from database theory. If the assumption of perfect recall is omitted, then Armstrong\u27s transitivity axiom is not valid, but it can be replaced by a weaker principle. The main technical results are soundness and completeness theorems for the logical systems describing properties of navigability with and without perfect recall
On Armstrong relations for strong dependencies
The strong dependency has been introduced and axiomatized in [2], [3], [4], [5]. The aim of this paper is to investigate on Armstrong relations for strong dependencies. We give a necessary and sufficient condition for an abitrary relation to be Armstrong relation of a given strong scheme. We also give an effective algorithm finding a relation r such that r is Armstrong relation of a given strong scheme G = (U,S) (i.e. Sr = S+, where Sr is a full family of strong dependencies of r, and S+ is a set of all strong dependencies that can be derived from S by the system of axioms). We estimate this algorithm. We show that the time complexity of this algorithm is polynomial in |U| and |S|
Lighthouse principle for diffusion in social networks
The article investigates an influence relation between two sets of agents in a social network. It proposes a logical system that captures propositional properties of this relation valid in all threshold models of social networks with the same structure. The logical system consists of Armstrong axioms for functional dependence and an additional Lighthouse axiom. The main results are soundness, completeness, and decidability theorems for this logical system
From IF to BI: a tale of dependence and separation
We take a fresh look at the logics of informational dependence and
independence of Hintikka and Sandu and Vaananen, and their compositional
semantics due to Hodges. We show how Hodges' semantics can be seen as a special
case of a general construction, which provides a context for a useful
completeness theorem with respect to a wider class of models. We shed some new
light on each aspect of the logic. We show that the natural propositional logic
carried by the semantics is the logic of Bunched Implications due to Pym and
O'Hearn, which combines intuitionistic and multiplicative connectives. This
introduces several new connectives not previously considered in logics of
informational dependence, but which we show play a very natural role, most
notably intuitionistic implication. As regards the quantifiers, we show that
their interpretation in the Hodges semantics is forced, in that they are the
image under the general construction of the usual Tarski semantics; this
implies that they are adjoints to substitution, and hence uniquely determined.
As for the dependence predicate, we show that this is definable from a simpler
predicate, of constancy or dependence on nothing. This makes essential use of
the intuitionistic implication. The Armstrong axioms for functional dependence
are then recovered as a standard set of axioms for intuitionistic implication.
We also prove a full abstraction result in the style of Hodges, in which the
intuitionistic implication plays a very natural r\^ole.Comment: 28 pages, journal versio
Indispensability Without Platonism
According to Quine’s indispensability argument, we ought to believe in just those mathematical entities that we quantify over in our best scientific theories. Quine’s criterion of ontological commitment is part of the standard indispensability argument. However, we suggest that a new indispensability argument can be run using Armstrong’s criterion of ontological commitment rather than Quine’s. According to Armstrong’s criterion, ‘to be is to be a truthmaker (or part of one)’. We supplement this criterion with our own brand of metaphysics, 'Aristotelian (...) realism', in order to identify the truthmakers of mathematics. We consider in particular as a case study the indispensability to physics of real analysis (the theory of the real numbers). We conclude that it is possible to run an indispensability argument without Quinean baggage
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