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In this paper, we generalize the definitions of transitivity, reflexivity, symmetry, euclidean and serial properties of relations in the context of a functional approach for temporal×modal logic. The main result is the proof of definability of these definitions which is obtained by using algebraic characterizations. As a consequence, we will have in our… (More)
Non-classical logics have proven to be an adequate framework to formalize knowledge representation. In this paper we focus on a multimodal approach to formalize order-of-magnitude qualitative reasoning, extending the recently introduced system MQ, by means of a certain notion of negligibility relation which satisfies a number of intuitively plausible… (More)
This work concentrates on the automated deduction of logics of order-of-magnitude reasoning. Specifically, a translation of the multimodal logic of qualitative order-of-magnitude reasoning into relational logics is provided; then, a sound and complete Rasiowa-Sikorski proof system is presented for the relational version of the language.
In this paper, we enrich the logic of order of magnitude qualitative reasoning by means of a new notion of negligibility which has very useful properties with respect to operations of real numbers. A complete axiom system is presented for the proposed logic, and the new negligibility relation is compared with previous ones and its advantages are presented… (More)
In this work we develop a logic for formalizing qualitative reasoning. This type of reasoning is generally used, for instance, when one has a lot of data from a real world example but the complexity of the numerical model suggests a qualitative (instead of quantitative) approach.
We introduce the syntax, semantics, and an axiom system for a PDL-based extension of the logic for order of magnitude qualitative reasoning, developed in order to deal with the concept of qualitative velocity, which together with qualitative distance and orientation, are important notions in order to represent spatial reasoning for moving objects, such as… (More)
This paper continues the research line on the multimodal logic of qualitative reasoning; specifically, it deals with the introduction of the notions non-closeness and distance. These concepts allow us to consider qualitative sum of medium and large numbers. We present a sound and complete axiomatization for this logic, together with some of its advantages… (More)
This work is focused on temporal $\times$ modal logics. We study the representation of properties of functions of interest because of their possible computational interpretations. The semantics is exposed in an algebraic style, and the definability of the basic properties of the functions is analysed. We introduce minimal systems for linear time with total… (More)
The syntax, semantics and an axiom system for an extension of Propositional Dynamic Logic (PDL) for order of magnitude qualitative reasoning which formalizes the concepts of closeness and distance is introduced in this paper. In doing this, we use some of the advantages of PDL: firstly, we exploit the possibility of constructing complex relations from… (More)