We introduce a weighted linear dynamic logic (weighted LDL for short) and show the expressive equivalence of its formulas to weighted rational expressions. This adds a new characterization for recognizable series to the fundamental Schützenberger theorem. Surprisingly, the equivalence does not require any restriction to our weighted LDL. Our results hold over arbitrary (resp. totally complete) ...

We introduce a new way of defining metric temporal logic on a real-numbers flow of time. The idea is based on having semantics which allow us to refer to a single universal clock of arbitrary precision in order to impose metric constraints. This gives us a new metric temporal logic which is very expressive, is natural to use, can be applied in very general situations, affords a wide range of us...

We propose a new qualitative spatial logic based on metric (distance) relations between spatial objects. We provide a sound and complete axiomatisation of the logic with respect to metric models. The logic is intended for use in checking consistency of matching geospatial individuals from different data sets, where some data sets may be imprecise (e.g. crowd-sourced data).

The finite-sample risk of the k nearest neighbor classifier that uses a weighted Lpmetric as a measure of class similarity is examined. For a family of classification problems with smooth distributions in Rn, an asymptotic expansion for the risk is obtained in decreasing fractional powers of the reference sample size. An analysis of the leading expansion coefficients reveals that the optimal we...

Weighted logic programming, a generalization of bottom-up logic programming, is a successful framework for specifying dynamic programming algorithms. In this setting, proofs correspond to the algorithm’s output space, such as a path through a graph or a grammatical derivation, and are given a weighted score, often interpreted as a probability, that depends on the score of the base axioms used i...

Fuzzy logic programs are a useful framework for handling uncertainty in logic programming; nevertheless, there is the need for modelling adaptation of fuzzy logic programs. In this paper, we first overview weighted fuzzy programs, which bring fuzzy logic programs and connectionist models closer together by associating significance weights with the atoms of a logic rule: by exploiting the existe...

Temporal logic has been successfully used for modeling and analyzing the behavior of reactive and concurrent systems. Standard temporal logic is inadequate for real-time applications because it only deals with qualitative timing properties. This is overcome by metric temporal logics which offer a uniform logical framework in which both qualitative and quantitative timing properties can be expre...

We study an extension of MTL in pointwise time with rational expression guarded modality RatI(re) where re is a rational expression over subformulae. We study the decidability and expressiveness of this extension (MTL+φURatI,reφ+RatI,reφ), called RatMTL, as well as its fragment SfrMTL where only star-free rational expressions are allowed. Using the technique of temporal projections, we show tha...

Many metrics used in coding theory are instances of a combinatorial metric introduced by Gabidulin. We define a weighted combinatorial quasimetric. Some relations between these two metrics are established. Given an error and erasure decoder for the combinatorial metric, we propose the Forney-Kovalev soft-input-decoder for the weighted combinatorial metric. The error correcting radius of the alg...

We extend Signal Temporal Logic (STL) to enable the specification of importance and priorities. The extension, called Weighted STL (wSTL), has same qualitative (Boolean) semantics as STL, but additionally defines weights associated with Boolean temporal operators that modulate its quantitative (robustness). show robustness wSTL can be defined weighted generalizations all known compatible functi...