Alfredo Burrieza

Relational approach to order-of-magnitude reasoning

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.

An implementation of a dual tableaux system for order-of-magnitude qualitative reasoning

Logic programming has been used as a natural framework to automate deduction in the logic of order-of-magnitude reasoning. Specifically, we introduce a Prolog implementation of the Rasiowa–Sikorski proof system associated with the relational translation Re(OM) of the multi-modal logic of order-of-magnitude qualitative reasoning OM.

A Logic for Order of Magnitude Reasoning with Negligibility, Non-closeness and Distance

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 by means of an example.

A Multimodal Logic Approach to Order of Magnitude Qualitative Reasoning

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.

A PDL APPROACH FOR QUALITATIVE VELOCITY

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.

Order of magnitude qualitative reasoning with bidirectional negligibility

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 on the basis of an example.

A new algebraic semantic approach and some adequate connectives for computation with temporal logic over discrete time

ABSTRACT In this paper we present a new semantic approach for propositional linear temporal logic with discrete time, strongly based in the well-order of IN (the set of natural numbers). We consider temporal connectives which express precedence, posteriority and simultaneity, and they provide a family of expressively complete temporal logics. The selection of the new semantics and connectives used in this work was principally to obtain a suitable executable temporal logic, which can be used for the specification and control of process behaviour in discrete time in a similar way to thai presented by D. Gabbay in [GAB 89], Our new approach has two advantages: firstly, the connectives are defined intuitively so that they have interpretations which relate to properties of interest in real systems; secondly, it provides a new semantics that facilitates simpler proofs of many valid formulas and metatheorems. To confirm this second advantage, we use our semantics to give a formal proof of the Separation Theorem ...

A logic framework for reasoning with movement based on fuzzy qualitative representation

Abstract We present a logic approach to reason with moving objects under fuzzy qualitative representation. This way, we can deal both with qualitative and quantitative information, and consequently, to obtain more accurate results. The proposed logic system is introduced as an extension of Propositional Dynamic Logic: this choice, on the one hand, simplifies the theoretical study concerning soundness, completeness and decidability; on the other hand, provides the possibility of constructing complex relations from simpler ones and the use of a language very close to programming languages.

A functional approach for temporal × modal logics

Abstract. This work is focused on temporal

Generalization of some properties of relations in the context of functional temporal×modal logic

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