a b s t r a c tDynamic Topological Logic (DT L) is a combination of S4, under its topological interpretation, and the temporal logic LT L interpreted over the natural numbers. DT L is used to reason about properties of dynamical systems based on topological spaces.Semantics are given by dynamic topological models, which are tuples X , T , f , V , where X , T is a topological space, f a function on X and V a truth valuation assigning subsets of X to propositional variables.Our main result is that the set of valid formulas of DT L over spaces with continuous functions is recursively enumerable. We show this by defining alternative semantics for DT L. Under standard semantics, DT L is not complete for Kripke frames. However, we introduce the notion of a non-deterministic quasimodel, where the function f is replaced by a binary relation g assigning to each world multiple temporal successors. We place restrictions on the successors so that the logic remains unchanged; under these alternative semantics, DT L becomes Kripke-complete. We then apply model-search techniques to enumerate the set of all valid formulas.
It is known that both S4 and the Intuitionistic prepositional calculus Int are P-SPACE complete. This guarantees that there is a polynomial translation from each system into the other.However, no sound and faithful polynomial translation from S4 into Int is commonly known. The problem of finding one was suggested by Dana Scott during a very informal gathering of logicians in February 2005 at UCLA. Grigori Mints then brought it to my attention, and in this paper I present a solution. It is based on Kripke semantics and describes model-checking for S4 using formulas of Int.A simple translation from Int into S4, the Gödel-Tarski translation, is wellknown; given a formula φ of Int, one obtains by prefixing □ to every subformula. For example,.That the translation is sound and faithful can be seen by considering topological semantics, which assign open sets both to □-formulas of S4 and arbitrary formulas of Int; the interpretation of φ and turn out to be identical. See Tarski's paper [6] for details. Gödel's original paper can be found in [3].In [2], Friedman and Flagg present a kind of inverse to Gödel-Tarski. Given a formula φ of S4 and a finite set of formulas Γ of Int, for each ε ∈ Γ one gets an intuitionistic formula given recursively by
Word spotting is the process of retrieving all instances of a queried keyword from a digital library of document images. In this paper we evaluate the performance of different word descriptors to assess the advantages and disadvantages of statistical and structural models in a framework of query-by-example word spotting in historical documents. We compare four word representation models, namely sequence alignment using DTW as a baseline reference, a bag of visual words approach as statistical model, a pseudo-structural model based on a Loci features representation, and a structural approach where words are represented by graphs. The four approaches have been tested with two collections of historical data: the George Washington database and the marriage records from the Barcelona Cathedral. We experimentally demonstrate that statistical representations generally give a better performance, however it cannot be neglected that large descriptors are difficult to be implemented in a retrieval scenario where word spotting requires the indexation of data with million word images.
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