Decidability of a Logic for Order of Magnitude Qualitative Reasoning with Comparability and Negligibility Relations

2013 ◽  
pp. 101-110
Author(s):  
Alfredo Burrieza
Keyword(s):  
Qualitative Reasoning ◽  
Order Of Magnitude

A PDL APPROACH FOR QUALITATIVE VELOCITY

2011 ◽  
Vol 19 (01) ◽  
pp. 11-26 ◽  
Author(s):  
A. BURRIEZA ◽  
E. MUÑOZ-VELASCO ◽  
M. OJEDA-ACIEGO
Keyword(s):  
Programming Languages ◽  
Moving Objects ◽  
Spatial Reasoning ◽  
Axiom System ◽  
Qualitative Reasoning ◽  
The Other ◽  
Other Hand ◽  
Order Of Magnitude ◽  
The One ◽  
Different Levels

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 robots. The main advantages of using a PDL-based approach are, on the one hand, all the well-known advantages of using logic in AI, and, on the other hand, the possibility of constructing complex relations from simpler ones, the flexibility for using different levels of granularity, its possible extension by adding other spatial components, and the use of a language close to programming languages.

A flexible logic-based approach to closeness using order of magnitude qualitative reasoning

2019 ◽  
Vol 28 (1) ◽  
pp. 121-133
Author(s):  
Alfredo Burrieza ◽  
Emilio Muñoz-Velasco ◽  
Manuel Ojeda-Aciego
Keyword(s):  
Qualitative Reasoning ◽  
Logical Approach ◽  
Multimodal Logic ◽  
Order Of Magnitude ◽  
Important Notion

Abstract In this paper, we focus on a logical approach to the important notion of closeness, which has not received much attention in the literature. Our notion of closeness is based on the so-called proximity intervals, which will be used to decide the elements that are close to each other. Some of the intuitions of this definition are explained on the basis of examples. We prove the decidability of the recently introduced multimodal logic for closeness and, then, we show some capabilities of the logic with respect to expressivity in order to denote particular positions of the proximity intervals.

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