Formalizing defeasible argumentation using a labeled deductive system

In the last years there has been an increasing demand of a variety of logical systems, prompted mostly by applications of logic in AI, logic programming and other related areas. Labeled Deductive Systems (LDS) were developed as a flexible methodology to formalize such a kind of complex logical systems. In the last decade, defeasible argumentation has proven to be a confluence point for many approaches to formalizing commonsense reasoning. Different formalisms have been developed, many of them sharing common features. This paper presents a formalization of an LDS for defensible argumentation, in which the main issues concerning defeasible argumentation are captured within a unified logical framework. The proposed framework is defined in two stages. First, defeasible inference will be formalized by characterizing an argumentative LDS. That system will be then extended in order to capture conflict among arguments using a dialectical approach. We also present some logical properties emerging from the proposed framework, discussing also its semantical characterization.

Em direção a uma representação para equações algébricas :uma lógica equacional local

The intervalar arithmetic well-known as arithmetic of Moore, doesn't possess the same properties of the real numbers, and for this reason, it is confronted with a problem of operative nature, when we want to solve intervalar equations as extension of real equations by the usual equality and of the intervalar arithmetic, for this not to possess the inverse addictive, as well as, the property of the distributivity of the multiplication for the sum doesn t be valid for any triplet of intervals. The lack of those properties disables the use of equacional logic, so much for the resolution of an intervalar equation using the same, as for a representation of a real equation, and still, for the algebraic verification of properties of a computational system, whose data are real numbers represented by intervals. However, with the notion of order of information and of approach on intervals, introduced by Acióly[6] in 1991, the idea of an intervalar equation appears to represent a real equation satisfactorily, since the terms of the intervalar equation carry the information about the solution of the real equation. In 1999, Santiago proposed the notion of simple equality and, later on, local equality for intervals [8] and [33]. Based on that idea, this dissertation extends Santiago's local groups for local algebras, following the idea of Σ-algebras according to (Hennessy[31], 1988) and (Santiago[7], 1995). One of the contributions of this dissertation, is the theorem 5.1.3.2 that it guarantees that, when deducing a local Σ-equation E t t in the proposed system SDedLoc(E), the interpretations of t and t' will be locally the same in any local Σ-algebra that satisfies the group of fixed equations local E, whenever t and t have meaning in A. This assures to a kind of safety between the local equacional logic and the local algebras

Two ways to common knowledge

It is not clear what a system for evidence-based common knowledge should look like if common knowledge is treated as a greatest fixed point. This paper is a preliminary step towards such a system. We argue that the standard induction rule is not well suited to axiomatize evidence-based common knowledge. As an alternative, we study two different deductive systems for the logic of common knowledge. The first system makes use of an induction axiom whereas the second one is based on co-inductive proof theory. We show the soundness and completeness for both systems.

Intuitionistic common knowledge or belief

Starting off from the usual language of modal logic for multi-agent systems dealing with the agents’ knowledge/belief and common knowledge/belief we define so-called epistemic Kripke structures for intu- itionistic (common) knowledge/belief. Then we introduce corresponding deductive systems and show that they are sound and complete with respect to these semantics.

Embedding logical frameworks in scala

El Framework Lógico de Edimburgo ha demostrado ser una poderosa herramienta en el estudio formal de sistemas deductivos, como por ejemplo lenguajes de programación. Sin embargo su principal implementación, el sistema Twelf, carece de expresividad, obligando al programador a escribir código repetitivo. Este proyecto presenta una manera alternativa de utilizar Twelf: a través de un EDSL (Lenguaje Embebido de Dominio Específico) en Scala que permite representar firmas del Framework Lógico, y apoyándonos en Twelf como backend para la verificación, abrimos la puerta a diversas posibilidades en términos de metaprogramación. El código fuente, así como instrucciones para instalar y configurar, está accesible en https://github.com/akathorn/elfcala. ---ABSTRACT---The Edinburgh Logical Framework has proven to be to be a powerful tool in the formal study of deductive systems, such as programming languages. However, its main implementation, the Twelf system, lacks expressiveness, requiring the programmer to write repetitive code. This project presents an alternative way of using Twelf: by providing a Scala EDSL (Embedded Domain Specific Language) that can encode Logical Framework signatures and relying on Twelf as a backend for the verification, we open the door to different possibilities in terms of metaprogramming. The source code, along with instructions to install and configure, is accessible at https://github.com/akathorn/elfcala

Behavioral equivalence of hidden k-logics: an abstract algebraic approach

This work advances a research agenda which has as its main aim the application of Abstract Algebraic Logic (AAL) methods and tools to the specification and verification of software systems. It uses a generalization of the notion of an abstract deductive system to handle multi-sorted deductive systems which differentiate visible and hidden sorts. Two main results of the paper are obtained by generalizing properties of the Leibniz congruence — the central notion in AAL. In this paper we discuss a question we posed in [1] about the relationship between the behavioral equivalences of equivalent hidden logics. We also present a necessary and sufficient intrinsic condition for two hidden logics to be equivalent.

Toward a Run-Time Verification Framework for Real-Time Safety-Critical Systems

Presented at SEMINAR "ACTION TEMPS RÉEL:INFRASTRUCTURES ET SERVICES SYSTÉMES". 10, Apr, 2015. Brussels, Belgium.

System for Automated Deduction (SAD): Linguistic and Deductive Peculiarities

In this paper a state of the art of a system of automated deduction called SAD is described . An architecture of SAD corresponds well to a modern vision of the Evidence Algorithm programme, initiated by Academician V.Glushkov.

Robot Control Using Inductive, Deductive and Case Based Reasoning

The paper deals with a problem of intelligent system’s design for complex environments. There is discussed a possibility to integrate several technologies into one basic structure that could form a kernel of an autonomous intelligent robotic system. One alternative structure is proposed in order to form a basis of an intelligent system that would be able to operate in complex environments. The proposed structure is very flexible because of features that allow adapting via learning and adjustment of the used knowledge. Therefore, the proposed structure may be used in environments with stochastic features such as hardly predictable events or elements. The basic elements of the proposed structure have found their implementation in software system and experimental robotic system. The software system as well as the robotic system has been used for experimentation in order to validate the proposed structure - its functionality, flexibility and reliability. Both of them are presented in the paper. The basic features of each system are presented as well. The most important results of experiments are outlined and discussed at the end of the paper. Some possible directions of further research are also sketched at the end of the paper.

The Knowledge: Its Presentation and Role in Recognition Systems

The concept of knowledge is the central one used when solving the various problems of data mining and pattern recognition in finite spaces of Boolean or multi-valued attributes. A special form of knowledge representation, called implicative regularities, is proposed for applying in two powerful tools of modern logic: the inductive inference and the deductive inference. The first one is used for extracting the knowledge from the data. The second is applied when the knowledge is used for calculation of the goal attribute values. A set of efficient algorithms was developed for that, dealing with Boolean functions and finite predicates represented by logical vectors and matrices.

A Proposed Structure of Knowledge-Based Hybrid Intelligent Systems for Sophisticated Environments

The paper deals with a problem of intelligent system’s design for complex environments. There is discussed a possibility to integrate several technologies into one basic structure. One possible structure is proposed in order to form a basis for intelligent system that would be able to operate in complex environments. The basic elements of the proposed structure have found their implemented in software system. This software system is shortly presented in the paper. The most important results of experiments are outlined and discussed at the end of the paper. Some possible directions of further research are sketched.

Economical analysis for investment on measuring systems

Metrology processes contribute to entire manufacturing systems that can have a considerable impact on financial investment in coordinate measuring systems. However, there is a lack of generic methodologies to quantify their economical value in today’s industry. To solve this problem, a mathematical model is proposed in this paper by statistical deductive reasoning. This is done through defining the relationships between Process Capability Index, measurement uncertainty and tolerance band. The correctness of the mathematical model is proved by a case study. Finally, several comments and suggestions on evaluating and maximizing the benefits of metrology investment are given.

Solving satisfiability, *implication, and equivalence problems in database systems

Satisfiability, implication and equivalence problems are important and widely-encountered database problems that need to be efficiently and effectively solved. We provide a comprehensive and systematic study of these problems. We consider three popular types of arithmetic inequalities, (X op C), (X op Y), and (X op Y + C), where X and Y are attributes, C is a constant of the domain of X, and op $\in\ \{{<},\ {\le},\ {=},\ {\not=},\ {>},\ {\ge}\}.$ These inequalities are most frequently used in a database system, since the first type of inequalities represents $\theta$-join, the second type represents selection, and the third type is popular in deductive databases. We study the problems under the integer domain and the real domain, as well as under two different operator sets.^ Our results show that solutions under different domains and/or different operator sets are quite different. In this dissertation, we either report the first necessary and sufficient conditions as well as their efficient algorithms with complexity analysis, or provide improved algorithms. ^