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A Satisfiability Algorithm For The Mu-Calculus For Trees With Presburger Constraints
TLDR
A satisfiability algorithm for the $\mu-$calculus interpreted on tree models and extended with converse modalities and Presburger arithmetic operators, based on a breadth-first search in a Fischer-Lardner construction of tree models is described. Expand
Global Numerical Constraints on Trees
TLDR
It is proved that the logic introduced in the present work is decidable in single exponential time even if the numerical constraints are in binary form, which implies a characterization of decidable counting extensions of XPath queries and XML schemas. Expand
Query Reasoning on Trees with Types, Interleaving, and Counting
TLDR
This work considers the problem of query containment in the presence of type constraints for a class of regular path queries extended with counting and interleaving operators, and provides a logic-based framework supporting these operators which can be used to solve common query reasoning problems such as satisfiability and containment of queries in exponential time. Expand
Expressive Reasoning on Tree Structures: Recursion, Inverse Programs, Presburger Constraints and Nominals
TLDR
This work studies the fully-enriched μ-calculus for trees extended with Presburger constraints and shows that the logic is decidable in EXPTIME, achieved by the introduction of a satisfiability algorithm based on a Fischer-Ladner model construction that is able to handle binary encodings of PresBurger constraints. Expand
Reasoning on expressive description logics with arithmetic constraints
TLDR
It is shown that μALCTIO, which is known to be undecidable and that subsumes ALCQIOreg, is inEXPTIME in the case of tree models, and that knowledge base reasoning, TBoxes and ABoxes, can also be decided in EXPTIME. Expand
LBP and Machine Learning for Diabetic Retinopathy Detection
TLDR
This paper presents a method for diabetic retinopathy detection, which has used local binary patterns (LBP) to extract local features, while in the second stage, it has applied artificial neural networks, random forest and support vector machines for the detection task. Expand
Presburger Constraints in Trees
TLDR
This work studies the fully-enriched µ-calculus for trees extended with Presburger constraints, and shows that this extension is decidable in EXPTIME, and identifies decidable extensions of regular tree languages (XML schemas) with interleaving and counting operators. Expand
On the Model Checking of the Graded μ-calculus on Trees
TLDR
A linear-time model checking algorithm for the graded \(\mu \)-calculus when models are finite unranked trees is introduced. Expand
Branching Path Planning with Modal Logics
TLDR
This work provides a plan generator based on a model checking algorithm for the μ -calculus, an expressive modal logic which subsumes many program logics such as LTL, PDL and CTL and shows the algorithm is sound and complete, that is, for any environment, there a satisfying plan for a given set of constraints, if and only if, the plan generator succeeds. Expand
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