We propose a framework for comparing the expressive power and computational behaviour of modal logics designed for reasoning about qualitative aspects of metric spaces. Within this framework we can compare such well-known logics as S4 (for the topology induced by the metric), wK4 (for the derivation operator of the topology), variants of conditional logic, as well as logics of comparative simil...

to evaluate land suitability of aq-qalla region for rainfed chickpea cropping, boolean logic and analytical hierarchy process (ahp) methods were used in geographic information system (gis). to achieve this, firstly, climatic and agronomical requirements of chickpea,were identified according to scientific resources. then, thematic requirement maps were provided. the studied environmental-compone...

In the first part of this investigation, [1], we generalized a weighted distance function of [2] and found necessary and sufficient conditions for it being a metric. In this paper some properties of this so–called M–relative metric are established. Specifically, isometries, quasiconvexity and local convexity results are derived. We also illustrate connections between our approach and generaliza...

Temporal logic has been successfully used for modeling and analyzing the behavior of reactive and concurrent systems. One shortcoming of (standard) temporal logic is that it is inadequate for real-time applications, because it only deals with qualitative timing properties. This is overcome by metric temporal logics which ooer a uniform logical framework in which both qualitative and quantitativ...

We introduce a weighted logic with discounting and we establish Büchi’s and Elgot’s theorem for weighted automata over finite words and arbitrary commutative semirings. Then we investigate Büchi and Muller automata with discounting over the max-plus and the min-plus semiring. We show their expressive equivalence with weighted MSO-sentences with discounting. In this case our logic has a purely s...

The M–relative distance, denoted by ρM is a generalization of the p–relative distance, which was introduced in [10]. We establish necessary and sufficient conditions under which ρM is a metric. In two special cases we derive complete characterizations of the metric. We also present a way of extending the results to metrics sensitive to the domain in which they are defined, thus finding some con...

The objective of this paper is to establish a class of models for solving the weight problem in fuzzy logic. First, some constraints that weighted fuzzy logic should satisfy are given based on Triangular norms and conorms. Then, based on these constraints, a class of models (referred to as relative weighted models) are established for handling weights in fuzzy logic. These models are novel in t...